Abstract
This paper proposes a Lomax-inverse exponential distribution as an improvement on the inverse exponential distribution in the form of Lomax-inverse Exponential using the Lomax generator (Lomax-G family) with two extra parameters to generalize any continuous distribution (CDF). The probability density function (PDF) and cumulative distribution function (CDF) of the Lomax-inverse exponential distribution are defined. Some basic properties of the new distribution are derived and extensively studied. The unknown parameters estimation of the distribution is done by method of maximum likelihood estimation. Three real-life datasets are used to assess the performance of the proposed probability distribution in comparison with some other generalizations of Lomax distribution. It is observed that Lomax-inverse exponential distribution is more robust than the competing distributions, inverse exponential and Lomax distributions. This is an evident that the Lomax generator is a good probability model.
Highlights
There are several ways of improving a distribution function one of which is by adding one or more parameters to the distribution to make the resulting distribution richer and more flexible for modeling data
Hassan and Al-Ghandi ( 2009)studied the optimal times of changing Mathematical definition of the Lomax-inverse Exponential stress level for k-level step stress accelerated life tests based on Distribution adaptive type-II progressive hybrid censoring with product's lifetime We introduce the cumulative distribution function (CDF) and probability density function (PDF) of the Lomax-inverse exponential following Lomax distribution
Given some values for the parameters, 0, we provide some possible curves for the probability density function and the cumulative distribution function of the LOMINEXD as shown in Figure 1 and 2 below: FUDMA Journal of Sciences (FJS)
Summary
There are several ways of improving a distribution function one of which is by adding one or more parameters to the distribution to make the resulting distribution richer and more flexible for modeling data. According to Cordeiro et al;(2014), the Lomax-G family (Lomaxbased generator) cumulative density function (CDF) and the probability density function (PDF) for any continuous probability distribution are given respectively as: The inverse exponential distribution with parameter θ>0 has the cumulative distribution function (CDF) and probability density function (PDF) given by: G
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