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taruma_hk127_gumbel.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "taruma_hk127_gumbel.ipynb",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyNr9g52UfD6yK+ycBgaTLhs",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/taruma/ffa77e6f50a19fa5d05ab10e27d3266a/taruma_hk127_gumbel.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"Berdasarkan isu [#127](https://github.com/hidrokit/hidrokit/issues/127): **anfrek: Gumbel**\n",
"\n",
"Referensi Isu:\n",
"- Soetopo, W., Montarcih, L., Press, U. B., & Media, U. (2017). Rekayasa Statistika untuk Teknik Pengairan. Universitas Brawijaya Press. https://books.google.co.id/books?id=TzVTDwAAQBAJ\n",
"- Limantara, L. (2018). Rekayasa Hidrologi.\n",
"- Soewarno. (1995). hidrologi: Aplikasi Metode Statistik untuk Analisa Data.NOVA.\n",
"- Al-Mashidani, G., Lal, P. B. B., & Mujda, M. F. (1978). A simple version of Gumbel’s method for flood estimation / Version simplifiée de la méthode de Gumbel pour l’estimation des crues. Hydrological Sciences Bulletin, 23(3), 373–380. https://doi.org/10.1080/02626667809491810\n",
"- https://github.com/anyarcherty/Seattle_Rainfall/blob/master/Seattle%20Weather.ipynb\n",
"- Gumbel, E. J. (2012). Statistics of Extremes. Dover Publications. https://books.google.co.id/books?id=ku18nuinb4wC\n",
"\n",
"\n",
"Deskripsi Isu:\n",
"- Mencari nilai ekstrim dengan kala ulang tertentu. Penerapan ini bisa digunakan untuk hujan rancangan atau debit banjir rancangan. \n",
"\n",
"Diskusi Isu:\n",
"- [#156](https://github.com/hidrokit/hidrokit/discussions/156) - Bagaimana menghitung periode ulang distribusi (analisis frekuensi) tanpa melihat tabel?\n",
"\n",
"Strategi:\n",
"- Akan mengikuti fungsi log pearson [#126](https://github.com/hidrokit/hidrokit/issues/126) seperti pada [manual](https://gist.github.com/taruma/60725ffca91dc6e741daee9a738a978b)."
],
"metadata": {
"id": "Q_EwdXLx2Gu_"
}
},
{
"cell_type": "markdown",
"source": [
"# PERSIAPAN DAN DATASET"
],
"metadata": {
"id": "VKZXpflFrwHy"
}
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "KMjOQ2iD15oh"
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"from scipy import stats"
]
},
{
"cell_type": "code",
"source": [
"# contoh data diambil dari buku\n",
"# hidrologi: Aplikasi Metode Statistik untuk Analisa Data hal. 125\n",
"\n",
"_DEBIT = [\n",
" 244, 217, 285, 261, 295, 252, 275, 204, 208, 194, 256, 207, 354, 445, \n",
" 350, 336, 328, 269, 323, 364, 247, 290, 302, 301, 284, 276, 261, 303, \n",
" 335, 320\n",
"]\n",
"\n",
"_TAHUN = list(range(1918, 1935)) + list(range(1973, 1986))\n",
"\n",
"data = pd.DataFrame(\n",
" data=np.stack([_TAHUN, _DEBIT], axis=1),\n",
" columns=['tahun', 'debit']\n",
")\n",
"data.tahun = pd.to_datetime(data.tahun, format='%Y')\n",
"data.set_index('tahun', inplace=True)\n",
"data"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "aZAOyMcC0OIs",
"outputId": "b3de6432-d0f8-49ba-9e7f-d87a78785a1e"
},
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" debit\n",
"tahun \n",
"1918-01-01 244\n",
"1919-01-01 217\n",
"1920-01-01 285\n",
"1921-01-01 261\n",
"1922-01-01 295\n",
"1923-01-01 252\n",
"1924-01-01 275\n",
"1925-01-01 204\n",
"1926-01-01 208\n",
"1927-01-01 194\n",
"1928-01-01 256\n",
"1929-01-01 207\n",
"1930-01-01 354\n",
"1931-01-01 445\n",
"1932-01-01 350\n",
"1933-01-01 336\n",
"1934-01-01 328\n",
"1973-01-01 269\n",
"1974-01-01 323\n",
"1975-01-01 364\n",
"1976-01-01 247\n",
"1977-01-01 290\n",
"1978-01-01 302\n",
"1979-01-01 301\n",
"1980-01-01 284\n",
"1981-01-01 276\n",
"1982-01-01 261\n",
"1983-01-01 303\n",
"1984-01-01 335\n",
"1985-01-01 320"
],
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" }\n",
"\n",
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" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>debit</th>\n",
" </tr>\n",
" <tr>\n",
" <th>tahun</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1918-01-01</th>\n",
" <td>244</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1919-01-01</th>\n",
" <td>217</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1920-01-01</th>\n",
" <td>285</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1921-01-01</th>\n",
" <td>261</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1922-01-01</th>\n",
" <td>295</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1923-01-01</th>\n",
" <td>252</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1924-01-01</th>\n",
" <td>275</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1925-01-01</th>\n",
" <td>204</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1926-01-01</th>\n",
" <td>208</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1927-01-01</th>\n",
" <td>194</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1928-01-01</th>\n",
" <td>256</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1929-01-01</th>\n",
" <td>207</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1930-01-01</th>\n",
" <td>354</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1931-01-01</th>\n",
" <td>445</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1932-01-01</th>\n",
" <td>350</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1933-01-01</th>\n",
" <td>336</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1934-01-01</th>\n",
" <td>328</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1973-01-01</th>\n",
" <td>269</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1974-01-01</th>\n",
" <td>323</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1975-01-01</th>\n",
" <td>364</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1976-01-01</th>\n",
" <td>247</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1977-01-01</th>\n",
" <td>290</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1978-01-01</th>\n",
" <td>302</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1979-01-01</th>\n",
" <td>301</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1980-01-01</th>\n",
" <td>284</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1981-01-01</th>\n",
" <td>276</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1982-01-01</th>\n",
" <td>261</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1983-01-01</th>\n",
" <td>303</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1984-01-01</th>\n",
" <td>335</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1985-01-01</th>\n",
" <td>320</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"metadata": {},
"execution_count": 2
}
]
},
{
"cell_type": "markdown",
"source": [
"# TABEL\n",
"\n",
"Terdapat 3 tabel untuk modul `hk127` yaitu:\n",
"- `t_gumbel_gb`: Tabel nilai $\\bar{y}_N$ (`yn`) dan $\\sigma_N$ (`sn`) dari Tabel 6.2.3 _Means and Standard Deviations of Reduced Extremes_ hal. 228. Sumber: _Statistics of Extremes_ oleh Gumbel, E. J. (2012)\n",
"- `t_gumbel_sw`: Tabel nilai Yn (`yn`) dan Sn (`sn`) dari Tabel 3.11A Hubungan Reduksi Variat Rata-rata (Yn) dengan Jumlah Data (n) dan Tabel 3.11B Hubungan antara deviasi standar dan reduksi variat dengan jumlah data. Sumber: hidrologi: _Aplikasi Metode Statistik untuk Analisa Data_ oleh Soewarno. (1995)\n",
"- `t_gumbel_st`: Tabel nilai $Y_n$ (`yn`) dan $S_n$ (`sn`) dari Tabel 12.1. $Y_n$ dan $S_n$ Gumbel. Sumber: _Rekayasa Statistika untuk Teknik Pengairan_ oleh Soetopo, W., Montarcih, L., Press, U. B., & Media, U. (2017).\n",
"\n",
"Dalam modul `hk127` nilai $Y_n$ dan $S_n$ akan menggunakan dari tabel `t_gumbel_gb` secara `default`. Mohon diperhatikan jika ingin menggunakan nilai $Y_n$ dan $S_n$ yang berasal dari sumber lain. \n",
"\n",
"Catatan: Sumber buku Gumbel dari yang tahun 1957."
