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: [0.5454536696630734, 0.616788653397946, 0.8844727104352373, 0.9649537759463168, 0.5267854970334768, 0.8949422602737718, 0.8353251174353518, 0.6073174564491296, 0.7513888233520454, 0.4090409200848881] Norm: [8.981797802036356, 8.47358466600041, 8.97996354979187, 7.784979340914291, 9.550453439597641, 8.11769933351979, 8.550122208303101, 9.919638829567267, 3.631784782359679, 8.287307480752158] Tri: [0.657348725294594, 0.37657698021968306, 0.3942772945009987, 0.15708726840875273, 0.5951159129583014, 0.5301519467670717, 0.5106300925327445, 0.2606829572216047, 0.020001500256364907, 0.74912810136182] Log: [2.6240102748624694, 5.299274617445328, 13.177209390411678, 6.637350033766177, 3.2701350017699613, 12.624751875340648, 11.491319709036862, 3.4517858088704, 5.111555314167762, 13.928261098285963] Exp: [1.8121093144022593, 23.94691697194954, 2.6430484923707858, 3.139712136747222, 7.838334247898203, 4.588022676786182, 1.9878004505299778, 19.768129128112886, 7.724117522541345, 0.8319348740533996] [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()