The exponential distribution is perhaps the most commonly used statistical distribution in reliability and the Lomax distribution is extensively studied with reference to order statistics. In this paper, we introduce a new statistical distribution constructed by combining the cumulative density function (cdf) of these two distributions and name it as the Lomax-exponential distribution. We derive expressions for its characteristic function, moments, hazard rate function, reliability, Rényi entropy and Shannon entropy. We plot some graphs for its probability density function (pdf) using the software ‘Mathematica’. We investigate the variation of the hazard rate function, variance, skewness and kurtosis and also discuss estimation by the method of maximum-likelihood. We also study the generalized order statistics from Lomax-exponential distribution.

Lomax-exponential distribution, moments, characteristic function, hazard rate function, entropy, reliability function, generalized order statistics.