Histograms   [Back] When we have data we often has a given pattern, such as fitting a normal distribution - such as with IQs and height of a person - or could be random. One of the best ways to look at these is a probability distribution with a histogram. The following shows a normal distribution and a random distribution. For a uniform random generator, we should get a flat trend across all the values, whereas the normal distribution depends on the μ and σ values. The more samples we have, the nearer it will get to the expected distribution: Options Normal- μ: Normal- σ: Samples: Bins: Determine Try an example μ=5, σ=3, Samples=100 Calc μ=5, σ=3, Samples=1,000 Calc μ=5, σ=3, Samples=10,000 Calc μ=5, σ=3, Samples=100,000 Calc μ=5, σ=3, Samples=1000, Bins=10 Calc μ=5, σ=3, Samples=1000, Bins=50 Calc μ=5, σ=3, Samples=1000, Bins=100 Calc μ=5, σ=3, Samples=1000, Bins=200 Calc μ=5, σ=10 Calc μ=5, σ=1 Calc μ=5, σ=0.5 Calc μ=5, σ=5 Calc μ=55, σ=10 Calc. This is the mark distribution we often aim for in academia. Normal distribution: \( f(x)=\frac{1}{\sqrt{2\pi}\sigma}e^{-(x-\mu)^2/(2\sigma^2)}\) eg: μ=9, σ=2 \( f(9)=\frac{1}{\sqrt{2\pi}2}e^{-(9-9)^2/(2(2)^2)}= 0.2\). This should be the value for x=9: Calc Uni: [0.968599136816952, 0.3178966902383562, 0.520647748036519, 0.2472502563671929, 0.9680835474135473, 0.9895110247262964, 0.40493173893835266, 0.9475205418482346, 0.37613084949183584, 0.3722149475869658] Norm: [10.674642514329394, 6.36229888018609, 11.140736545528979, 5.493199536963528, 8.719268263545182, 8.540944082599717, 11.438786197339574, 13.351626974581162, 10.852936691841075, 6.619877753591915] Tri: [0.1034264682258155, 0.6103318738491834, 0.42740760538217343, 0.6008147622935542, 0.557051881588976, 0.6211614226419844, 0.5160641532660541, 0.09591136866630315, 0.8204815221350237, 0.17646377023145707] Log: [14.861996942446945, 10.119765858896905, 6.929603169194577, 16.707552107589112, 7.47144213211984, 10.488770772309975, 4.671147703887049, 5.58798387415875, 10.444017710112877, 6.716700795272331] Exp: [0.08886978486690532, 3.4923599364586946, 12.80270212519967, 22.52581393118599, 6.986423676644629, 3.123898409547022, 6.3773915524562925, 3.680098749832002, 14.282735449906196, 0.442384345620384] [View]

Source code

The following outlines the Python code used:

import matplotlib.pyplot as plt
import numpy as np
import sys
import random

file ='1111'
mu=9.0
sig=2.0
samples=10000



if (len(sys.argv)>1):
        file=str(sys.argv[1])

if (len(sys.argv)>2):
        mu=float(sys.argv[2])

if (len(sys.argv)>3):
        sig=float(sys.argv[3])

if (len(sys.argv)>4):
        samples=int(sys.argv[4])



fig,myplot = plt.subplots(4, 1,figsize=(8,8))
plt.tight_layout(w_pad=1.5, h_pad=2.0)


uniSamples = [random.random() for i in xrange(samples)]


myplot[0].hist(uniSamples, bins=100, normed=True)
myplot[0].set_title("Uniform random number generator histogram")
myplot[0].set_xlabel("x")
myplot[0].set_ylabel("Frequency of occurrence")
print "Uni: ",uniSamples[0:10]  #Take a look at the first 10


normSamples = [random.normalvariate(mu,sig) for i in xrange(samples)]

myplot[1].hist(normSamples, bins=100, normed=True)
myplot[1].set_title(r"Normal Histogram RNG $\mu = "+str(mu)+"$ and $\sigma = "+str(sig)+"$")
myplot[1].set_xlabel("x")
myplot[1].set_ylabel("Frequency of occurrence")

print "Norm: ",normSamples[0:10]  #Take a look at the first 10


triSamples = [random.triangular(0,1,0.5) for i in xrange(samples)]

myplot[2].hist(triSamples, bins=100, normed=True)
myplot[2].set_title(r"Triangular Histogram RNG")
myplot[2].set_xlabel("x")
myplot[2].set_ylabel("Frequency of occurrence")

print "Tri: ",triSamples[0:10]  #Take a look at the first 10
    

logSamples = [random.weibullvariate(mu,sig) for i in xrange(samples)]

myplot[3].hist(logSamples, bins=100, normed=True)
myplot[3].set_title(r"Weibull Histogram RNG")
myplot[3].set_xlabel("x")
myplot[3].set_ylabel("Frequency of occurrence")
   
print "Log: ",logSamples[0:10]  #Take a look at the first 10

plt.show()