A New Parametric Lifetime Distribution with Modified  Chi-square Type Test for Right Censored Validation, Characterizations and Different Estimation Methods

Haitham M. Yousof; Khaoula Aidi; G.G. Hamedani; Mohamed Ibrahim

doi:10.18187/pjsor.v17i2.3631

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A New Parametric Lifetime Distribution with Modified Chi-square Type Test for Right Censored Validation, Characterizations and Different Estimation Methods

Author(s)

Haitham M. Yousof . Department of Statistics, Mathematics and Insurance, Benha University,Benha,Egypt

Khaoula Aidi Laboratory of probability and statistics LaPS, University Badji Mokhtar,Annaba,Algeria

G.G. Hamedani Department of Mathematical and Statistical Sciences, Marquette University,USA

Mohamed Ibrahim . Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University,Damietta,

Abstract

A new three-parameter extension of the generalized Nadarajah-Haghighi model is introduced and studied. Some of its statistical properties are derived. Characterization results are presented. The failure rate can be "increasing", "decreasing", "bathtub", "upside-down", "upside-down-constant", "increasing-constant" or "constant". Different non-Bayesian estimation methods under uncensored scheme are considered. Numerical simulations are performed for comparing the estimation methods using different sample sizes. The censored Barzilai-Borwein algorithm is employed via a simulation study. Using the approach of the Bagdonavicius-Nikulin chi-square goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. Based on the maximum likelihood estimators on initial data, the modified Bagdonavicius-Nikulin chi-square goodness-of-fit test recovers the loss in information. The modified Bagdonavicius-Nikulin test for validation under the right censored data is applied to four real and right censored data sets. The new model is compared with many other competitive models by means of a real data set.

Publication Details

Page(s) 399-425

DOI 10.18187/pjsor.v17i2.3631

Published Journal: Pakistan Journal of Statistics and Operation Research, Volume: 17, Issue: 2, Year: 2021

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Keywords

Simulation, Numerical analysis, Moments, Clayton Copula, Morgenstern Family, Characterizations, Censored Barzilai-Borwein., Nadarajah Haghighi Model, Non-Bayesian, Bagdonavicius-Nikulin test

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