The package jhplot.stat can be used for descriptive analysis of random distributions

As example, let us consider calculations of normalised factorial moments (NFM) for several distributions. They are defined as

.

where “n” is a random number (integer) number. According to this definition, a Poisson distribution has all moments equal to 1. A broader than a Poisson distribution have moments larger then one. Let us calculate the NFM up to 4th order for a Poisson distribution Binomial and a Negative-binomial distributions

example.py

from jhplot  import *
from jhplot.stat  import MomentsFacNorm
from cern.jet.random.engine import *
from cern.jet.random  import *
from jhplot.shapes  import Line
from java.awt import Color
 
c1 = HPlot("Canvas")
c1.visible(1)
c1.setNameX("NFM order")
c1.setNameY("Values")
c1.setRange(0,5,0,2) 
 
line = Line(0.0,1, 5., 1.) # draw  a vertical line in the NDC system
line.setPosCoord("USER"); line.setColor(Color.gray); line.setTransparency(0.5)
c1.add(line)
 
# build a random engine
engine=MersenneTwister()
 
poisson=Poisson(10,engine) # a Possonian distribution
m=MomentsFacNorm(4)        # calculates moments up to 4th order
 
for i in range(100):
        m.process( poisson.nextInt())
p1=m.getResults()
p1.setTitle("NFM for Poissson"); p1.setSymbol(4); p1.setSymbolSize(10)
c1.draw(p1)
print(p1.toString())
 
binomial=Binomial(10, 0.2, engine)  # Binomial distribution
m=MomentsFacNorm(4) # calculates moments up to 4th order
for i in range(200):
       m.process( binomial.nextInt())
p2=m.getResults(); p2.setTitle("NFM for Binomial"); p2.setSymbol(5); p2.setSymbolSize(10)
c1.draw(p2)
print(p2.toString())
 
nbinom=NegativeBinomial(10, 0.4, engine) # NegativeBinomial distribution (NBD)
m=MomentsFacNorm(4) 
for i in range(300):
       m.process( nbinom.nextInt())
p3=m.getResults(); p3.setTitle("NFM for NBD"); p3.setSymbol(6); p3.setSymbolSize(10)
c1.draw(p3)
print(p3.toString())

The output file shows the NFM for all three distributions together with statistical errors.

Read the book "Scientific data analysis using Jython scripting and Java for advanced examples.