We provide a compact survey and brief interpretations and comments on some 170 publications on process capability indices which appeared in widely scattered sources during the years 1992 to 2000. A...

Process capability indices- a review. 1992–2000

Summary. Models based on the bivariate Poisson distribution are used for modelling sports data. Independent Poisson distributions are usually adopted to model the number of goals of two competing teams. We replace the independence assumption by considering a bivariate Poisson model and its extensions. The models proposed allow for correlation between the two scores, which is a plausible assumption in sports with two opposing teams competing against each other. The effect of introducing even slight correlation is discussed. Using just a bivariate Poisson distribution can improve model fit and prediction of the number of draws in football games. The model is extended by considering an inflation factor for diagonal terms in the bivariate joint distribution. This inflation improves in precision the estimation of draws and, at the same time, allows for overdispersed, relative to the simple Poisson distribution, marginal distributions. The properties of the models proposed as well as interpretation and estimation procedures are provided. An illustration of the models is presented by using data sets from football and water-polo.

https://www.jstor.org/stable/pdfplus/4128211.pdf

Analysis of sports data by using bivariate Poisson models

Bivariate discrete distributions

https://ir.nctu.edu.tw:443/bitstream/11536/7703/1/000264002300010.pdf

An overview of theory and practice on process capability indices for quality assurance

Mixed Poisson distributions have been used in a wide range of scientific fields for modelling non-homogeneous populations. This paper aims at reviewing the existing literature on Poisson mixtures by bringing together a great number of properties, while, at the same time, providing tangential information on general mixtures. A selective presentation of some of the most prominent members of the family of Poisson mixtures is made.

Mixed Poisson Distributions

In this paper we study some problems associated with count data from a bivariate Poisson distribution, in which the marginal means are functions of explanatory variables. The estimates of these regression coefficients are developed under a variety of conditions: unrestricted linear model; parallelism of the regression planes; the coincidence of the regression planes. Tests are also developed for the validity of hypotheses involved in these models. The techniques are illustrated using simulated data.

Regression in the bivariate poisson distribution

Some alternative procedures for testing goodness of fit in discrete distributions are discussed here.. These procedures are based on the probability generating functions.. The methods considered are quite general, being applicable in multidimensional situations., The strength of the tests lies in that no ambiguity as to classification of the data arises.. Hov-ever, some difficulties in the proposed procedures are also pointed out.

Goodness of fit tests for discrete distributions

Estimators for σ, I/σ and the process capability index based on m preliminary samples, each of size n, are derived and their properties are discussed. A test of hypothesis and a confidence bound for CP are developed.

K. Kocherlakota

Papers

Bivariate discrete distributions

Regression in the bivariate poisson distribution

Goodness of fit tests for discrete distributions

Estimation of σ and the process capability index based on subsamples

Bivariate Discrete Distributions.