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: [0.7225226745490497, 0.20866971195761108, 0.7015444959612367, 0.3832574482037112, 0.49257016865678016, 0.7437826880275894, 0.7708268658743611, 0.05168236269596893, 0.0477727910110648, 0.9182066615784782] Norm: [10.963390688234224, 7.027695982150908, 11.22130883376517, 9.046480566929077, 10.678233774866165, 5.895729636870434, 6.688910158075421, 10.622958394413251, 10.595496234753664, 11.257197199290296] Tri: [0.9309057500526059, 0.2997518453614622, 0.5011791064296438, 0.8046598266488834, 0.5211071800295426, 0.8236154735784202, 0.5370944091141518, 0.20472964130834956, 0.6334782518817645, 0.8293818843551469] Log: [9.252085764603612, 6.027939613233617, 6.695981577977579, 8.518366626136501, 7.0780621516052715, 4.021588818331878, 1.0680063500765837, 12.34421602992532, 7.935427917027084, 14.735718974564481] Exp: [1.1311360559727406, 4.6509937504223595, 0.3465268674621659, 7.517309324364817, 5.955738638103983, 11.503446213764422, 16.78533210142853, 4.534739147482289, 5.460630676769349, 10.796648816941863] [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()