A Discrete Analogue of Teissier Distribution: Properties and Classical Estimation with Application to Count Data

This article presents a novel discrete distribution with a single parameter, called the discrete Teissier distribution. It is noted that this model, with one parameter, offers a high degree of fitting flexibility as it is capable of modelling equi-, over-, and under-dispersed, positive and negative skewed, and increasing failure rate datasets. In this article, we have explored its numerous essential distributional features such as recurrence relation, moments, generating function, index of dispersion, coefficient of variation, entropy, survival and hazard rate functions, mean residual life and mean past life functions, stress-strength reliability, order statistics, and infinite divisibility. The classical point estimators have been developed using the method of maximum likelihood, method of moment, and least-squares estimation, whilst an interval estimation based on Fisher’s information has also been presented. Finally, the applicability of the suggested discrete model has been demonstrated using two complete real datasets. © Reliability: Theory and Applications 2022.