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A size-biased Ishita distribution and application to real data

Author

Listed:
  • Amer Ibrahim Al-Omari

    (Al al-Bayt University)

  • Amjad D. Al-Nasser

    (Yarmouk University)

  • Enrico Ciavolino

    (University of Salento)

Abstract

The present paper offers a new extension to the Ishita distribution called Size-Biased Ishia distribution (SBID). Various structural statistical properties of this distribution are derived such as the jth moment, moment generating function, the coefficients of variation, skewness and kurtosis. Also, the distribution of order statistics, harmonic mean, mode, reliability analysis, maximum likelihood estimation are provided, as well as the Fisher’s information, generalized and Renyi entropies are derived. The main advantage of using sized-based distributions appears when the sample are recorded with unequal probabilities. Accordingly, the superiority of the SBI distribution is illustrated to ball bearings data. It is shown that the SBID is the most appropriate model for this data set as compared to Rama distribution, Ishita distribution and Marshall–Olkin Esscher Transformed Laplace distribution. We believe that the SBID is an alternative distribution to lifetime data analysis.

Suggested Citation

  • Amer Ibrahim Al-Omari & Amjad D. Al-Nasser & Enrico Ciavolino, 2019. "A size-biased Ishita distribution and application to real data," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(1), pages 493-512, January.
    • Handle: RePEc:spr:qualqt:v:53:y:2019:i:1:d:10.1007_s11135-018-0765-y
    DOI: 10.1007/s11135-018-0765-y
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    References listed on IDEAS

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    1. Heggland, Knut & Lindqvist, Bo H., 2007. "A non-parametric monotone maximum likelihood estimator of time trend for repairable system data," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 575-584.
    2. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
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    1. Khaldoon Alhyasat & Ibrahim Kamarulzaman & Amer Ibrahim Al-Omari & Mohd Aftar Abu Bakar, 2020. "Power Size Biased Two-Parameter Akash Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 73-91, September.

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