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CHARACTERIZATION FOR ADDITIVE WEIBULL DISTRIBUTION BASED ON PROGRESSIVE FIRST FAILURE CENSORING

Year 2025, Volume: 15 Issue: 9, 2202 - 2215, 01.09.2025

Abstract

In this article, we establish recurrence relations (RR) for single and product moments based on progressive first failure censoring (PFFC). Characterizations for additive Weibull distribution (AWD) using the relation between the probability density function and distribution function and using the RR of single and product moments based on PFFC are also obtained. Further, the results are specialized to the progressively type-II right censored order statistics (PTIIRCOS).

Thanks

The authors would like to extend their gratitude to the referees and the associate editor for many valuable suggestions and comments that have helped to improve the paper significantly.

References

  • Abu-Moussa, M. H., Alsadat, N., and Sharawy, A. M., (2023), On Estimation of Reliability Functions for the Extended Rayleigh Distribution under Progressive First-Failure Censoring Model, Axioms, 12(7), pp. 680.
  • Aggarwala, R., and . Balakrishnan, N., (1996), Recurrence relations for single and product moments of progressive Type-II right censored order statistics from exponential and truncated exponential distributions, Ann. Inst. Stat. Math., 48 , pp. 757-771.
  • Alsadat, N., Abu-Moussa, M. H., and Sharawy, A. M., (2024), On the study of the recurrence relations and characterizations based on progressive first-failure censoring, AIMS Math., 9(1) , pp. 481-494.
  • Balakrishnan, N., Cramer, E., Kamps, U., and Schenk, N., (2001), Progressive type II censored order statistics from exponential distributions, Statistics: J. Theor. Appl. Stat., 35(4), pp. 537-556.
  • Davis, H. T., and Feldstein, M. L., (1979), The generalized Pareto law as a model for progressively censored survival data, Biometrika, 66(2), pp. 299-306.
  • Guilbaud, O., (2001), Exact non‐parametric confidence intervals for quantiles with progressive type‐II censoring, Scand. J. Stat, 28(4), pp. 699-713.
  • Hwang, J. S., and Lin, G. D., (1984), Extensions of Müntz-Szász theorem and applications, Analysis, 4(1-2), pp. 143-160.
  • El-Din, M. M., and Sharawy, A. M., (2021), Characterization for generalized exponential distribution, Math. Sci. Lett., 10(1), pp. 15-21.
  • El-Din, M. M., Sadek, A., El-Din, M. M. M., and Sharawy, A. M., (2017), Characterization for Gompertz distribution based on general progressively type-ii right censored orderstatistics, Int. J. Adv. Stat. Probab., 5(1), pp. 52-56.
  • El-Din, M. M., Sadek, A., El-Din, M. M. M., and Sharawy, A. M., (2017), Characterization of linear failure rate distribution by general progressively Type-II right censored order statistics, Am. J. Theor. Appl. Stat., 6, pp. 129-140.
  • El-Din, M. M. M., Sadek, A., and Sharawy, A. M., (2017), Characterization of the generalized Pareto distribution by general progressively Type-II right censored order statistics, J. Egypt. Math. Soc, 25(4), pp. 369-374.
  • Kotb, M. S., Sharawy, A., and El-Din, M. M. M., (2021), E-Bayesian Estimation for Kumaraswamy Distribution Using Progressive First Failure Censoring, Math. Model. Eng. Probl., 8(5), pp. 689-702.
  • Lemonte, A. J., Cordeiro, G. M., and Ortega, E. M., (2014), On the additive Weibull distribution, Commun. Stat. Theory Methods., 43(10-12), pp. 2066-2080.
  • Sadek, A., El-Din, M. M. M., and Sharawy, A. M., (2018), Characterization for generalized power function distribution using recurrence relations based on general progressively type-II right censored order statistics, J. Stat. Appl. Probab. Lett, 5, pp. 7-12.
  • Sharawy, A. M., (2024), Recurrence Relations for Moment Generating Function of Progressive First Failure Censoring and Characterizations of Right Truncated Exponential Distribution, ERU Research J., 3(1), pp. 781-790.
  • Xie, M., and Lai, C. D., (1996), Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function, Reliab. Eng. Syst. Saf., 52(1), pp. 87-93.

