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.
Resumo
Nos últimos anos diversas distribuições de probabilidade foram propostas na literatura com propósitos de se obter funções densidade e de risco mais flexíveis. Por exemplo, Ghitany et al. (2013) propuseram uma generalização da distribuição Lindley e a nomearam de distribuição Lindley potência enquanto que Sharma et al. (2015a) propuseram a distribuição Lindley inversa. A partir destas duas generalizações, Barco et al. (2017) estudaram a distribuição Lindley potência inversa, também chamada por Sharma et al. (2015b)
AbstractIn the last years several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. For instance, Ghitany et al. (2013)
proposed a new generalization of the Lindley distribution, called power Lindley distribution, whereas Sharma et al. (2015a) proposed the inverse Lindley distribution. From these two generalizations Barco et al. (2017) studied the inverse power Lindley distribution, also called by Sharma et al. (2015b) as generalized inverse Lindley distribution. Considering the inverse power Lindley distribution, in this paper is evaluate the performance, through Monte Carlo simulations, with respect to the bias and consistency of nine different methods of estimations (the maximum likelihood method and eight others based on the distance between the empirical and theoretical cumulative distribution function
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