Abstract
In this paper, a Poisson mixture of the Amarendra distribution, introduced by Shanker (2016 c), is proposed, and called the, “Poisson-Amarendra distribution”. The first four raw moments (about the origin) and central moments (about the mean) are obtained. The expression for coefficient of variation, skewness and kurtosis are also given. For the estimation of its parameter, the maximum likelihood estimation and the method of moments are discussed. Moreover, the distribution is fitted using maximum likelihood estimate to certain data sets to test its goodness of fit over Poisson, Poisson-Lindley and Poisson-Sujatha distributions. The corresponding fitting are found to be quite satisfactory in almost all data sets.
Highlights
In this paper, a Poisson mixture of the Amarendra distribution, introduced by Shanker (2016 c), is proposed, and called the, “Poisson-Amarendra distribution”
The distribution is fitted using its maximum likelihood estimate on certain data sets in order to test its goodness of fit over Poisson distribution, Poisson-Lindley distribution (PLD), a Poisson-mixture of Lindley (1958) distribution, introduced by Sankaran (1970) and PoissonSujatha distribution (PSD) of Shanker (2016 b), a Poisson mixture of Sujatha distribution, introduced by Shanker (2016 a)
Shanker and Hagos (2016 d) have provided a detailed study regarding applications of the zero-truncated Poisson distribution (ZTPD), the zero-truncated PoissonLindley distribution (ZTPLD), and the zero-truncated Poisson-Sujatha distribution (ZTPSD) for modeling data sets from demography and biological sciences and concluded that in majority of data sets zerotruncated Poisson-Sujatha distribution (ZTPSD) gives better fit than ZTPD and ZTPLD
Summary
Assuming the parameter λ of the Poisson distribution to follows Amarendra distribution (1), the Poisson mixture of Amarendra distribution can be obtained as. Shanker and Hagos (2015) has discussed the applications of PLD for modeling count data-sets from biological sciences and observed that it gives better fit than Poisson distribution. Shanker and Hagos (2016 a) provided a detailed study about the application of the Poisson-Sujatha distribution (PSD) when modeling biological science data, and observed a better fit than the Poisson-Lindley distribution (PLD) and Poisson-distribution. Shanker and Hagos (2016 d) have provided a detailed study regarding applications of the zero-truncated Poisson distribution (ZTPD), the zero-truncated PoissonLindley distribution (ZTPLD), and the zero-truncated Poisson-Sujatha distribution (ZTPSD) for modeling data sets (with zero counts excluded) from demography and biological sciences and concluded that in majority of data sets ZTPSD gives better fit than ZTPD and ZTPLD
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