bivpoispy

Highlights

• Easy way of handle two dimensional count values.
• Shows contour and likelihood profile plots.
• Bivariate Poisson regression soon ...

Overview

Bivariate Poisson distribution for Python. Utilities for density evaluation, random sampling, maximum likelihood estimation, goodness-of-fit testing, and visualization.

Installation

pip install bivpoispy

Usage

We present some of the function of the package

import bivpoispy as bp
import numpy as np
 
# Simulate data from BP(6, 1, 3)
data = bp.random(lam1=6, lam2=1, lam3=3, size=1000)
 
# Compute the ML estimators and confidence intervals
result = bp.mle(data)
print(result)

lambda: [6.316995621845176, 1.1619956218451764, 2.8510043781548235]
rho: 0.4700304589772127
observed ci: [2.5932249797302585, 3.1087837765793886]
asymptotic ci: [2.5763621899957716, 3.1256465663138755]
loglik: [-4629.4336004690895, -4500.3484671610495]
pvalues: [4.29892277253514e-58, 1.6936755393462774e-104, 2.5194599844374772e-92]

# Plot the contour distribution of BP(6, 1, 3)
bp.contour(data, lam1=6, lam2 =1, lam3=3)

An introductory notebook with detailed explanation of the functions and examples is available in examples/bivpoispy_intro.ipynb.

References

• Kawamura K. (1984). Direct calculation of maximum likelihood estimator for the bivariate Poisson distribution. Kodai Mathematical Journal, 7(2): 211–221.
• Kocherlakota S. and Kocherlakota K. (1998). Bivariate discrete distributions. Wiley Online Library.
• Karlis D. and Ntzoufras I. (2003). Analysis of sports data by using bivariate Poisson models. Journal of the Royal Statistical Society: Series D, 52(3): 381–393.
• Lakshminarayana J., Pandit S. N. N., and Srinivasa Rao K. (1999). On a bivariate Poisson distribution