On Estimation and Prediction for the Inverted Kumaraswamy Distribution Based on General Progressive Censored Samples

Mahmoud H. Abu-Moussa, Mostafa M. Mohie El-Din

Abstract


In this article, the problem of estimating unknown parameters of the inverted kumaraswamy (IKum) distribution is considered based on general progressive Type-II censored Data. The maximum likelihood (MLE) estimators of the parameters are obtained while the Bayesian estimates are obtained using the squared error loss(SEL) as symmetric loss function. Also we used asymmetric loss functions as the linear-exponential loss (LINEX), generalized entropy (GE) and Al-Bayyati loss function (AL-Bayyati). Lindely's approximation method is used to evaluate the Bayes estimates. We also derived an approximate confidence interval for the parameters of the inverted Kumaraswamy distribution. Two-sample Bayesian prediction intervals are constructed with an illustrative example. Finally, simulation study concerning different sample sizes and different censoring schemes were reported.

Keywords


Maximum likelihood and Bayesian estimation, General progressive Type-II censored Data, Inverted Kumaraswamy distribution, Asymptotic confidence intervals, Two-sample Bayesian prediction

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DOI: http://dx.doi.org/10.18187/pjsor.v14i3.2103

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Title

On Estimation and Prediction for the Inverted Kumaraswamy Distribution Based on General Progressive Censored Samples

Keywords

Maximum likelihood and Bayesian estimation, General progressive Type-II censored Data, Inverted Kumaraswamy distribution, Asymptotic confidence intervals, Two-sample Bayesian prediction

Description

In this article, the problem of estimating unknown parameters of the inverted kumaraswamy (IKum) distribution is considered based on general progressive Type-II censored Data. The maximum likelihood (MLE) estimators of the parameters are obtained while the Bayesian estimates are obtained using the squared error loss(SEL) as symmetric loss function. Also we used asymmetric loss functions as the linear-exponential loss (LINEX), generalized entropy (GE) and Al-Bayyati loss function (AL-Bayyati). Lindely's approximation method is used to evaluate the Bayes estimates. We also derived an approximate confidence interval for the parameters of the inverted Kumaraswamy distribution. Two-sample Bayesian prediction intervals are constructed with an illustrative example. Finally, simulation study concerning different sample sizes and different censoring schemes were reported.

Date

2018-09-22

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 14 No. 3, 2018



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810