APPLICATIONS OF TWO NON-CENTRAL HYPERGEOMETRIC DISTRIBUTIONS OF BIASED SAMPLING STATISTICAL MODELS

K O Adetunji,T Alanamu,E J Adefila,K A Muhammed,A A Issa

doi:10.33003/fjs-2020-0404-498

Abstract

Statistical models of biased sampling of two non-central hypergeometric distributions Wallenius' and Fisher's distribution has been extensively used in the literature, however, not many of the logic of hypergeometric distribution have been investigated by different techniques. This research work examined the procedure of the two non-central hypergeometric distributions and investigates the statistical properties which includes the mean and variance that were obtained. The parameters of the distribution were estimated using the direct inversion method of hyper simulation of biased urn model in the environment of R statistical software, with varying odd ratios (w) and group sizes (mi). It was discovered that the two non - central hypergeometric are approximately equal in mean, variance and coefficient of variation and differ as odds ratios (w) becomes higher and differ from the central hypergeometric distribution with ω = 1. Furthermore, in univariate situation we observed that Fisher distribution at (ω = 0.2, 0.5, 0.7, 0.9) is more consistent than Wallenius distribution, although central hypergeometric is more consistent than any of them. Also, in multinomial situation, it was observed that Fisher distribution is more consistent at (ω = 0.2, 0.5), Wallenius distribution at (ω = 0.7, 0.9) and central hypergeometric at (ω = 0.2) 

Highlights

INRODUCTION The hyper geometric distribution occupies a place of great significance in statistic theory
In univariate situation we observed that Fisher distribution at (ω = 0.2, 0.5, 0.7, 0.9) is more consistent than Wallenius distribution, central hypergeometric is more consistent than any of them
The description of biased urn models is complicated by the fact that there is more than one non central hypergeometric distribution, depending on whether items are sampled in a manner where there is competition between the items or they are sampled independently of each other

Summary

Introduction

INRODUCTION The hyper geometric distribution occupies a place of great significance in statistic theory It applies to sampling without replacement from a finite population whose element can be classified into two categories, one which possesses certain characteristics. One instance could be a case of picking from an urn containing biasedly colored tagged balls, so that balls of one color are more likely to be picked than balls of another color Another instance could be a case of an opinion poll, conducted by calling random telephone numbers and it is assumed that unemployed people are more likely to be home and answer the phone than employed people an unemployed respondent are likely to be over-represented in the sample.

Objectives

Methods

Discussion

Conclusion