],
"metadata": {
"id": "tydu0qwR135n"
}
},
{
"cell_type": "code",
"source": [
"# tabel dari gumbel\n",
"# Statistics of Extremes oleh Gumbel p.228\n",
"\n",
"# KODE: GB\n",
"\n",
"_DATA_GB = [\n",
" [0.48430, 0.90430],\n",
" [0.49020, 0.92880],\n",
" [0.49520, 0.94970],\n",
" [0.49960, 0.96760],\n",
" [0.50350, 0.98330],\n",
" [0.50700, 0.99720],\n",
" [0.51000, 1.00950],\n",
" [0.51280, 1.02057],\n",
" [0.51570, 1.03160],\n",
" [0.51810, 1.04110],\n",
" [0.52020, 1.04930],\n",
" [0.52200, 1.05660],\n",
" [0.52355, 1.06283],\n",
" [0.52520, 1.06960],\n",
" [0.52680, 1.07540],\n",
" [0.52830, 1.08110],\n",
" [0.52960, 1.08640],\n",
" [0.53086, 1.09145],\n",
" [0.53200, 1.09610],\n",
" [0.53320, 1.10040],\n",
" [0.53430, 1.10470],\n",
" [0.53530, 1.10860],\n",
" [0.53622, 1.11238],\n",
" [0.53710, 1.11590],\n",
" [0.53800, 1.11930],\n",
" [0.53880, 1.12260],\n",
" [0.53960, 1.12550],\n",
" [0.54034, 1.12847],\n",
" [0.54100, 1.13130],\n",
" [0.54180, 1.13390],\n",
" [0.54240, 1.13630],\n",
" [0.54300, 1.13880],\n",
" [0.54362, 1.14132],\n",
" [0.54420, 1.14360],\n",
" [0.54480, 1.14580],\n",
" [0.54530, 1.14800],\n",
" [0.54580, 1.14990],\n",
" [0.54630, 1.15185],\n",
" [0.54680, 1.15380],\n",
" [0.54730, 1.15570],\n",
" [0.54770, 1.15740],\n",
" [0.54810, 1.15900],\n",
" [0.54854, 1.16066],\n",
" [0.54890, 1.16230],\n",
" [0.54930, 1.16380],\n",
" [0.54970, 1.16530],\n",
" [0.55010, 1.16670],\n",
" [0.55040, 1.16810],\n",
" [0.55080, 1.16960],\n",
" [0.55110, 1.17080],\n",
" [0.55150, 1.17210],\n",
" [0.55180, 1.17340],\n",
" [0.55208, 1.17467],\n",
" [0.55270, 1.17700],\n",
" [0.55330, 1.17930],\n",
" [0.55380, 1.18140],\n",
" [0.55430, 1.18340],\n",
" [0.55477, 1.18536],\n",
" [0.55520, 1.18730],\n",
" [0.55570, 1.18900],\n",
" [0.55610, 1.19060],\n",
" [0.55650, 1.19230],\n",
" [0.55688, 1.19382],\n",
" [0.55720, 1.19530],\n",
" [0.55760, 1.19670],\n",
" [0.55800, 1.19800],\n",
" [0.55830, 1.19940],\n",
" [0.55860, 1.20073],\n",
" [0.55890, 1.20200],\n",
" [0.55920, 1.20320],\n",
" [0.55950, 1.20440],\n",
" [0.55980, 1.20550],\n",
" [0.56002, 1.20649],\n",
" [0.56461, 1.22534],\n",
" [0.56715, 1.23598],\n",
" [0.56878, 1.24292],\n",
" [0.56993, 1.24786],\n",
" [0.57144, 1.25450],\n",
" [0.57240, 1.25880],\n",
" [0.57377, 1.26506],\n",
" [0.57450, 1.26851]\n",
"]\n",
"\n",
"_INDEX_GB = (\n",
" list(range(8, 61)) +\n",
" list(range(62, 101, 2)) +\n",
" list(range(150, 301, 50)) +\n",
" [400, 500, 750, 1000]\n",
")\n",
"\n",
"_COL_GB = ['yn', 'sn']\n",
"\n",
"t_gumbel_gb = pd.DataFrame(\n",
" data=_DATA_GB, index=_INDEX_GB, columns=_COL_GB\n",
")\n",
"t_gumbel_gb"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 424
},
"id": "Q3uSbmX-21L3",
"outputId": "a877d0bf-53cf-448b-d288-0336772209b2"
},
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" yn sn\n",
"8 0.48430 0.90430\n",
"9 0.49020 0.92880\n",
"10 0.49520 0.94970\n",
"11 0.49960 0.96760\n",
"12 0.50350 0.98330\n",
"... ... ...\n",
"300 0.56993 1.24786\n",
"400 0.57144 1.25450\n",
"500 0.57240 1.25880\n",
"750 0.57377 1.26506\n",
"1000 0.57450 1.26851\n",
"\n",
"[81 rows x 2 columns]"
],
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>yn</th>\n",
" <th>sn</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>0.48430</td>\n",
" <td>0.90430</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>0.49020</td>\n",
" <td>0.92880</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>0.49520</td>\n",
" <td>0.94970</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>0.49960</td>\n",
" <td>0.96760</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>0.50350</td>\n",
" <td>0.98330</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>300</th>\n",
" <td>0.56993</td>\n",
" <td>1.24786</td>\n",
" </tr>\n",
" <tr>\n",
" <th>400</th>\n",
" <td>0.57144</td>\n",
" <td>1.25450</td>\n",
" </tr>\n",
" <tr>\n",
" <th>500</th>\n",
" <td>0.57240</td>\n",
" <td>1.25880</td>\n",
" </tr>\n",
" <tr>\n",
" <th>750</th>\n",
" <td>0.57377</td>\n",
" <td>1.26506</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1000</th>\n",
" <td>0.57450</td>\n",
" <td>1.26851</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>81 rows × 2 columns</p>\n",
"</div>"
]
},
"metadata": {},
"execution_count": 3
}
]
},
{
"cell_type": "code",
"source": [
"# tabel dari soewarno\n",
"# Tabel 3.11A & 3.11B p.129-130\n",
"\n",
"# KODE: GB\n",
"\n",
"_DATA_SW = [\n",
" [0.4592, 0.9496],\n",
" [0.4996, 0.9676],\n",
