A New Generalized Family of Distributions for Lifetime Data

A new class of continuous distributions called the generalized Burr X-G family is introduced. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi entropy are derived. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets

The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution