Journal of Statistics and Data Science
Vol. 5 No. 1 (2026)

A Review of the Convolution of Geometric Distributions and Its Properties

Ayenigba, Alfred Ayo (Unknown)
Afariogun, David (Unknown)
Olajide Oyewole , AGBOOLA (Unknown)
Ivande , James Serumun (Unknown)

Article Info

Publish Date
30 Mar 2026

Abstract

This review explores the convolution of geometric distributions, a key operation in probability theory for deriving the distribution of the sum of independent random variables. Geometric distributions quantify the number of Bernoulli trials needed for the first success and are foundational in discrete probability models. Convolving multiple geometric distributions with a common success probability produces a negative binomial distribution, modelling the number of trials needed to achieve a given number of successes. We present a concise derivation of this result, highlighting the relationship between geometric and negative binomial distributions. The review also outlines essential properties of the negative binomial distribution, including its mean, variance, moment-generating function, and some applications.

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Journal Info
Journal of Statistics and Data Science
Website

Abbrev

jsds

Publisher

Universitas Bengkulu

Subject

Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Mathematics Other

Description

Established in 2022, Journal of Statistics and Data Science (JSDS) publishes scientific papers in the fields of statistics, data science, and its applications. Published papers should be research-based papers on the following topics: experimental design and analysis, survey methods and analysis, ...