" [0.5053, 0.9933],\n",
" [0.5070, 0.9971],\n",
" [0.5100, 1.0095],\n",
" [0.5128, 1.0206],\n",
" [0.5157, 1.0316],\n",
" [0.5181, 1.0411],\n",
" [0.5202, 1.0493],\n",
" [0.5220, 1.0565],\n",
" [0.5236, 1.0628],\n",
" [0.5252, 1.0696],\n",
" [0.5268, 1.0754],\n",
" [0.5283, 1.0811],\n",
" [0.5296, 1.0864],\n",
" [0.5309, 1.0915],\n",
" [0.5320, 1.1961],\n",
" [0.5332, 1.1004],\n",
" [0.5343, 1.1047],\n",
" [0.5353, 1.1086],\n",
" [0.5362, 1.1124],\n",
" [0.5371, 1.1159],\n",
" [0.5380, 1.1193],\n",
" [0.5388, 1.1226],\n",
" [0.5396, 1.1255],\n",
" [0.5402, 1.1285],\n",
" [0.5410, 1.1313],\n",
" [0.5418, 1.1339],\n",
" [0.5424, 1.1363],\n",
" [0.5430, 1.1388],\n",
" [0.5436, 1.1413],\n",
" [0.5442, 1.1436],\n",
" [0.5448, 1.1458],\n",
" [0.5453, 1.1480],\n",
" [0.5458, 1.1499],\n",
" [0.5463, 1.1519],\n",
" [0.5468, 1.1538],\n",
" [0.5473, 1.1557],\n",
" [0.5477, 1.1574],\n",
" [0.5481, 1.1590],\n",
" [0.5485, 1.1607],\n",
" [0.5489, 1.1623],\n",
" [0.5493, 1.1638],\n",
" [0.5497, 1.1658],\n",
" [0.5501, 1.1667],\n",
" [0.5504, 1.1681],\n",
" [0.5508, 1.1696],\n",
" [0.5511, 1.1708],\n",
" [0.5518, 1.1721],\n",
" [0.5518, 1.1734],\n",
" [0.5521, 1.1747],\n",
" [0.5524, 1.1759],\n",
" [0.5527, 1.1770],\n",
" [0.5530, 1.1782],\n",
" [0.5533, 1.1793],\n",
" [0.5535, 1.1803],\n",
" [0.5538, 1.1814],\n",
" [0.5540, 1.1824],\n",
" [0.5543, 1.1834],\n",
" [0.5545, 1.1844],\n",
" [0.5548, 1.1854],\n",
" [0.5550, 1.1863],\n",
" [0.5552, 1.1873],\n",
" [0.5555, 1.1881],\n",
" [0.5557, 1.1890],\n",
" [0.5559, 1.1898],\n",
" [0.5561, 1.1906],\n",
" [0.5563, 1.1915],\n",
" [0.5565, 1.1923],\n",
" [0.5567, 1.1930],\n",
" [0.5569, 1.1938],\n",
" [0.5570, 1.1945],\n",
" [0.5572, 1.1953],\n",
" [0.5574, 1.1959],\n",
" [0.5576, 1.1967],\n",
" [0.5578, 1.1973],\n",
" [0.5580, 1.1980],\n",
" [0.5581, 1.1987],\n",
" [0.5583, 1.1994],\n",
" [0.5585, 1.2001],\n",
" [0.5586, 1.2007],\n",
" [0.5587, 1.2013],\n",
" [0.5589, 1.2020],\n",
" [0.5591, 1.2026],\n",
" [0.5592, 1.2032],\n",
" [0.5593, 1.2038],\n",
" [0.5595, 1.2044],\n",
" [0.5596, 1.2049],\n",
" [0.5598, 1.2055],\n",
" [0.5599, 1.2060],\n",
" [0.5600, 1.2065],\n",
"]\n",
"\n",
"_INDEX_SW = list(range(10, 101))\n",
"\n",
"_COL_SW = ['yn', 'sn']\n",
"\n",
"t_gumbel_sw = pd.DataFrame(\n",
" data=_DATA_SW, index=_INDEX_SW, columns=_COL_SW\n",
")\n",
"t_gumbel_sw"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 424
},
"id": "dMgC8ZMU4aFH",
"outputId": "afa836c5-a9a0-4719-e1a0-1f81a81407d4"
},
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" yn sn\n",
"10 0.4592 0.9496\n",
"11 0.4996 0.9676\n",
"12 0.5053 0.9933\n",
"13 0.5070 0.9971\n",
"14 0.5100 1.0095\n",
".. ... ...\n",
"96 0.5595 1.2044\n",
"97 0.5596 1.2049\n",
"98 0.5598 1.2055\n",
"99 0.5599 1.2060\n",
"100 0.5600 1.2065\n",
"\n",
"[91 rows x 2 columns]"
],
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>yn</th>\n",
" <th>sn</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>0.4592</td>\n",
" <td>0.9496</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>0.4996</td>\n",
" <td>0.9676</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>0.5053</td>\n",
" <td>0.9933</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>0.5070</td>\n",
" <td>0.9971</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>0.5100</td>\n",
" <td>1.0095</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>96</th>\n",
" <td>0.5595</td>\n",
" <td>1.2044</td>\n",
" </tr>\n",
" <tr>\n",
" <th>97</th>\n",
" <td>0.5596</td>\n",
" <td>1.2049</td>\n",
" </tr>\n",
" <tr>\n",
" <th>98</th>\n",
" <td>0.5598</td>\n",
" <td>1.2055</td>\n",
" </tr>\n",
" <tr>\n",
" <th>99</th>\n",
" <td>0.5599</td>\n",
" <td>1.2060</td>\n",
" </tr>\n",
" <tr>\n",
" <th>100</th>\n",
" <td>0.5600</td>\n",
" <td>1.2065</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>91 rows × 2 columns</p>\n",
"</div>"
]
},
"metadata": {},
"execution_count": 4
}
]
},
{
"cell_type": "code",
"source": [
"# Tabel dari Soetopo hal. 98\n",
"# Tabel 12.1 Yn dan Sn Gumbel \n",
"\n",
"# KODE: ST\n",
"\n",
"_DATA_ST = [\n",
" [0.4843, 0.9043],\n",
" [0.4902, 0.9288],\n",
" [0.4952, 0.9497],\n",
" [0.4996, 0.9676],\n",
" [0.5035, 0.9833],\n",
" [0.5070, 0.9972],\n",
" [0.5100, 1.0095],\n",
" [0.5128, 1.0205],\n",
" [0.5157, 1.0316],\n",
" [0.5181, 1.0411],\n",
" [0.5202, 1.0493],\n",
" [0.5220, 1.0566],\n",
" [0.5235, 1.0628],\n",
" [0.5252, 1.0696],\n",
" [0.5268, 1.0754],\n",
