An Alternative Reparametrization for the Weighted Lindley Distribution

Abstract

ABSTRACT. Recently, [12] introduced a generalization of a one parameter Lindley distribution and named it as a weighted Lindley distribution. Considering this new introduced weighted Lindley distribution, we propose a reparametrization on the shape parameter leading it to be orthogonal to the other shape parameter. In this alternative parametrization, we get a direct interpretation for this transformed parameter which is the mean survival time. For illustrative purposes, the weighted Lindley distribution on the new parametrization is applied on two real data sets. The one parameter Lindley distribution and its generalized form are fitted for the considered data sets.

A Reparameterized Weighted Lindley Distribution: Properties, Estimation and Applications

“…In recent years, some traditional distributions have been reparameterized in terms of their mean to model real problems; see, e.g., Cepeda & Gamerman (2005), Santos-Neto et al (2016), Rigby et al (2019), Bourguignon & Gallardo (2020). In our bibliographical review, we noted that not much attention has been paid to parameterizations of the Lindley distribution, as well as its generalizations, except the work proposed by Mazucheli et al (2016). The authors introduced an alternative parameterization for the WL distribution in the context of orthogonal parameters (Cox & Reid 1987).…”

“…Although Mazucheli et al (2016) have proposed the RWL distribution, the authors did not study its properties and, in addition, they also did not consider the maximum likelihood estimation for the parameters under censored data. Our objective in this paper is to derive and discuss many mathematical properties of this distribution, including its moments, quantile function, characteristic function, mean and median deviations, hazard rate function, mean residual life function, and Laplace transform function.…”

Modeling survival data based on a reparameterized weighted Lindley distribution

“…Some advantages of using reparameterized distributions in statistical modeling are: (i) they simplify the classical and Bayesian inferences; (ii) they facility the interpretation of results; (iii) they allow us to model heteroscedasticity (in regression); (iv) in survival analysis, they can be an alternative to existing frailty distributions (LEÃO et al, 2018;LEÃO et al, 2017). Following this approach, Mazucheli, Coelho-Barros and Achcar (2016) introduced an alternative parameterization for the WL distribution in the context of orthogonal parameters (COX; REID, 1987), which we will call reparameterized WL (RWL) distribution throughout the thesis. Orthogonal parameters have many advantages in the inference results as, for example, for large sample sizes we have independence among the maximum likelihood of the orthogonal parameters, since the Fisher information matrix is diagonal.…”

“…Although Mazucheli, Coelho-Barros and Achcar (2016) have proposed the RWL distribution, the authors did not study its properties and, in addition, they also did not consider the ML estimation for the parameters under censored data. Our objective in this chapter is to derive and discuss many mathematical properties of this distribution, including its moments, mean and median deviations, quantile, characteristic, hazard, mean residual life, and Laplace transform functions.…”

“…Finally, the applicability of the RWL distribution is illustrated in two real data sets. Mazucheli, Coelho-Barros and Achcar (2016) proposed a new parameterization of the WL distribution, which allows diverse features of data modeling to be considered. The RWL distribution is obtained by transforming (λ , φ ) into (µ, φ ), where…”