Exponential Inverse Exponential (EIE) Distribution with Applications to Lifetime Data

Aims: This study aimed to obtain the shape parameter of an Exponential Inverted Exponential distribution using different prior distributions under different loss functions. Methodology: The Bayes’ theorem was adopted to obtain the posterior distribution of the shape parameter of an Exponential inverted Exponential distribution for both non-information prior (such as Jeffreys prior, Hartigen prior and Uniform prior) and an informative prior (such as Gamma distribution and chi-square distribution). Different loss functions (such as Entropy loss function, Square error loss function, Al-Bayyati’s loss function and Precautionary loss function) were employed to obtain the estimate parameter of the shape parameter with an assumption that the scale parameter is known. Results: The posterior distribution of the shape parameter of an Exponential Inverted Exponential distribution follows a Gamma distribution for all the prior distribution in the study. Also the Bayes estimate for the simulated datasets and real life dataset were obtained. Conclusion: The Bayes’ estimates for different prior distribution under different loss functions are close to the true parameter value of the shape parameter. The estimators are then compared in terms of their Mean Square Error (MSE) which is computed using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian Approach in Estimation of Shape Parameter of an Exponential Inverse Exponential Distribution

Sule¹,

Adegoke²

2020

“…This data represents the survival times of 121 patients with breast cancer obtained from a large hospital in a period from 1929-1938 from [45,46] and [47]. Its summary is given as follows: [48] and also used by [39].…”

Section: Data Set Imentioning

confidence: 99%

Properties and Applications of a Transmuted Power Gompertz Distribution

Eraikhuemen

Chama

Asongo

et al. 2020

This article introduces and studies a new probability distribution called “Transmuted Power Gompertz distribution”. It looks at the properties of the transmuted power Gompertz distribution. The article also estimates the four parameters of the new model using the method of maximum likelihood estimation. The article further evaluates the goodness-of-fit of the proposed distribution compared to other distributions by means of applications of the model to two real life datasets and the result show that the proposed distribution is more flexible than the fitted existing distributions.

“…Due to the abovementioned facts, [15] developed an exponential inverse exponential distribution (EIED) with two parameters (a shape and scale parameter). This distribution has been found to be skewed and flexible with an increasing hazard rate and different shapes and also performed better than the exponential distribution based on applications of the models to three lifetime datasets [15].…”

Section: Introductionmentioning

confidence: 99%

Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach

Eraikhuemen

Mohammed

Sule

2020

This paper aims at making Bayesian analysis on the shape parameter of the exponential inverse exponential distribution using informative and non-informative priors. Bayesian estimation was carried out through a Monte Carlo study under 10,000 replications. To assess the effects of the assumed prior distributions and loss function on the Bayesian estimators, the mean square error has been used as a criterion. Overall, simulation results indicate that Bayesian estimation under QLF outperforms the maximum likelihood estimation and Bayesian estimation under alternative loss functions irrespective of the nature of the prior and the sample size. Also, for large sample sizes, all methods perform equally well.