" [0.5283, 1.0811],\n",
" [0.5296, 1.0864],\n",
" [0.5309, 1.0915],\n",
" [0.5320, 1.0961],\n",
" [0.5332, 1.1004],\n",
" [0.5343, 1.1047],\n",
" [0.5353, 1.1086],\n",
" [0.5362, 1.1124],\n",
" [0.5371, 1.1159],\n",
" [0.5380, 1.1193],\n",
" [0.5388, 1.1226],\n",
" [0.5396, 1.1255],\n",
" [0.5402, 1.1285],\n",
" [0.5410, 1.1313],\n",
" [0.5418, 1.1339],\n",
" [0.5424, 1.1363],\n",
" [0.5430, 1.1388],\n",
" [0.5436, 1.1413],\n",
" [0.5442, 1.1436],\n",
" [0.5448, 1.1458],\n",
" [0.5453, 1.1480],\n",
" [0.5458, 1.1499],\n",
" [0.5463, 1.1519],\n",
" [0.5468, 1.1538],\n",
" [0.5473, 1.1557],\n",
" [0.5477, 1.1574],\n",
" [0.5481, 1.1590],\n",
" [0.5485, 1.1607],\n",
" [0.5489, 1.1623],\n",
" [0.5493, 1.1638],\n",
" [0.5497, 1.1658],\n",
" [0.5501, 1.1667],\n",
" [0.5504, 1.1681],\n",
" [0.5508, 1.1696],\n",
" [0.5511, 1.1708],\n",
" [0.5515, 1.1721],\n",
" [0.5518, 1.1734],\n",
" [0.5521, 1.1747],\n",
" [0.5524, 1.1759],\n",
" [0.5527, 1.1770],\n",
" [0.5530, 1.1782],\n",
" [0.5533, 1.1793],\n",
" [0.5535, 1.1803],\n",
" [0.5538, 1.1814],\n",
" [0.5540, 1.1824],\n",
" [0.5543, 1.1834],\n",
" [0.5545, 1.1844],\n",
" [0.5548, 1.1854],\n",
" [0.5550, 1.1863],\n",
" [0.5552, 1.1873],\n",
" [0.5555, 1.1881],\n",
" [0.5557, 1.1890],\n",
" [0.5559, 1.1898],\n",
" [0.5561, 1.1906],\n",
" [0.5563, 1.1915],\n",
" [0.5565, 1.1923],\n",
" [0.5567, 1.1930],\n",
" [0.5569, 1.1938],\n",
" [0.5570, 1.1945],\n",
" [0.5572, 1.1953],\n",
" [0.5574, 1.1959],\n",
" [0.5576, 1.1967],\n",
" [0.5578, 1.1973],\n",
" [0.5580, 1.1980],\n",
" [0.5581, 1.1987],\n",
" [0.5583, 1.1994],\n",
" [0.5585, 1.2001],\n",
" [0.5586, 1.2007],\n",
" [0.5587, 1.2013],\n",
" [0.5589, 1.2020],\n",
" [0.5591, 1.2026],\n",
" [0.5592, 1.2032],\n",
" [0.5593, 1.2038],\n",
" [0.5595, 1.2044],\n",
" [0.5596, 1.2049],\n",
" [0.5598, 1.2055],\n",
" [0.5599, 1.2060],\n",
" [0.5600, 1.2065],\n",
"]\n",
"\n",
"_INDEX_ST = list(range(8, 101))\n",
"\n",
"_COL_ST = ['yn', 'sn']\n",
"\n",
"t_gumbel_st = pd.DataFrame(\n",
" data=_DATA_ST, index=_INDEX_ST, columns=_COL_ST\n",
")\n",
"t_gumbel_st"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 424
},
"id": "gcHHA1gb_MvM",
"outputId": "1574a9f3-9a0c-45c0-efed-21dbfc6e5b81"
},
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" yn sn\n",
"8 0.4843 0.9043\n",
"9 0.4902 0.9288\n",
"10 0.4952 0.9497\n",
"11 0.4996 0.9676\n",
"12 0.5035 0.9833\n",
".. ... ...\n",
"96 0.5595 1.2044\n",
"97 0.5596 1.2049\n",
"98 0.5598 1.2055\n",
"99 0.5599 1.2060\n",
"100 0.5600 1.2065\n",
"\n",
"[93 rows x 2 columns]"
],
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>yn</th>\n",
" <th>sn</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>0.4843</td>\n",
" <td>0.9043</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>0.4902</td>\n",
" <td>0.9288</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>0.4952</td>\n",
" <td>0.9497</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>0.4996</td>\n",
" <td>0.9676</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>0.5035</td>\n",
" <td>0.9833</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>96</th>\n",
" <td>0.5595</td>\n",
" <td>1.2044</td>\n",
" </tr>\n",
" <tr>\n",
" <th>97</th>\n",
" <td>0.5596</td>\n",
" <td>1.2049</td>\n",
" </tr>\n",
" <tr>\n",
" <th>98</th>\n",
" <td>0.5598</td>\n",
" <td>1.2055</td>\n",
" </tr>\n",
" <tr>\n",
" <th>99</th>\n",
" <td>0.5599</td>\n",
" <td>1.2060</td>\n",
" </tr>\n",
" <tr>\n",
" <th>100</th>\n",
" <td>0.5600</td>\n",
" <td>1.2065</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>93 rows × 2 columns</p>\n",
"</div>"
]
},
"metadata": {},
"execution_count": 5
}
]
},
{
"cell_type": "markdown",
"source": [
"# KODE"
],
"metadata": {
"id": "ULqzeasu2P2f"
}
},
{
"cell_type": "code",
"source": [
"def _find_in_table(val, table, y_col=None, x_col=None):\n",
" x = table.index if x_col is None else table[x_col]\n",
" y = table.iloc[:, 0] if y_col is None else table[y_col]\n",
" return np.interp(val, x, y)\n",
"\n",
"def _find_Yn_Sn(n, table):\n",
" yn = _find_in_table(n, table, y_col='yn')\n",
" sn = _find_in_table(n, table, y_col='sn')\n",
" return yn, sn"
],
"metadata": {
"id": "XEqz2ZHWf4gf"
},
"execution_count": 6,
"outputs": []
},
{
"cell_type": "code",
"source": [
"def find_coef(n, source='gumbel'):\n",
" if source.lower() == 'gumbel':\n",
" return _find_Yn_Sn(n, t_gumbel_gb)\n",
" if source.lower() == 'soewarno':\n",
" return _find_Yn_Sn(n, t_gumbel_sw)\n",
