Abstract
The inverse exponential distribution is widely used in the field of reliability. In this article, we present a generalization of the inverse exponential distribution in formation of Topp-Leone odd log-logistic inverse exponential distribution. We provide a comprehensive account of some mathematical properties of the Topp-Leone odd log-logistic inverse exponential distribution. The possible shapes of the corresponding probability density function and hazard function are obtained and graphical demonstration are presented. The distribution is found to be unimodal. The results for moment, moment-generating function, and probability-generating function are computed. The residual and reversed residual functions are also obtained. The proposed method of maximum likelihood is used for the estimation of model parameters. The performance of the parameters is investigated through simulation. The usefulness of the proposed model is illustrated by means of a real data set.
Highlights
Keller and Kamath [1] introduced the inverse exponential (IEx) distribution to study the reliability of computer control (CNC) machine tools
We introduce a generalization of the IEx distribution named as the Topp-Leone odd log-logistic inverse exponential (TLOLLIEx) distribution
The corresponding density of the TLOLL-IEx distribution is obtained by differentiating Eq (2.1) and given as f(x)
Summary
Keller and Kamath [1] introduced the inverse exponential (IEx) distribution to study the reliability of computer control (CNC) machine tools. Lin et al [2] discussed the IEx distribution in term of different causes of failure for the machines They obtained the maximum likelihood estimator and confidence limits for the parameter and the reliability function using complete samples. They compared this model with the inverted Gaussian and log-normal distributions based on a maintenance data set. We introduce a generalization of the IEx distribution named as the Topp-Leone odd log-logistic inverse exponential (TLOLLIEx) distribution. The motivation of this generalization of IEx distribution is to enhance its applicability and adaptability.
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