Abstract
Methods to generate a discrete analogue of a continuous distribution have been widely considered in recent decades. In general, the discretization procedure comprises in transform continuous attributes into discrete attributes generating new probability distributions that could be an alternative to the traditional discrete models, such as Poisson and Binomial models, commonly used in analysis of count data. It also avoids the use of continuous in the analysis of strictly discrete data. In this paper, using the discretization method based on the survival function, it is introduced a discrete analogue of power Lindley distribution. Some mathematical properties are studied. The maximum likelihood theory is considered for estimation and asymptotic inference concerns. A simulation study is also carried out in order to evaluate some properties of the maximum likelihood estimators of the proposed model. The usefulness and accurate of the proposed model are evaluated using real datasets provided by the literature.
Highlights
The methods to generate a discrete analogue of a continuous distribution has been widely considered and studied in recent decades by several authors such as Good (1953), Nakagawa and Osaki (1975), Roy and Ghosh (2009) and Ghosh et al (2013)
There are several methods to obtain a discrete distribution from a continuous distribution: the discretization method based on the survival function (NAKAGAWA and OSAKI, 1975), the discretization method based on an infinite series (GOOD, 1953; KULASEKERA and TONKYN, 1992; KEMP, 1997; SATO et al, 1999), the discretization method based on the hazard function (STEIN, 1984), the compound two-phase method (CHAKRABORTY, 2015), the discretization method based on reverse hazard function (GHOSH et al, 2013), among many others
Assuming the power Lindley distribution as baseline distribution with the survival function given by (5) and using the discretization method based on the survival function, the discrete power Lindley distribution, hereafter DPL distribution, has probability function written as: βxα P (X = x | α, β) = 1 +
Summary
The methods to generate a discrete analogue of a continuous distribution has been widely considered and studied in recent decades by several authors such as Good (1953), Nakagawa and Osaki (1975), Roy and Ghosh (2009) and Ghosh et al (2013). The method of discretization by survival function was proposed by Nakagawa and Osaki (1975). The main goal of this paper is to use Nakagawa and Osaki’s discretization method to propose a discrete analogue for power Lindley distribution (GHITANY et al, 2013).
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