" if source.lower() == 'soetopo':\n",
" return _find_Yn_Sn(n, t_gumbel_st)\n",
"\n",
"def calc_K(n, return_period, source='gumbel', show_stat=False):\n",
" return_period = np.array(return_period)\n",
"\n",
" if source.lower() == 'scipy':\n",
" # todo: perhitungan probabilitasnya belum dapat dipastikan formulanya\n",
" prob = 1 - 1/return_period\n",
" # prob = 1 - np.log(return_period/(return_period-1))\n",
" return stats.gumbel_r.ppf(prob)\n",
" elif source.lower() == 'powell':\n",
" return -np.sqrt(6)/np.pi *(np.euler_gamma+np.log(np.log(return_period/(return_period-1))))\n",
" else:\n",
" # dibuku Soewarno dinyatakan T>=20 menggunakan\n",
" # ln(T), tapi dicontohnya tidak mengikuti formula tersebut\n",
" # jadi yang digunakan rumus umumnya saja.\n",
" # if source.lower() == 'soewarno':\n",
" # yt = []\n",
" # for t in return_period:\n",
" # if t <= 20:\n",
" # yt += [-np.log(-np.log((t - 1)/t))]\n",
" # else:\n",
" # yt += [np.log(t)]\n",
" # yt = np.array(yt)\n",
" # else:\n",
" # yt = -np.log(-np.log((return_period - 1)/return_period))\n",
"\n",
" yn, sn = find_coef(n, source=source)\n",
" yt = -np.log(-np.log((return_period - 1)/return_period))\n",
" K = (yt - yn) / sn\n",
"\n",
" if show_stat:\n",
" print(f'y_n = {yn}')\n",
" print(f's_n = {sn}')\n",
" print(f'y_t = {yt}')\n",
" return K\n",
"\n",
"def calc_x_gumbel(x, return_period=[5], source='gumbel', show_stat=False):\n",
"\n",
" x_mean = np.mean(x)\n",
" x_std = np.std(x, ddof=1)\n",
" n = len(x)\n",
"\n",
" k = calc_K(n, return_period, source=source, show_stat=show_stat)\n",
"\n",
" if show_stat:\n",
" print(f'x_mean = {x_mean:.5f}')\n",
" print(f'x_std = {x_std:.5f}')\n",
" print(f'k = {k}')\n",
" \n",
" val_x = x_mean + k * x_std\n",
" return val_x\n",
"\n",
"def freq_gumbel(\n",
" df, col=None,\n",
" return_period=[2, 5, 10, 20, 25, 50, 100], source='gumbel', show_stat=False,\n",
" col_name='Gumbel', index_name='Kala Ulang'):\n",
"\n",
" col = df.columns[0] if col is None else col\n",
"\n",
" x = df[col].copy()\n",
"\n",
" arr = calc_x_gumbel(\n",
" x, return_period=return_period, show_stat=show_stat,\n",
" source=source\n",
" )\n",
"\n",
" result = pd.DataFrame(\n",
" data=arr, index=return_period, columns=[col_name]\n",
" )\n",
"\n",
" result.index.name = index_name\n",
" return result"
],
"metadata": {
"id": "hVrQdk5ZicdA"
},
"execution_count": 7,
"outputs": []
},
{
"cell_type": "code",
"source": [
"def _calc_T(P):\n",
" return 1 / (1-np.exp(-np.exp(-P)))\n",
"\n",
"def _calc_prob_from_table(k, n, source='gumbel'):\n",
" yn, sn = find_coef(n, source=source)\n",
" P = k * sn + yn\n",
" T = _calc_T(P)\n",
" return np.around(1-1/T, 3)\n",
"\n",
"def calc_prob(k, n, source='gumbel'):\n",
" if source.lower() == 'gumbel':\n",
" return _calc_prob_from_table(k, n, source=source)\n",
" if source.lower() == 'soewarno':\n",
" return _calc_prob_from_table(k, n, source=source)\n",
" if source.lower() == 'soetopo':\n",
" return _calc_prob_from_table(k, n, source=source)\n",
" if source.lower() == 'scipy':\n",
" return stats.gumbel_r.cdf(k)\n",
" if source.lower() == 'powell':\n",
" # persamaan ini ditemukan menggunakan wolfram alpha\n",
" # x = e^(e^(-(π K)/sqrt(6) - p))/(e^(e^(-(π K)/sqrt(6) - p)) - 1)\n",
" _top = np.exp(np.exp(-(np.pi*k)/np.sqrt(6)-np.euler_gamma))\n",
" _bot = _top - 1\n",
" T = _top / _bot\n",
" return 1-1/T"
],
"metadata": {
"id": "kf11-u4Jbx_G"
},
"execution_count": 8,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"# FUNGSI"
],
"metadata": {
"id": "K-SN5xLw0AP_"
}
},
{
"cell_type": "markdown",
"source": [
"## Fungsi `find_coef(n, ...)`\n",
"\n",
"Function: `find_coef(n, source='gumbel')`\n",
"\n",
"Fungsi `find_coef(...)` digunakan untuk mencari nilai $Y_n$ dan $S_n$ dari berbagai sumber berdasarkan nilai $n$ yaitu jumlah banyaknya data. \n",
"\n",
"- Argumen Posisi:\n",
" - `n`: jumlah banyaknya data.\n",
"- Argumen Opsional:\n",
" - `source`: sumber nilai $Y_n$ dan $S_n$, `'gumbel'` (default). Sumber yang dapat digunakan antara lain: Soewarno (`'soewarno'`), Soetopo (`'soetopo'`).\n",
"\n",
"Perlu dicatat bahwa batas jumlah data $N$ untuk masing-masing sumber berbeda-beda. \n",
"- Untuk `'gumbel'` batasan dimulai dari $[8, ∞]$ akan tetapi pada tabel hanya sampai $1000$.\n",
"- Untuk `'soewarno'` batasan dimulai dari $[10, 100]$.\n",
"- Untuk `'soetopo'` batasan dimulai dari $[10, 100]$. "
],
"metadata": {
"id": "KQoovCuO0_sH"
}
},
{
"cell_type": "code",
