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: [0.16938886326748925, 0.1943821292873198, 0.8082831168020577, 0.786485563621865, 0.23524613726601462, 0.5831870333717987, 0.20854527011653834, 0.7193457594933877, 0.4754861319657996, 0.08626949873608647] Norm: [10.896733471647163, 11.821436518310588, 10.384901506842827, 7.699793364838863, 7.908265142918851, 8.468274664419319, 8.215034196715047, 9.287557883365201, 8.807600475387956, 9.427466778917498] Tri: [0.35017488000551966, 0.4144210903627259, 0.6594686160817773, 0.5147871577724867, 0.5766406806259426, 0.8217712729767147, 0.32159608512380056, 0.7321454327688468, 0.49246382926478643, 0.3736749189829533] Log: [5.253510637145376, 13.26826250438539, 4.2156937152984115, 11.220488486691291, 12.125191772798107, 7.301186046889142, 3.429720878124477, 4.461841599798317, 7.582845778441989, 8.91167855866292] Exp: [20.521720610832375, 20.922918855952364, 14.309060787224018, 4.1056378927498365, 0.2559896251775289, 0.9797159460406631, 10.334173963122037, 7.812444268869989, 1.9324625284447925, 21.919393960528975] [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()