Bayesian Approximation Techniques of Inverse Exponential Distribution with Applications in Engineering

In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model.

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Empirical Bayes Test for Parameter of Inverse Exponential Distribution

Science Journal of Applied Mathematics and Statistics ◽

10.11648/j.sjams.20160405.17 ◽

2016 ◽

Vol 4 (5) ◽

pp. 236

Author(s):

Guobing Fan

Keyword(s):

Exponential Distribution ◽

Empirical Bayes ◽

Inverse Exponential Distribution ◽

Bayes Test

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An Exponentiated Odd Lindley Inverse Exponential Distribution and its Application to Infant Mortality and HIV Transmission Rates in Nigeria

International STD Research & Reviews ◽

10.9734/isrr/2021/v10i130120 ◽

2021 ◽

pp. 12-30

Author(s):

Innocent Boyle Eraikhuemen ◽

Gerald Ikechukwu Onwuka ◽

Bassa Shiwaye Yakura ◽

Hassan Allahde

Keyword(s):

Infant Mortality ◽

Exponential Distribution ◽

Hiv Transmission ◽

Transmission Rate ◽

Probability Distributions ◽

Real Life ◽

Information Criteria ◽

Infant Mortality Rate ◽

Unknown Parameters ◽

Inverse Exponential Distribution

Recently, researchers have shown much interest in developing new continuous probability distributions by adding one or two parameter(s) to the some existing baseline distributions. This act has been beneficial to the field of statistical theory especially in modeling of real life situations. Also, the exponentiated family as used in developing new distributions is an efficient method proposed and studied for defining more flexible continuous probability distributions for modeling real life data. In this study, the method of exponentiation has been used to develop a new distribution called “Exponentiated odd Lindley inverse exponential distribution”. Some properties of the proposed distribution and estimation of its unknown parameters has been done using the method of maximum likelihood estimation and its application to real life datasets. The new model has been applied to infant mortality rate and mother-to-child HIV transmission rate. The results of these two applications reveal that the proposed model is a better model compared to the other fitted existing models by some selection information criteria.

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On the Extended Generalized Inverse Exponential Distribution with Its Applications

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2020/v7i330184 ◽

2020 ◽

pp. 14-27

Author(s):

Sule Ibrahim ◽

Bello Olalekan Akanji ◽

Lawal Hammed Olanrewaju

Keyword(s):

Exponential Distribution ◽

Hazard Rate ◽

Generalized Inverse ◽

Real Data ◽

Quantile Function ◽

Exponential Model ◽

Data Sets ◽

Proposed Model ◽

Method Of Maximum Likelihood ◽

Inverse Exponential Distribution

We propose a new distribution called the extended generalized inverse exponential distribution with four positive parameters, which extends the generalized inverse exponential distribution. We derive some mathematical properties of the proposed model including explicit expressions for the quantile function, moments, generating function, survival, hazard rate, reversed hazard rate and odd functions. The method of maximum likelihood is used to estimate the parameters of the distribution. We illustrate its potentiality with applications to two real data sets which show that the extended generalized inverse exponential model provides a better fit than other models considered.

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