A Reverse Exponential-Generalized Truncated Logarithmic (Rev-EGTL) Distribution For Ordered Spacing Statistics

This paper extends the exponential-generalized truncated logarithmic (EGTL) distribution to model reverse ordered statistics. Our procedure generalizes the exponential-logarithmic (EL) distribution to a distribution more appropriate for modelling the mth-largest value of lifetime instead of the maximum lifetime. We give a general form of the new family of spacing distribution appropriate for descending ordered statistics. General forms of the pdf and the failure rate function as well as their properties are presented for some special cases. The parameters’ estimation is attained by the maximum likelihood (ML) and the expectation maximization (EM) algorithms. The application study is illustrated based on four real data sets