Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 2, 293--305

CERTAIN q-ANALOGUES OF THE BINOMIAL DISTRIBUTION

By

ADRIENNE W. KEMP, University of St Andrews, Scotland

SUMMARY. The paper studies the relationships between various $q$-analogues of the binomial distribution, both extant and new, using the now generally accepted Gasper-Rahman notation. Some properties and models are explored. Two fitted examples are given.

*AMS (1991) subject classification}. *Primary 60E10, 62E15; secondary 33D15.

*Key words and phrases: *$q$-binomial distribution, direct absorption sampling, log-linear odds, log-linear probabilities, $q$-deformed binomial state, Euler distribution, $q$-Poisson distribution, Rogers-Szeg\"o polynomial, Stieltjes-Wigert polynomial, Jackson transformation, Wall polynomial, conditionality models, stationary state-dependant processes.