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Abstract
We introduce a new three-parameter extension of the exponential distribution called the odd exponentiated half-logistic exponential distribution. Various of its properties including quantile and generating functions, ordinary and incomplete moments, mean residual life, mean inactivity time and some characterizations are investigated. The new density function can be expressed as a linear mixture of exponential densities. The hazard rate function of the new model can be decreasing, increasing or bathtub shaped. The maximum likelihood is used for estimating the model parameters. We prove empirically the flexibility of the new distribution using two real data sets.
Highlights
There are hundreds of generalized distributions which have several applications from biomedical sciences, environmental, engineering, financial, among other fields
The cumulative distribution function (CDF) and probability density function (PDF) of the odd exponentiated half-logisticG (OEHL-G) family are given by 1 − exp
The odd exponentiated half-logistic exponential (OEHLEx) density function can be expressed as a linear mixture of exponential densities
Summary
There are hundreds of generalized distributions which have several applications from biomedical sciences, environmental, engineering, financial, among other fields. These applications have indicated that many data sets following the classical distributions are more often the exception rather than the reality. Afify et al [1] proposed a wider class of distributions called the odd exponentiated half-logisticG (OEHL-G) family. We propose and study a new three-parameter model called the odd exponentiated half-logistic exponential (OEHLEx) distribution. Based on the OEHL-G family proposed by Afify et al [1], we construct the new OEHLEx model and give a comprehensive description of some of its mathematical properties.
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