On a modified binomial distribution of order k
type: Item
instance of: scholarly article
title: On a modified binomial distribution of order k
zbMATH Open document ID: 0726.60013
DOI: 10.1016/0167-7152(91)90129-F
author: Wentao Huang
author: Chiou-Shiang Tsai
published in: Statistics \& Probability Letters
publication date: 1991-01-01T00:00:00Z
review text: The paper provides two extensions of the binomial distribution of order k defined by \textit{K. Hirano} [Fibonacci numbers and their applications, Pap. 1st Int. Conf., Patras/Greece 1984, Math. Appl., D. Reidel Publ. Co. 28, 43-53 (1986; Zbl 0601.62023)], derives their probability generating functions, moment generating functions and shows that the Poisson distribution is a limiting form of one of them. These are based on a generalization of the notion of success so as to be the occurrence of the event \[ FFF...F\quad SS...S\quad (F\quad k_ 1-fold\text{ and } S\quad k_ 2-fold) \] in a series of Bernoulli trials where S stands for a successful trial and F for an unsuccessful trial. Further it examines the distribution of the number of trials between two consecutive ``successes'' in the above sense.
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 4199141
zbMATH Keywords: binomial distribution of order k
zbMATH Keywords: generating functions
zbMATH Keywords: Bernoulli trials
reviewed by: Evdokia Xekalaki
MaRDI profile type: Publication
cites work: Discrete distributions of order k on a binary sequence
cites work: On discrete distributions of order k
cites work: Q5538132
cites work: Q3736693
cites work: Q5539502
cites work: On generalized binomial and multinomial distributions and their relation to generalized Poisson distributions
cites work: On multiparameter distributions of order k
cites work: A generalized geometric distribution and some of its properties
cites work: Successes, runs and longest runs
cites work: Q3933686
cites work: On some distributions arising in inverse cluster sampling
cites work: Q3756211
full work available at URL: 0167-7152(91)90129-f
OpenAlex ID: W2057060079
description: scientific article; zbMATH DE number 4199141