"source": [
"find_coef(10)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "0Bs_qxqb2v1R",
"outputId": "d89e43d3-6b7d-4d4c-9912-7d921811cd8f"
},
"execution_count": 9,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(0.4952, 0.9497)"
]
},
"metadata": {},
"execution_count": 9
}
]
},
{
"cell_type": "code",
"source": [
"find_coef(30, source='soetopo') # menggunakan tabel dari soetopo"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "vegebmxq2yOr",
"outputId": "f8d5c2ad-1913-4080-89c9-bcf69378aaa8"
},
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(0.5362, 1.1124)"
]
},
"metadata": {},
"execution_count": 10
}
]
},
{
"cell_type": "code",
"source": [
"# perbandingan antara masing-masing sumber\n",
"\n",
"_n = 25\n",
"source_test = ['gumbel', 'soewarno', 'soetopo']\n",
"\n",
"for _source in source_test:\n",
" print(f'Yn, Sn {_source:10}= {find_coef(_n, source=_source)}')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "UtBTkAZg3BLc",
"outputId": "10407bdf-ed7c-4fb9-a552-9e7e5414d8bc"
},
"execution_count": 11,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Yn, Sn gumbel = (0.53086, 1.09145)\n",
"Yn, Sn soewarno = (0.5309, 1.0915)\n",
"Yn, Sn soetopo = (0.5309, 1.0915)\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"## Fungsi `calc_K(n, return_period, ...)`:\n",
"\n",
"Function: `calc_K(n, return_period, source='gumbel', show_stat=False)`\n",
"\n",
"Fungsi `calc_K(...)` digunakan untuk menghitung nilai frequency factor $K$ yang digunakan untuk menghitung nilai $X$ pada kala ulang tertentu. \n",
"\n",
"- Argumen Posisi:\n",
" - `n`: jumlah banyaknya data.\n",
" - `return_period`: kala ulang. Bisa dalam skalar ataupun _array_like_.\n",
"- Argumen Opsional:\n",
" - `source`: sumber nilai $Y_n$ dan $S_n$ (untuk `'gumbel'`, `'soewarno'`, dan `'soetopo'`), `'gumbel'` (default). Sumber yang dapat digunakan antara lain: Soewarno (`'soewarno'`), Soetopo (`'soetopo'`), fungsi `stats.gumbel_r.ppf` dari Scipy (`'scipy'`), dan metode Powell (`'powell'`).\n",
" - `show_stat`: menampilkan parameter statistik. `False` (default).\n",
"\n",
"Catatan:\n",
"Untuk metode Powell (`'powell'`) menggunakan persamaan:\n",
"$$K = - \\frac{\\sqrt{6}}{\\pi} \\left( \\gamma + \\ln{\\ln\\left({\\frac{T}{T-1}}\\right)}\\right)$$\n",
"dengan $\\gamma = 0.5772$ (`np.euler_gamma`) atau merupakan bilangan [**Euler–Mascheroni constant**](https://en.wikipedia.org/wiki/Euler%27s_constant). "
],
"metadata": {
"id": "SXHRrtpc35Dm"
}
},
{
"cell_type": "code",
"source": [
"calc_K(10, 10)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "xYeTcR7v77S5",
"outputId": "a0b8344c-4a85-45af-b33f-f2546048ca2b"
},
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"1.8481281744892548"
]
},
"metadata": {},
"execution_count": 12
}
]
},
{
"cell_type": "code",
"source": [
"calc_K(10, [10, 20, 50], source='soetopo')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "in7gOJJm8fSL",
"outputId": "0496f1f8-e140-4b29-a78d-a1492ba88ceb"
},
"execution_count": 13,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([1.84812817, 2.60608113, 3.58717348])"
]
},
"metadata": {},
"execution_count": 13
}
]
},
{
"cell_type": "code",
"source": [
"calc_K(10, [10, 20, 50], source='soewarno', show_stat=True)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "ViEpU_wE8nLS",
"outputId": "fd1c4aeb-6798-49b1-e7d7-fcffa1f290df"
},
"execution_count": 14,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"y_n = 0.4592\n",
"s_n = 0.9496\n",
"y_t = [2.25036733 2.97019525 3.90193866]\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([1.8862335 , 2.64426627, 3.62546194])"
]
},
"metadata": {},
"execution_count": 14
}
]
},
{
"cell_type": "markdown",
"source": [
"## Fungsi `calc_x_gumbel(x, ...)`\n",
"\n",
"Function: `calc_x_gumbel(x, return_period=[5], source='gumbel', show_stat=False)`\n",
"\n",
"Fungsi `calc_x_gumbel(...)` digunakan untuk mencari besar $X$ berdasarkan kala ulang (_return period_), yang hasilnya dalam bentuk `numpy.array`. \n",
"\n",
"- Argumen Posisi:\n",
" - `x`: _array_.\n",
"- Argumen Opsional:\n",
" - `return_period`: Kala Ulang (Tahun). `[5]` (default). \n",
" - `source`: sumber nilai $K$, `'gumbel'` (default). Sumber yang dapat digunakan antara lain: Soewarno (`'soewarno'`), Soetopo (`'soetopo'`), fungsi `stats.gumbel_r.ppf` dari Scipy (`'scipy'`), dan metode Powell (`'powell'`).\n",
" - `show_stat`: menampilkan parameter statistik. `False` (default)."
