Abstract
In this paper, we propose a new class of distributions by compounding Lindley distributed random variates with the number of variates being zero-truncated Poisson distribution. This model is called a compound zero-truncated Poisson–Lindley distribution with two parameters. Different statistical properties of the proposed model are discussed. We describe different methods of estimation for the unknown parameters involved in the model. These methods include maximum likelihood, least squares, weighted least squares, Cramer–von Mises, maximum product of spacings, Anderson–Darling and right-tail Anderson–Darling methods. Numerical simulation experiments are conducted to assess the performance of the so obtained estimators developed from these methods. Finally, the potentiality of the model is studied using one real data set representing the monthly highest snowfall during February 2018, for a subset of stations in the Global Historical Climatological Network of USA.
Highlights
In recent years, many researches are interested in obtaining several new continuous distributions by compounding an absolutely continuous distribution with a discrete distribution
The exponential Poisson (EP) and exponential logarithmic distributions were introduced by Kus
A new family of distributions is proposed based on a maxima of Poisson number of Lindely random variates
Summary
Many researches are interested in obtaining several new continuous distributions by compounding an absolutely continuous distribution with a discrete distribution. This method is used widely in engineering applications including risk measurement, floods reliability and survical analysis. Adamidis and Loukas [1] proposed a two-parameter lifetime distribution by compounding exponential and geometric distributions. The exponential Poisson (EP) and exponential logarithmic distributions were introduced by Kus [2] and Tahmasbi and Rezaei [3], respectively. Marshall and Olkin [4] developed some new extensions based on random minimum and maximum. Barreto-Souza and Cribari-Neto [5] introduced the exponentiated exponential Poisson (EEP)
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