Abstract
In this paper, we propose a bimodal extension of the Birnbaum–Saunders model by including an extra parameter. This new model is termed flexible Birnbaum–Saunders (FBS) and includes the ordinary Birnbaum–Saunders (BS) and the skew Birnbaum–Saunders (SBS) model as special cases. Its properties are studied. Parameter estimation is considered via an iterative maximum likelihood approach. Two real applications, of interest in environmental sciences, are included, which reveal that our proposal can perform better than other competing models.
Highlights
The BS distribution was originally introduced in [1] to model the fatigue in the lifetime of certain materials
We focus on those situations in which extra asymmetry or bimodality are present in our data, and a generalization of the BS model should be considered to deal with these issues
Other recent proposals in the contemporary literature dealing with bimodality are the extended two-pieces skew-normal model (ETN), introduced in [7] and the uni-bi-modal asymmetric power normal model given in [8] whose properties are based on results given in [9,10]
Summary
The BS distribution was originally introduced in [1] to model the fatigue in the lifetime of certain materials. Mainly due to its good properties, the use of this model spread out to other fields, such as economics and environmental sciences In these applied scenarios, quite often, departures of the BS model are found, and it is necessary to introduce some improvements. We focus on those situations in which extra asymmetry or bimodality are present in our data, and a generalization of the BS model should be considered to deal with these issues. To reach this end, a flexible BS model is introduced. These are asymmetry, bimodality and main features of the basic BS model
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