],
"metadata": {
"id": "vRZNOKdT9icS"
}
},
{
"cell_type": "code",
"source": [
"calc_x_gumbel(data.debit)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "IdlaPmzS-Bxz",
"outputId": "7a920728-dbc8-4947-873f-bf834f3c2da4"
},
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([334.33496634])"
]
},
"metadata": {},
"execution_count": 15
}
]
},
{
"cell_type": "code",
"source": [
"calc_x_gumbel(data.debit, show_stat=True)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "aGebieZ--EO2",
"outputId": "72fc91b6-6383-4c54-9c93-fd2930ce1be8"
},
"execution_count": 16,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"y_n = 0.53622\n",
"s_n = 1.11238\n",
"y_t = [1.49993999]\n",
"x_mean = 286.20000\n",
"x_std = 55.56009\n",
"k = [0.86635861]\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([334.33496634])"
]
},
"metadata": {},
"execution_count": 16
}
]
},
{
"cell_type": "code",
"source": [
"calc_x_gumbel(data.debit, return_period=[5, 10, 15, 20, 21], show_stat=True)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "RkQBT7jawK_J",
"outputId": "12940ece-f907-44a9-ccf1-62782e3f53e7"
},
"execution_count": 17,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"y_n = 0.53622\n",
"s_n = 1.11238\n",
"y_t = [1.49993999 2.25036733 2.67375209 2.97019525 3.02022654]\n",
"x_mean = 286.20000\n",
"x_std = 55.56009\n",
"k = [0.86635861 1.5409728 1.92158443 2.18807894 2.23305574]\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([334.33496634, 371.81659511, 392.96341332, 407.7698733 ,\n",
" 410.2687885 ])"
]
},
"metadata": {},
"execution_count": 17
}
]
},
{
"cell_type": "markdown",
"source": [
"## Fungsi `freq_gumbel(df, ...)`\n",
"\n",
"Function: `freq_gumbel(df, col=None, return_period=[2, 5, 10, 20, 25, 50, 100], source='gumbel', show_stat=False, col_name='Gumbel')`\n",
"\n",
"Fungsi `freq_gumbel(...)` merupakan fungsi kembangan lebih lanjut dari `calc_x_gumbel(...)` yang menerima input `pandas.DataFrame` dan memiliki luaran berupa `pandas.DataFrame`. \n",
"\n",
"- Argumen Posisi:\n",
" - `df`: `pandas.DataFrame`.\n",
"- Argumen Opsional:\n",
" - `col`: nama kolom, `None` (default). Jika tidak diisi menggunakan kolom pertama dalam `df` sebagai data masukan.\n",
" - `return_period`: Kala Ulang (Tahun), `[2, 5, 10, 20, 25, 50, 100]` (default).\n",
" - `source`: sumber nilai $K$, `'gumbel'` (default). Sumber yang dapat digunakan antara lain: Soewarno (`'soewarno'`), Soetopo (`'soetopo'`), fungsi `stats.gumbel_r.ppf` dari Scipy (`'scipy'`), dan metode Powell (`'powell'`).\n",
" - `show_stat`: menampilkan parameter statistik. `False` (default).\n",
" - `col_name`: Nama kolom luaran, `Gumbel` (default). "
],
"metadata": {
"id": "0mwOcZiB8xmm"
}
},
{
"cell_type": "code",
"source": [
"freq_gumbel(data)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 300
},
"id": "PKckL9dA-U12",
"outputId": "a5008eb2-129a-4272-f1a0-b10a4a54491e"
},
"execution_count": 18,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" Gumbel\n",
"Kala Ulang \n",
"2 277.723633\n",
"5 334.334966\n",
"10 371.816595\n",
"20 407.769873\n",
"25 419.174732\n",
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{
"cell_type": "code",
"source": [
"freq_gumbel(data, source='soewarno', col_name='Gumbel (Soewarno)')"
],
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"base_uri": "https://localhost:8080/",
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{
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" Gumbel (Soewarno)\n",
"Kala Ulang \n",
"2 277.724784\n",
"5 334.335100\n",
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"metadata": {},
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},
{
"cell_type": "code",
"source": [
"freq_gumbel(data, 'debit', source='soetopo', col_name=f'LP3 (soetopo)', show_stat=True)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 439
},
"id": "Mn4MywymyWio",
"outputId": "52c1e5e2-0293-4a6a-f112-9d989f75ce6f"
},
"execution_count": 20,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"y_n = 0.5362\n",
"s_n = 1.1124\n",
"y_t = [0.36651292 1.49993999 2.25036733 2.97019525 3.19853426 3.90193866\n",
" 4.60014923]\n",
"x_mean = 286.20000\n",
"x_std = 55.56009\n",
"k = [-0.15254142 0.86636101 1.54096308 2.18805758 2.39332458 3.02565503\n",
" 3.65331646]\n"
]
},
{
"output_type": "execute_result",
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" LP3 (soetopo)\n",
"Kala Ulang \n",
"2 277.724784\n",
"5 334.335100\n",
"10 371.816055\n",
"20 407.768686\n",
"25 419.173341\n",
"50 454.305681\n",
"100 489.178609"
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" <th>100</th>\n",
" <td>489.178609</td>\n",
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"cell_type": "code",
"source": [
"_res = []\n",
"\n",
"for _s in ['gumbel', 'soewarno', 'soetopo', 'powell', 'scipy', ]:\n",
" _res += [freq_gumbel(data, 'debit', source=_s, col_name=f'Gumbel ({_s})')]\n",
"\n",
"pd.concat(_res, axis=1)"
],
"metadata": {
"id": "2wiAa9sp2SBt",
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{
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"data": {
"text/plain": [
" Gumbel (gumbel) Gumbel (soewarno) Gumbel (soetopo) \\\n",
"Kala Ulang \n",
"2 277.723633 277.724784 277.724784 \n",
"5 334.334966 334.335100 334.335100 \n",
"10 371.816595 371.816055 371.816055 \n",
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"50 454.307704 454.305681 454.305681 \n",
"100 489.181259 489.178609 489.178609 \n",
"\n",
" Gumbel (powell) Gumbel (scipy) \n",
"Kala Ulang \n",
"2 277.072351 306.563493 \n",
"5 326.172444 369.536808 \n",
"10 358.680977 411.230622 \n",
"20 389.863943 451.224330 \n",
"25 399.755596 463.910867 \n",
"50 430.227094 502.992082 \n",
"100 460.473595 541.784727 "