Year 2025, Volume: 15 Issue: 9, 2202 - 2215, 01.09.2025

Abstract

References

  • Abu-Moussa, M. H., Alsadat, N., and Sharawy, A. M., (2023), On Estimation of Reliability Functions for the Extended Rayleigh Distribution under Progressive First-Failure Censoring Model, Axioms, 12(7), pp. 680.
  • Aggarwala, R., and . Balakrishnan, N., (1996), Recurrence relations for single and product moments of progressive Type-II right censored order statistics from exponential and truncated exponential distributions, Ann. Inst. Stat. Math., 48 , pp. 757-771.
  • Alsadat, N., Abu-Moussa, M. H., and Sharawy, A. M., (2024), On the study of the recurrence relations and characterizations based on progressive first-failure censoring, AIMS Math., 9(1) , pp. 481-494.
  • Balakrishnan, N., Cramer, E., Kamps, U., and Schenk, N., (2001), Progressive type II censored order statistics from exponential distributions, Statistics: J. Theor. Appl. Stat., 35(4), pp. 537-556.
  • Davis, H. T., and Feldstein, M. L., (1979), The generalized Pareto law as a model for progressively censored survival data, Biometrika, 66(2), pp. 299-306.
  • Guilbaud, O., (2001), Exact non‐parametric confidence intervals for quantiles with progressive type‐II censoring, Scand. J. Stat, 28(4), pp. 699-713.
  • Hwang, J. S., and Lin, G. D., (1984), Extensions of Müntz-Szász theorem and applications, Analysis, 4(1-2), pp. 143-160.
  • El-Din, M. M., and Sharawy, A. M., (2021), Characterization for generalized exponential distribution, Math. Sci. Lett., 10(1), pp. 15-21.
  • El-Din, M. M., Sadek, A., El-Din, M. M. M., and Sharawy, A. M., (2017), Characterization for Gompertz distribution based on general progressively type-ii right censored orderstatistics, Int. J. Adv. Stat. Probab., 5(1), pp. 52-56.
  • El-Din, M. M., Sadek, A., El-Din, M. M. M., and Sharawy, A. M., (2017), Characterization of linear failure rate distribution by general progressively Type-II right censored order statistics, Am. J. Theor. Appl. Stat., 6, pp. 129-140.
  • El-Din, M. M. M., Sadek, A., and Sharawy, A. M., (2017), Characterization of the generalized Pareto distribution by general progressively Type-II right censored order statistics, J. Egypt. Math. Soc, 25(4), pp. 369-374.
  • Kotb, M. S., Sharawy, A., and El-Din, M. M. M., (2021), E-Bayesian Estimation for Kumaraswamy Distribution Using Progressive First Failure Censoring, Math. Model. Eng. Probl., 8(5), pp. 689-702.
  • Lemonte, A. J., Cordeiro, G. M., and Ortega, E. M., (2014), On the additive Weibull distribution, Commun. Stat. Theory Methods., 43(10-12), pp. 2066-2080.
  • Sadek, A., El-Din, M. M. M., and Sharawy, A. M., (2018), Characterization for generalized power function distribution using recurrence relations based on general progressively type-II right censored order statistics, J. Stat. Appl. Probab. Lett, 5, pp. 7-12.
  • Sharawy, A. M., (2024), Recurrence Relations for Moment Generating Function of Progressive First Failure Censoring and Characterizations of Right Truncated Exponential Distribution, ERU Research J., 3(1), pp. 781-790.
  • Xie, M., and Lai, C. D., (1996), Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function, Reliab. Eng. Syst. Saf., 52(1), pp. 87-93.
There are 16 citations in total.

Details

Primary Language English
Subjects Statistics (Other)
Journal Section Research Articles
Authors

Ali M. Sharawy This is me 0000-0001-7003-1839

Rashad M. El-sagheer 0000-0002-7828-3536

Publication Date September 1, 2025
Submission Date August 3, 2024
Acceptance Date October 15, 2024
Published in Issue Year 2025 Volume: 15 Issue: 9

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