Birnbaum–Saunders distribution based on Laplace kernel and some properties and inferential issues

On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples

“…As in the case of BS distribution, Zhu and Balakrishnan (2015) have shown that the following properties of LBS distribution.…”

“…Here, we study in detail the GBS distribution based on the Laplace kernel, denoted hereafter by LBS. Zhu and Balakrishnan (2015) discussed some properties of this distribution and showed that the MLEs of LBS distribution uniquely exist for complete samples. There is much research on the BS distribution based on censored samples.…”

A class of generalized Birnbaum‐Saunders distributions for reliability modeling

“…There are some potential extensions of the proposed generalized BS distributions. First, normal kernel can be replaced by some other kernels, for example, univariate elliptical family of distributions,15 epsilon‐skew‐symmetric family of distributions,6 Laplace kernel,9 and so on. The second extension is that the generalized IG distribution16 can be utilized other than IG distribution in the mixture representation.…”

“…Castillo et al6 defined the epsilon generalized‐BS distribution by assuming that X follows an epsilon skew‐symmetric distribution 7. Genc8 generalized the BS distribution using the generalized t distribution alternatively to the normal distribution, while Zhu and Balakrishnan9 utilized a Laplace kernel in place of normal kernel to generalize BS distribution. Other generalizations are mainly proposed by incorporating BS distribution into another CDF structure, see Refs.…”

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

“…For different inference‐related issues, one may refer to the works of Ahmed et al, Arellano‐Valle et al, Athayde et al, Audrey et al, Azevedo et al, Balakrishnan et al, Balakrishnan and Zhu, Barros et al, Chang and Tang, Cordeiro et al, Cysneiros et al, Desmond and Yang, Farias and Lemonte, Guo et al, Jeng, Lachos et al, Lemonte, Lemonte and Cordeiro, Lemonte et al, Lemonte and Ferrari, Lemonte and Patriota, Li et al, Li and Xu, Lillo et al, Lu and Chang, Meintanis, Moala et al, Niu et al, Padgett and Tomlinson, Pérez and Correa, Qu and Xie, Riquelme et al, Sánchez et al, Santana et al, Santos‐Neto et al, Saulo et al, Sha and Ng, Teimouri et al, Tsionas, Upadhyay and Mukherjee, Vanegas and Paula, Vanegas et al, Vilca et al, Wang, Wang and Fei, Wang et al, Xiao et al, Xie and Wei, Xu and Tang, Xu et al, Zhu and Balakrishnan, and the references cited therein.…”