A three-parameter continuous distribution is constructed, using a power transformation related to the transmuted inverse Rayleigh (TIR) distribution. A comprehensive account of the statistical properties is provided, including the following: the quantile function, moments, incomplete moments,...

In this paper the analysis of the collective risk model assuming Erlang loss, when the claim frequency follows the discrete generalized Lindley distribu- tion, is considered. After providing some new results of this discrete model, analytical expressions for the aggregate claim size distribution...

The study describes the general concept of the XLindley distribution. Forms of density and hazard rate functions are investigated. Moreover, precise formulations for several numerical properties of distributions are derived. Extreme order statistics are established using stochastic ordering, the...

In recent years, modifications of the classical Lindley distribution have been considered by many authors. In this paper, we introduce a new generalization of the Lindley distribution based on a mixture of exponential and gamma distributions with different mixing proportions and compare its...

In this paper, a new three-parameter lifetime model, called the odd log-logistic generalised Lindley distribution, is introduced. Some structural properties of the new distribution including ordinary and incomplete moments, quantile and generating functions and order statistics are obtained. The...

In this paper, we develop an autoregressive process of order one, assuming that the innovation random variable has a Lindley distribution. The key properties of the process are investigated. Five distinct estimation techniques are used to estimate the parameters and simulation studies are...