Aplicações de alguns métodos de discretização nas distribuições Lindley contínuas

Abstract

The methods of constructing a probability function from a probability density function has long been used in recent years. In general the discretization process of a continuous variable produces probability functions that can be rivals to traditional distributions used in the count data analysis - Poisson and negative binomial for example. The discretization also avoids the use of a continuous distribution in the analysis of strictly discrete data. By the method based on an infinite series, proposed by Good (1953), by the method based on the survival function, proposed by Nakagawa e Osaki (1975), and by the method based on the hazard rate function, proposed by Roy e Ghosh (2009), the objective of this study is to propose new discrete analogues of Lindley (LINDLEY, 1958) distribution and the variants power Lindley distribution (GHITANY et al., 2013) and weighted Lindley distribution (GHITANY et al., 2011) and also propose zero- runcated, shifted and weighted (just in case of Lindley distribution) for these new distributions. For each proposed distributions were carried out Monte Carlo simulation studies to evaluate BIAS and the MSE of maximum likelihood estimators. Two applications where not observed response x = 0 are considered to illustrate the applicability of the proposed distributions. The first refers to the length of wet spells and the second to the length of positive runs in the financial market prices.