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.
In this paper we introduce a new bivariate model called bivariate compound Poisson-gamma model. The corresponding variable of this model are based on compounding the Poisson number of occurrences and maximum of independent identically distributed gamma variates. For this proposed model, several distributional properties have been established. We implement the EM algorithm based on the missing value principle to find the maximum likelihood estimators. Moreover, we use the observed Fisher information matrix to construct approximate confidence intervals. The performance of the EM type algorithm is illustrated via numerical simulation studies. Finally, a natural environment data have been analyzed to see how the proposed model and the respective methods work in practice.
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