The mean time to failure (MTTF) function in age replacement is used to evaluate the performance and effectiveness of the age replacement policy. In this paper, based on the MTTF function, we introduce two new nonparametric classes of lifetime distributions with nonmonotonic mean time to failure in age replacement; increasing then decreasing MTTF (IDMTTF) and decreasing then increasing MTTF (DIMTTF). The implications between these classes of distributions and some existing classes of nonmonotonic ageing classes are studied. The characterizations of IDMTTF and DIMTTF in terms of the scaled total time on test transform are also obtained.
In this paper, a new generalization of Alpha-Skew-Normal distribution is considered. Some properties of this distribution, which is denoted by GAS N(α, λ), including moments, maximum likelihood estimation of parameters and some other properties are studied. Finally, using a real data set, we show that our new distribution is the best fitted distribution for the used data among Normal, Skew Normal, Alpha-Skew-Normal and Skew-Bimodal-Normal distributions.
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