Reliability and estimation of the zero-inflated transmuted geometric distribution with applications and actuarial insights.

Abstract

Overdispersion is a phenomenon which is quite common in many real-life count data sets and these variability often results due to an excessive number of zeros. To address this issue, zero-inflated distributions provide a flexible modeling approach capable of capturing high levels of dispersion. In this paper we introduce a new count distribution known as the zero-inflated transmuted geometric distribution. We explore its key statistical properties, reliability aspects and actuarial traits. Additionally we employ different estimation strategies and conduct a simulation study to assess the performance of the estimators. We demonstrate the practical utility of the proposed model through the analysis of three empirical data sets. Lastly, we also carry out the likelihood ratio test to justify the use of the proposed zero-inflated distribution.