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The two-parameter Birnbaum–Saunders (BS) distribution was originally proposed as a failure time distribution
for fatigue failure caused under cyclic loading. BS model is a positively skewed statistical distribution which has
received great attention in recent decades. Several extensions of this distribution with various degrees of skewness,
kurtosis and modality are considered. In particular, a generalized version of this model was derived based on symmetrical
distributions in the real line named the generalized BS (GBS) distribution. In this article, we propose a
new family of life distributions, generated from elliptically contoured distributions, and the density and some of its
properties are obtained. Explicit expressions for the density of a number of specific elliptical distributions, such as
Pearson type VII, t, Cauchy, Kotz type, normal, Laplace and logistic are found. Another generalization of the BS
distribution is also presented using skew-elliptical distribution which makes its symmetry more flexible. Finally,
some examples are provided to illustrate application of the distribution.

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When the observations reflect a multimodal‎, ‎asymmetric or truncated construction or a combination of them‎, ‎using usual unimodal and symmetric distributions leads to misleading results‎. ‎Therefore‎, ‎distributions with ability of modeling skewness‎, ‎multimodality and truncation have been in the core of interest in statistical literature‎, ‎always‎. ‎There are different methods to contract a distribution with these abilities‎, ‎which using the weighted distribution is one of these methods‎. ‎In this paper‎, ‎it is shown that by using a weight function one can create such desired abilities in the corresponding weighted distribution.

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To make statistical inferences about regression model parameters, it is necessary to assume a specific distribution on the random error expression. A basic assumption in a linear regression model is that the random error expression follows a normal distribution. However, in some statistical researches, data simultaneously display skewness and bimodality features. In this setting, the normality assumption is  violated. A common approach to avoiding this problem is to use a mixture of skew-normal distributions. But such models involve many parameters, which it makes difficult to fit the models to the data. Moreover, these models are faced with the non-identifiability issue.
In this situation, a suitable solution is to use flexible distributions, which can take into account the skewness and bimodality observed in the data distribution. In this direction, various methods have been proposed based on developing of the skew-normal distribution in recent years. In this paper, these methods are used to introduce more flexible regression models than the regression models based on skew-normal distribution and a mixture of two skew-normal distributions. Their performance is compared using a simulation example. The methodology is then illustrated in a practical example related to a horses dataset.