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Entropy
Volume 22
Issue 5
10.3390/e22050592
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Article

A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods

by
Mahmoud Mansour
1,2,
Mahdi Rasekhi
3,
Mohamed Ibrahim
4,*,
Khaoula Aidi
5,
Haitham M. Yousof
2 and
Enayat Abd Elrazik
1,2
1
Management Information System Department, Yanbu, Taibah University, Yanbu 46421, Saudi Arabia
2
Department of Statistics, Mathematics and Insurance, Benha University, Benha 13513, Egypt
3
Department of Statistics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer 25569, Iran
4
Department of Applied Statistics and Insurance, Faculty of Commerce, Damietta University, Damietta 34519, Egypt
5
Laboratory of probability and statistics LaPS, University Badji Mokhtar, Annaba 23000, Algeria
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(5), 592; https://doi.org/10.3390/e22050592
Submission received: 9 May 2020 / Revised: 20 May 2020 / Accepted: 21 May 2020 / Published: 25 May 2020
(This article belongs to the Section Information Theory, Probability and Statistics)
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Abstract

In this paper, we first study a new two parameter lifetime distribution. This distribution includes “monotone” and “non-monotone” hazard rate functions which are useful in lifetime data analysis and reliability. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, δ-entropy, order statistics and probability weighted moments are derived. Non-Bayesian estimation methods such as the maximum likelihood, Cramer-Von-Mises, percentile estimation, and L-moments are used for estimating the model parameters. The importance and flexibility of the new distribution are illustrated by means of two applications to real data sets. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for the right censored validation, we then propose and apply a modified chi-square goodness-of-fit test for the Burr X Weibull model. The modified goodness-of-fit statistics test is applied for the right censored real data set. Based on the censored maximum likelihood estimators on initial data, the modified goodness-of-fit test recovers the loss in information while the grouped data follows the chi-square distribution. The elements of the modified criteria tests are derived. A real data application is for validation under the uncensored scheme.
Keywords: Bagdonavicius–Nikulin; Burr X Family; non-Bayesian methods; maximum likelihood estimation; Cramer-Von-Mises; moments; order statistics; L-moments; percentile estimation; Weibull model Bagdonavicius–Nikulin; Burr X Family; non-Bayesian methods; maximum likelihood estimation; Cramer-Von-Mises; moments; order statistics; L-moments; percentile estimation; Weibull model

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MDPI and ACS Style

Mansour, M.; Rasekhi, M.; Ibrahim, M.; Aidi, K.; Yousof, H.M.; Abd Elrazik, E. A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods. Entropy 2020, 22, 592. https://doi.org/10.3390/e22050592

AMA Style

Mansour M, Rasekhi M, Ibrahim M, Aidi K, Yousof HM, Abd Elrazik E. A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods. Entropy. 2020; 22(5):592. https://doi.org/10.3390/e22050592

Chicago/Turabian Style

Mansour, Mahmoud, Mahdi Rasekhi, Mohamed Ibrahim, Khaoula Aidi, Haitham M. Yousof, and Enayat Abd Elrazik. 2020. "A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods" Entropy 22, no. 5: 592. https://doi.org/10.3390/e22050592

APA Style

Mansour, M., Rasekhi, M., Ibrahim, M., Aidi, K., Yousof, H. M., & Abd Elrazik, E. (2020). A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods. Entropy, 22(5), 592. https://doi.org/10.3390/e22050592

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