Statistics' tasks

gistfile1.py

# coding: utf-8

import numpy as np
import cmath as math
import scipy.stats as stats
import random


def generate_exponential(exp_lambda, size):
    scale = 1 / exp_lambda
    return np.random.exponential(scale, size)

def exponential_mean(exp_lambda):
    return 1 / exp_lambda

def exponential_variance(exp_lambda):
    return exponential_mean(exp_lambda)**2

def sample_variance(sample):
    diff = sum([(x - sample.mean())**2 for x in sample])
    return (1.0 / (len(sample) - 1)) * diff

def noncentral_student(df, noncentral, size_ = 1):
    return stats.nct.rvs(df, noncentral, size=size_)

def combination_of_distributions(size, conditioner = 0.1):
    result = []
    for i in range(0, size):
        is_exp = (1 - conditioner) >= random.random()
        if is_exp:
            result.append(generate_exponential(0.25, 1)[0])
        else:
            result.append(noncentral_student(3, 4, 1)[0])

    return np.array(result)

def confidential_interval(sample):
    low = sample.mean() - 3*sample_variance(sample) / math.sqrt( len(sample) )
    high = sample.mean() + 3*sample_variance(sample) / math.sqrt( len(sample) )
    return [low, high]

def is_mean_in_conf_interval(conf_interval, mean):
    return (mean >= conf_interval[0] and mean <= conf_interval[1])

def task1():
    size = 8
    exp_lambda = 0.25

    sample = generate_exponential(exp_lambda, size)

    print "Sample: " + str(sample)

    print "Sample mean: " + str(sample.mean())
    print "Sample variance: " + str(sample_variance(sample))

    mean = exponential_mean(exp_lambda)
    print "Theoretical mean: " + str(mean)
    print "Theoretical variance: " + str(exponential_variance(exp_lambda))

    conf_interval = confidential_interval(sample)
    print "Condidence interval: " + str(conf_interval)

    print "Mean in conf interval: " + str(is_mean_in_conf_interval(conf_interval, mean))

def task2():
    size = 8000
    exp_lambda = 0.25

    conditioner = 0.05
    for i in range(0,4):
        conditioner = conditioner*2
        print "conditioner is " + str(conditioner)

        sample = combination_of_distributions(size, conditioner)
        # print sample

        print "Sample mean: " + str(sample.mean())
        print "Sample variance: " + str(sample_variance(sample))

        mean = exponential_mean(exp_lambda)
        print "Theoretical mean: " + str(mean)

        conf_interval = confidential_interval(sample)
        print "Condidence interval: " + str(conf_interval)
        print "Mean in conf interval: " + str(is_mean_in_conf_interval(conf_interval, mean))

        print "\n"

def task3():
    h0_m = -1
    h0_s = 1

    h1_m = -9
    h1_s = 3

    vec = np.random.uniform(-18, 2, 6)
    norms = np.random.normal(h0_m, h0_s)
    print vec
    print norms
    
    # Uncomplete yet