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" <th>25</th>\n",
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" <td>463.910867</td>\n",
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" <th>50</th>\n",
" <td>454.307704</td>\n",
" <td>454.305681</td>\n",
" <td>454.305681</td>\n",
" <td>430.227094</td>\n",
" <td>502.992082</td>\n",
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" <th>100</th>\n",
" <td>489.181259</td>\n",
" <td>489.178609</td>\n",
" <td>489.178609</td>\n",
" <td>460.473595</td>\n",
" <td>541.784727</td>\n",
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},
"metadata": {},
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}
]
},
{
"cell_type": "markdown",
"source": [
"## Fungsi `calc_prob(k, n, ...)`\n",
"\n",
"Function: `calc_prob(k, n, source='gumbel')`\n",
"\n",
"Fungsi `calc_prob(...)` digunakan untuk menghitung nilai probabilitas/peluang berdasarkan nilai $K$ (_frequency factor_).\n",
"\n",
"- Argumen Posisi:\n",
" - `k`: nilai $K$ (_frequency factor_). Nilai $K$ diperoleh menggunakan persamaan $K = \\frac{x - \\bar{x}}{s}$\n",
" - `n`: jumlah banyaknya data.\n",
"- Argumen Opsional:\n",
" - `source`: sumber nilai $Y_n$ dan $S_n$ (untuk `'gumbel'`, `'soewarno'`, dan `'soetopo'`), `'gumbel'` (default). Sumber yang dapat digunakan antara lain: Soewarno (`'soewarno'`), Soetopo (`'soetopo'`), fungsi `stats.gumbel_r.ppf` dari Scipy (`'scipy'`), dan metode Powell (`'powell'`).\n",
"\n",
"Catatan:\n",
"\n",
"- Metode tabel (`'gumbel', 'soewarno', 'soetopo'`)\n",
"\n",
" Nilai probabilitas/peluang diperoleh menggunakan formula $P=1-\\frac{1}{T}$\n",
"\n",
"- Metode Powell (`'powell'`)\n",
"\n",
" Nilai kala ulang $T$ (Tahun) untuk metode Powell menggunakan persamaan berikut:\n",
" $$T=\\frac{e^{e^{-\\left(\\pi k\\right)/\\sqrt{6}-\\gamma}}}{e^{e^{-\\left(\\pi k\\right)/\\sqrt{6}-\\gamma}}-1}$$\n",
" dengan $\\gamma = 0.5772$ (`np.euler_gamma`) atau merupakan bilangan [**Euler–Mascheroni constant**](https://en.wikipedia.org/wiki/Euler%27s_constant). \n",
"\n",
" Nilai probabilitas/peluang diperoleh menggunakan formula $P=1-\\frac{1}{T}$\n",
"\n",
"- Metode scipy (`'scipy'`)\n",
"\n",
" Nilai probabilitas diperoleh menggunakan fungsi `stats.gumbel_r.cdf(...)`."
],
"metadata": {
"id": "3ZLvMbrzb1Sw"
}
},
{
"cell_type": "code",
"source": [
"_k = calc_K(data.size, [1.001, 1.005, 1.01, 1.05, 1.11, 1.25, 1.33, 1.43, 1.67, 2, 2.5, 3.33, 4, 5, 10, 20, 50, 100, 200, 500, 1000])\n",
"_k"
],
"metadata": {
"id": "bPBdmAN5b2X4",
"outputId": "73b284e9-138f-4b55-b764-ffeafb419668",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 22,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([-2.21957372, -1.98183192, -1.85688162, -1.48291416, -1.23534677,\n",
" -0.90985544, -0.78056388, -0.64718086, -0.40052 , -0.15256215,\n",
" 0.12181718, 0.44365066, 0.63798281, 0.86635861, 1.5409728 ,\n",
" 2.18807894, 3.02569145, 3.65336416, 4.2787466 , 5.10381998,\n",
" 5.72739088])"
]
},
"metadata": {},
"execution_count": 22
}
]
},
{
"cell_type": "code",
"source": [
"calc_prob(_k, data.size)"
],
"metadata": {
"id": "C6mSu3Bxb3zD",
"outputId": "ad92ab9a-b505-4743-a76e-a97b13ce1dce",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 23,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([0.001, 0.005, 0.01 , 0.048, 0.099, 0.2 , 0.248, 0.301, 0.401,\n",
" 0.5 , 0.6 , 0.7 , 0.75 , 0.8 , 0.9 , 0.95 , 0.98 , 0.99 ,\n",
" 0.995, 0.998, 0.999])"
]
},
"metadata": {},
"execution_count": 23
}
]
},
{
"cell_type": "code",
"source": [
"calc_prob(_k, data.size, source='scipy').round(3)"
],
"metadata": {
"id": "33Ud0MTDb59Q",
"outputId": "a80d8d6f-5ea2-4407-8b3a-120dee4a86a4",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 24,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([0. , 0.001, 0.002, 0.012, 0.032, 0.083, 0.113, 0.148, 0.225,\n",
" 0.312, 0.413, 0.526, 0.59 , 0.657, 0.807, 0.894, 0.953, 0.974,\n",
" 0.986, 0.994, 0.997])"
]
},
"metadata": {},
"execution_count": 24
}
]
},
{
"cell_type": "code",
"source": [
"calc_prob(_k, data.size, source='powell').round(3)"
],
"metadata": {
"id": "u1z412RCb7MC",
"outputId": "a137c730-871c-4de6-fcb0-8e22e63871bc",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 25,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([0. , 0.001, 0.002, 0.023, 0.065, 0.165, 0.217, 0.276, 0.391,\n",
" 0.505, 0.619, 0.728, 0.781, 0.831, 0.925, 0.967, 0.988, 0.995,\n",
" 0.998, 0.999, 1. ])"
]
},
"metadata": {},
"execution_count": 25
}
]
},
{
"cell_type": "code",
"source": [
"calc_prob(_k, data.size, source='soewarno')"
],
"metadata": {
"id": "T_cZzfCxcEnx",
"outputId": "819a280a-f792-47ad-ba04-d6517b6e6df5",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 26,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([0.001, 0.005, 0.01 , 0.048, 0.099, 0.2 , 0.248, 0.301, 0.401,\n",
" 0.5 , 0.6 , 0.7 , 0.75 , 0.8 , 0.9 , 0.95 , 0.98 , 0.99 ,\n",
" 0.995, 0.998, 0.999])"
]
},
"metadata": {},
"execution_count": 26
}
]
},
{
"cell_type": "markdown",
"source": [
"# Changelog\n",
"\n",
"```\n",
"- 20220323 - 1.1.0 - tambah argumen index_name=\"Kala Ulang\" pada fungsi freq_gumbel() untuk penamaan index\n",
"- 20220315 - 1.0.1 - Tambah fungsi `calc_prob(...)`\n",
"- 20220310 - 1.0.0 - Initial\n",
"```\n",
"\n",
"#### Copyright &copy; 2022 [Taruma Sakti Megariansyah](https://taruma.github.io)\n",
"\n",
"Source code in this notebook is licensed under a [MIT License](https://choosealicense.com/licenses/mit/). Data in this notebook is licensed under a [Creative Common Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/). \n"
],
"metadata": {
"id": "w324QF-g-4HU"
}
}
]
}
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