The Beta-Weibull Logaritmic Distribution: Some Properties and Applications

In this paper, we introduce a new five-parameter distribution with increasing, decreasing, bathtub-shaped failure rate called the Beta-Weibull-Logarithmic (BWL) distribution. Using the Sterling Polynomials, various properties of the new distribution such as its probability density function, its reliability and failure rate functions, quantiles and moments, R$acute{e}$nyi and Shannon entropies, moments of order statistics, Bonferroni and Lorenz curves were derived. then the maximum likelihood estimation of BWL distribution for the parameters of BWL distribution are found. Finally the usefulness of this distribution for real data are presented.