A family of weighted distributions based on the mean inactivity time and cumulative past entropies

In this paper, a family of mean past weighted (MPWα) distributions of order α is introduced. For the construction of this family, the concepts of the mean inactivity time and cumulative α-class past entropy are used. Distributional properties and stochastic comparisons with other known weighted distributions are given. Furthermore, an upper bound for the k-order moment of the random variables associated with the new family and a characterization result are obtained. Generalized discrete mixtures that involve MPWα distributions and other weighted distributions are also explored.