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

Author

Listed:
  • 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
    Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44511, Egypt)

  • Ahmed Z. Afify

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

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.

Suggested Citation

  • Abdulhakim A. Al-Babtain & Mohammed K. Shakhatreh & Mazen Nassar & Ahmed Z. Afify, 2020. "A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications," Mathematics, MDPI, vol. 8(8), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1345-:d:397943
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    References listed on IDEAS

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    1. Abbas Mahdavi & Debasis Kundu, 2017. "A new method for generating distributions with an application to exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6543-6557, July.
    2. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    3. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    4. C. Satheesh Kumar & S. H. S. Dharmaja, 2017. "The exponentiated reduced Kies distribution: Properties and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8778-8790, September.
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    Cited by:

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    2. Mazen Nassar & Farouq Mohammad A. Alam, 2022. "Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring," Mathematics, MDPI, vol. 10(5), pages 1-26, March.

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