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

In this paper, we discuss the existence and uniqueness of the maximum likelihood estimates (MLEs) of the parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples. We first derive the relationship between the MLEs of the two parameters and then discuss the monotonicity property of the profile likelihood function. Numerical iterative procedure is then discussed for determining the MLEs of the parameters. Finally, for illustrative purpose, we analyze one real data from the literature and present some graphical illustrations of the approach.