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

Abdulhakim A. Al-Babtain, Mohammed K. Shakhatreh, Mazen Nassar and Ahmed Z. Afify
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Abdulhakim A. Al-Babtain: Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia
Mohammed K. Shakhatreh: Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan
Mazen Nassar: Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudia Arabia
Ahmed Z. Afify: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Mathematics, 2020, vol. 8, issue 8, 1-24

Abstract: 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.

Keywords: kies distribution; T-X family; order statistics; mean residual life; maximum likelihood estimation; type-II censoring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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