Conway Maxwell Binomial Distribution

This package defines a class of Conway-Maxwell-Binomial distribution objects for Python 3. It also defines some useful functions for working with the objects.

Requirements

• Python3.6 or above
• numpy
• scipy

Conway-Maxwell-Binomial distributions

If you would like to learn more about this probability distribution, see this article: https://en.wikipedia.org/wiki/Conway-Maxwell-binomial_distribution

Or this paper: https://arxiv.org/pdf/1404.1856v1.pdf

Initialising a COMB distribution

To initialse a Conway-Maxwell-Binomial distribution use the following lines of code

import ConwayMaxwellBinomial as cmb
p = 0.4
nu = 0.9
m = 100
com_distn = cmb.ConwayMaxwellBinomial(p, nu, m)

To sample from the distribution run

com_distn.rvs(size=10)

and to evaluate the probability mass function for some outcome, run

com_distn.pmf(99)
com_distn.pmf(40)

Estimating the parameters of the distribution

To estmiate the parameters of the Conway Maxwell Binomial distribution given a sample, run the following lines

sample = com_distn.rvs(size=15)
initial_params = [0.5, 1]
cmb.estimateParams(m, sample, initial_params)

To evaluate the negative log-likelihood of a sample, run

cmb.conwayMaxwellNegLogLike([p, nu], m, sample)