Lindley-Logarithmic Distribution: Model and Properties

In this paper we propose a new two-parameters distribution, which is an extension of the Lindley distribution with increasing and bathtub-shaped failure rate, called as the Lindley-logarithmic (LL) distribution. The new distribution is obtained by compounding Lindley (L) and Logarithmic distributions. We obtain several properties of the new distribution such as its probability density function, its failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented in this paper. At the end, in order to show the flexibility and potentiality of this new class, some series of real data is used to fit.