On the Properties and Applications of Lomax-Exponential Distribution

Abstract

The Exponential distribution is memoryless and has a constant failure rate which makes it unsuitable for real life problems. This paper introduces a new distribution powered by an exponential random variable which gives a more flexible model for modelling real-life data. This new extension of the Exponential Distribution is called “Lomax-Exponential distribution (LED)”. The extension of the new distribution became possible with the help of a Lomax generator proposed by [1]. This paper derives and studies some expressions for various statistical properties of the new distribution including distribution function, moments, quantile function, survival function and hazard function known as reliability functions. The inference for the Lomax-Exponentially distributed random variable were investigated based on some plots of the distribution and others revealed its behaviour and usefulness in real life situations. The parameters of the distribution are estimated using the method of maximum likelihood estimation. The performance of the new Lomax-Exponential distribution has been tested and compared to the Weibull-Exponential, Transmuted Exponential and the conventional Exponential distribution using three real life data sets.