EconometricsBySimulation

I recently found myself in need of a function to sample randomly from an arbitrarily defined probability density function. An excellent post by Quantitations shows how to accomplish this using some of Rs fairly sophisticated functional approximation tools such as integrate and uniroot. The only problem with this excellent post was that the machine cost was enormous with samples of 1000 draws taking 10 seconds on my machine and repeated samples of 100,000+ draws (which I was after) clearly being unworkable.

Thus I decided to take my own crack at it. First let us review the basics of drawing random variables from non-uniform distributions. The standard method I think most algorithms use works as follows:
  
  Assumptions
1. You can draw pseudo-random uniform variable u
2. You can integrate the pdf to construct a cdf
$$p = F(x) = \int_{-\infty}^\infty f(x) dx$$
  3. You can invert the cdf in order to solve for p
$$G(F(x))=F^{-1}(F(x))=F^{-1}(p)=x$$

EconometricsBySimulation

# This set of functions comes entirely form Andrie on stackoverflow
# http://stackoverflow.com/questions/22873602/importing-data-into-r-from-google-spreadsheet

readGoogleSheet <- function(url, na.string="", header=TRUE){
  stopifnot(require(XML))
  # Suppress warnings because Google docs seems to have incomplete final line
  suppressWarnings({
    doc <- paste(readLines(url), collapse=" ")
  })
  if(nchar(doc) == 0) stop("No content found")

EconometricsBySimulation

# First let's load some libraries
require('XML'); require('reshape2'); require('ggplot2')
require('magrittr') # See 
# http://goo.gl/Wj5F87

# I have borrowed Andrie's code from stackoverflow
# http://goo.gl/noYVo7
source("http://goo.gl/w64gfp")

# Load in the google spreadsheet

EconometricsBySimulation

library('rgl'); library('magrittr')

cube <- function(x=0,y=0,z=0, bordered=TRUE, 
                 filled = TRUE, lwd=2, scale=1,
                 fillcol = gray(.95),
                 bordercol ='black', ...) {
  
  mycube <- cube3d()
  
  # Reduce size to unit

EconometricsBySimulation

# adapted from John Fox's numbers2words function

require(magrittr); require(Rmpfr)

make.digits <- function(x) {
  # This is a function breaks an input number x into the positive (left)
  # and negative(right) elements and returns these as numbers
  x <- toString(x)
  negative <- substr(x,1,1)=="-"
  if (negative) x <- substring(x,2)

EconometricsBySimulation

rm(list=ls())

library(data.table)
library(dplyr)
library(ggplot2)
library(scales)

setwd('Z:/Data/FEC')

dsum <- function(...) dplyr::summarize(...)

EconometricsBySimulation

rm(list=ls())

library(data.table)
library(dplyr)
library(ggplot2)

setwd('Z:/Data/FEC')

dsum <- function(...) dplyr::summarize(...)
to.data.table <- function(x) {(class(x) <- class(data.table())) ;x} 

EconometricsBySimulation

# Estimating Weekly consumption from periodic purchasing data

library(dplyr)
library(data.table)
library(reshape)
library(tidyr)
library(ggplot2)


# Day Purchase

EconometricsBySimulation

emailto: psteiner@umd.edu student: Francis Smart fsmart@gmail.com EDMS769G

# Text Network graph
#           Student Ability _______________________
#            /           |                         \_____
#          /             |  Public/Private Transport     \
#         ↓              ↓     ↓                          ↘

EconometricsBySimulation