Abstract
In this paper, we introduce a discrete version of the Pseudo Lindley (PsL) distribution, namely, the discrete Pseudo Lindley (DPsL) distribution, and systematically study its mathematical properties. Explicit forms gathered for the properties such as the probability generating function, moments, skewness, kurtosis and stress–strength reliability made the distribution favourable. Two different methods are considered for the estimation of unknown parameters and, hence, compared with a broad simulation study. The practicality of the proposed distribution is illustrated in the first-order integer-valued autoregressive process. Its empirical importance is proved through three real datasets.
Highlights
Count data reflect the non-negative integers which represent the frequency of occurrence of a discrete event
The main objective of the present work is to introduce a two-parameter discrete distribution, the discrete Pseudo Lindley (DPsL) distribution, which can serve as a model to analyse under as well as over-dispersed datasets, having a simple pmf and cdf
From the information contained in these tables, it is clear that the DPsL distribution would be an appropriate option for modelling under as well as over-dispersed and positively skewed datasets
Summary
Count data reflect the non-negative integers which represent the frequency of occurrence of a discrete event. Researchers have assembled many approaches concerning innovations in modelling over-dispersed time series count datasets. By [17] and the INAR(1) process with Bell innovations (INAR(1)BL) by [18] are some of the recently developed over-dispersed INAR(1) processes Even though these processes provide better solutions to over-dispersed time series count datasets, they have some limitations that can sometimes cause computing difficulties. The main objective of the present work is to introduce a two-parameter discrete distribution, the discrete Pseudo Lindley (DPsL) distribution, which can serve as a model to analyse under as well as over-dispersed datasets, having a simple pmf and cdf. The INAR(1) process with DPsL innovations is developed in Section 4 with its parameter estimation and simulation study.
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