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Article

A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications

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Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia
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Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan
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Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudia Arabia
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Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44511, Egypt
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Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
*
Author to whom correspondence should be addressed.
Received: 27 July 2020 / Revised: 7 August 2020 / Accepted: 9 August 2020 / Published: 12 August 2020
(This article belongs to the Special Issue Probability, Statistics and Their Applications)
In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of the hazard rate and the mean residual life functions of the modified Kies exponential distribution are discussed. We use the method of maximum likelihood to estimate the distribution parameters based on complete and type-II censored samples. The approximate confidence intervals are also obtained under the two schemes. A simulation study is conducted and two real data sets from the engineering field are analyzed to show the flexibility of the new distribution in modeling real life data. View Full-Text
Keywords: kies distribution; T-X family; order statistics; mean residual life; maximum likelihood estimation; type-II censoring kies distribution; T-X family; order statistics; mean residual life; maximum likelihood estimation; type-II censoring
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MDPI and ACS Style

Al-Babtain, A.A.; Shakhatreh, M.K.; Nassar, M.; Afify, A.Z. A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications. Mathematics 2020, 8, 1345. https://0-doi-org.brum.beds.ac.uk/10.3390/math8081345

AMA Style

Al-Babtain AA, Shakhatreh MK, Nassar M, Afify AZ. A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications. Mathematics. 2020; 8(8):1345. https://0-doi-org.brum.beds.ac.uk/10.3390/math8081345

Chicago/Turabian Style

Al-Babtain, Abdulhakim A., Mohammed K. Shakhatreh, Mazen Nassar, and Ahmed Z. Afify. 2020. "A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications" Mathematics 8, no. 8: 1345. https://0-doi-org.brum.beds.ac.uk/10.3390/math8081345

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