A new weighted distribution based on the mixture of asymmetric Laplace family with application in survival analysis

The generalization of asymmetric Laplace (AL) distribution has recently received considerable attention in dealing with skewed and long-tailed data. In this article, we introduce a new family of distributions based on the location mixture of asymmetric Laplace (LM-AL) distribution. Some properties of this family, such as expressions for mean, variance, skewness and kurtosis coefficients and characteristic function, are derived. We show that this family of distributions is quite flexible because it has wider ranges of skewness and kurtosis than the other skew distributions introduced in the literature. We also introduce a family of weighted distributions based on the survival function of the exponential distribution and will show that truncated LM-AL distribution in zero which can be used in survival analysis, belongs to this family. In order to compute the maximum likelihood (ML) estimation of the parameters in the location mixture of AL distribution, an EM-type algorithm is developed and the estimation of parameters of model in survival analysis performed using a maximization algorithm, due to the problem complexity. Finally, the performance and applicability of the truncated LM-AL model in survival analysis is illustrated through analyzing a simulation study and two real data set. This family of distributions represent a suitable alternative to existing models such as Weibull, log-normal, log-logistic, gamma and Lindley distributions.