Abstract
The aim of this article is to propose a new three-parameter discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, index of dispersion, mean residual life, mean past life and stress-strength reliability. These properties are expressed in explicit forms. The maximum likelihood approach is used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of the estimators. Using the proposed distribution, a new first-order integer-valued autoregressive process is introduced for the over-dispersed, equi-dispersed and under-dispersed time series of counts. To demonstrate the importance of the proposed distribution, three data sets on coronavirus, length of stay at psychiatric ward and monthly counts of larceny calls are analyzed.
Highlights
Statistical distributions play an important role in data modeling, inference, and forecasting processes
The recently introduced discrete distribution based on the survival discretization method can be cited as follows: discrete Lindley (DLi) distribution by Gómez-Déniz and Calderín-Ojeda (2011), discrete inverse Weibull (DIW) distribution by Jazi et al (2010), discrete Burr type XII (DB-XII) distribution by Para and Jan (2014), discrete Pareto (DPa) distribution by Krishna and Pundir (2009), The associate editor coordinating the review of this manuscript and approving it for publication was Giambattista Gruosso
The statistical properties of the DLi-3P distribution are derived in great detail
Summary
Statistical distributions play an important role in data modeling, inference, and forecasting processes. The occurrence times, frequencies and effects of many events in nature are analyzed by statistical modeling techniques. There are two popular methods used to introduce a new discrete distribution. These are mixed-Poisson type discrete distributions and survival discretization method. The recently introduced discrete distribution based on the survival discretization method can be cited as follows: discrete Lindley (DLi) distribution by Gómez-Déniz and Calderín-Ojeda (2011), discrete inverse Weibull (DIW) distribution by Jazi et al (2010), discrete Burr type XII (DB-XII) distribution by Para and Jan (2014), discrete Pareto (DPa) distribution by Krishna and Pundir (2009), The associate editor coordinating the review of this manuscript and approving it for publication was Giambattista Gruosso
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