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: [0.4778915451715814, 0.30174546886521236, 0.7044608950073236, 0.4559359919187841, 0.9258722827268353, 0.10362009707891595, 0.719097804807644, 0.9153915352615909, 0.8376479199834229, 0.43385293910077916] Norm: [9.100970605447069, 8.223756587831208, 5.528642814085064, 7.344028742900231, 11.25537614351693, 10.030910783084089, 9.729216128027806, 8.930689539230801, 4.96677728348392, 9.283397377809855] Tri: [0.45000856760815416, 0.19553467567744884, 0.7296870632339634, 0.697251105414321, 0.31567859423380606, 0.42171266218016346, 0.5138035025203709, 0.4377490963670751, 0.688777773255248, 0.5096449599690658] Log: [9.14150131188522, 3.0941241789779435, 6.41160054521203, 4.054259039265503, 10.144989676902778, 10.67100631829843, 1.5604257783533069, 5.763263799120814, 3.2448621668409663, 3.617047577173457] Exp: [2.1120375260279816, 3.209517564355096, 38.27817339150131, 4.320148398601968, 19.79974861578987, 4.060539756417002, 6.047552606080205, 12.550960100702628, 3.954320707518012, 1.9709516834506753] [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()