on the relationships between cubic transmutations and the mixture of failure distributions of k-out-of-3 systems

In this study, at first a new polynomial rank transmutation is proposed. then, a new cubic rank transmutation is introduced by simplifying the set of transmutation parameters in order to improve its usefulness in statistical modeling. the probability density function, moment generating function, survival and hazard rate functions of cubic rank transmuted distribution are examined. moreover, existence of stochastic, hazard rate and likelihood ratio orderings are investigated with respect to the baseline distribution. the processes of estimating of the parameters with maximum likelihood and em algorithm are mentioned. the modeling performance of the distribution is showed by considering real data sets obtained from different areas.