Search Advanced

AIMS Mathematics

2024, Volume 9, Issue 1: 481-494. doi: 10.3934/math.2024026
Previous Article Next Article
Research article

On the study of the recurrence relations and characterizations based on progressive first-failure censoring

  • 1.
    Department of Quantitative Analysis, College of Business Administration, King Saud University, P. O. Box 71115, Riyadh 11587, Saudi Arabia
  • 2.
    Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
  • 3.
    Department of Mathematics, Faculty of Science, Galala University, Galala, Suez 43511, Egypt
  • 4.
    Faculty of Engineering, Egyptian Russian University, Badr 11829, Egypt
  • Received: 22 August 2023 Revised: 18 November 2023 Accepted: 23 November 2023 Published: 30 November 2023

  • MSC : 62E10, 62N99

  • In this research, the progressive first-failure censored data (PFFC) from the Kumaraswamy modified inverse-Weibull distribution (KMIWD) were used to obtain the recurrence relations and characterizations for single and product moments. The recurrence relationships allow for a rapid and efficient assessment of the means, variances and covariances for any sample size. Additionally, the paper outcomes can be boiled down to the traditional progressive type-II censoring. Also, some special cases are limited to some lifetime distributions as the exponentiated modified inverse Weibull and Kumaraswamy inverse exponential.

    Citation: Najwan Alsadat, Mahmoud Abu-Moussa, Ali Sharawy. On the study of the recurrence relations and characterizations based on progressive first-failure censoring[J]. AIMS Mathematics, 2024, 9(1): 481-494. doi: 10.3934/math.2024026

    Related Papers:

  • In this research, the progressive first-failure censored data (PFFC) from the Kumaraswamy modified inverse-Weibull distribution (KMIWD) were used to obtain the recurrence relations and characterizations for single and product moments. The recurrence relationships allow for a rapid and efficient assessment of the means, variances and covariances for any sample size. Additionally, the paper outcomes can be boiled down to the traditional progressive type-II censoring. Also, some special cases are limited to some lifetime distributions as the exponentiated modified inverse Weibull and Kumaraswamy inverse exponential.


    加载中


    [1] N. Balakrishnan, R. Aggarwala, Progressive censoring: theory, methods, and applications, Springer Science & Business Media, 2000. http://doi.org/10.1007/978-1-4612-1334-5
    [2] N. Balakrishnan, Progressive censoring methodology: an appraisal, Test, 16 (2007), 211–259. http://doi.org/10.1007/s11749-007-0061-y doi: 10.1007/s11749-007-0061-y
    [3] U. Balasooriya, Failure-censored reliability sampling plans for the exponential distribution, J. Stat. Comput. Simul., 52 (1995), 337–349. https://doi.org/10.1080/00949659508811684 doi: 10.1080/00949659508811684
    [4] J. W. Wu, W. L. Hung, C. H. Tsai, Estimation of the parameters of the Gompertz distribution under the first failure-censored sampling plan, Statistics, 37 (2003), 517–525. https://doi.org/10.1080/02331880310001598864 doi: 10.1080/02331880310001598864
    [5] J. W. Wu, H. Y. Yu, Statistical inference about the shape parameter of the Burr type XII distribution under the failure-censored sampling plan, Appl. Math. Comput., 163 (2005), 443–482. https://doi.org/10.1016/j.amc.2004.02.019 doi: 10.1016/j.amc.2004.02.019
    [6] S. J. Wu, C. Kuş, On estimation based on progressive first-failure-censored sampling, Comput. Stat. Data Anal., 53 (2009), 3659–3670. https://doi.org/10.1016/j.csda.2009.03.010 doi: 10.1016/j.csda.2009.03.010
    [7] A. A. Soliman, A. H. A. Ellah, N. A. Abou-Elheggag, A. A. Modhesh, Estimation from Burr type XII distribution using progressive first-failure censored data, J. Stat. Comput. Simul., 83 (2013), 2270–2290. https://doi.org/10.1080/00949655.2012.690157 doi: 10.1080/00949655.2012.690157
    [8] M. Dube, R. Garg, H. Krishna, On progressively first failure censored Lindley distribution, Comput. Stat., 31 (2016), 139–163. https://doi.org/10.1007/s00180-015-0622-6 doi: 10.1007/s00180-015-0622-6
    [9] E. A. Ahmed, Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application, J. Appl. Stat., 44 (2017), 1576–1608. https://doi.org/10.1080/02664763.2016.1214692 doi: 10.1080/02664763.2016.1214692
    [10] T. Kayal, Y. M. Tripathi, L. Wang, Inference for the Chen distribution under progressive first-failure censoring, J. Stat. Theory Pract., 13 (2019), 52. https://doi.org/10.1007/s42519-019-0052-9 doi: 10.1007/s42519-019-0052-9
    [11] M. A. W. Mahmoud, M. G. M. Ghazal, H. M. M. Radwan, Bayesian estimation and optimal censoring of inverted generalized linear exponential distribution using progressive first failure censoring, Ann. Data Sci., 10 (2023), 527–554. https://doi.org/10.1007/s40745-020-00259-z doi: 10.1007/s40745-020-00259-z
    [12] M. S. Kotb, A. Sharawy, M. M. M. El-Din, E-Bayesian estimation for Kumaraswamy distribution using progressive first failure censoring, Math. Modell. Eng. Probl., 5 (2021), 689–702. https://doi.org/10.18280/mmep.080503
    [13] M. H. Abu-Moussa, N. Alsadat, A. Sharawy, On estimation of reliability functions for the extended Rayleigh distribution under progressive first-failure censoring model, Axioms, 12 (2023), 680. https://doi.org/10.3390/axioms12070680 doi: 10.3390/axioms12070680
    [14] R. Aggarwala, N. Balakrishnan, 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 (1996), 757–771. https://doi.org/10.1007/BF00052331 doi: 10.1007/BF00052331
    [15] M. M. El-Din, A. Sadek, M. M. M. El-Din, A. M. Sharawy, Characterization for Gompertz distribution based on general progressively type-II right censored orderstatistics, Int. J. Adv. Stat. Probab., 5 (2017), 52–56. https://doi.org/10.14419/ijasp.v5i1.7524 doi: 10.14419/ijasp.v5i1.7524
    [16] M. M. El-Din, A. Sadek, M. M. M. El-Din, A. M. Sharawy, Characterization of the generalized Pareto distribution by general progressively type-II right censored order statistics, J. Egypt. Math. Soc., 25 (2017), 369–374. http://doi.org/10.1016/j.joems.2017.05.002 doi: 10.1016/j.joems.2017.05.002
    [17] A. Sadek, M. M. M. El-Din, A. M. Sharawy, 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 (2018), 7–12. http://doi.org/10.18576/jsapl/050102 doi: 10.18576/jsapl/050102
    [18] M. M. M. El-Din, A. M. Sharawy, Characterization for generalized exponential distribution, Math. Sci. Lett., 10 (2021), 15–21. https://doi.org/10.18576/msl/100103 doi: 10.18576/msl/100103
    [19] H. M. Alshanbari, A. A. A. H. El-Bagoury, A. M. Gemeay, E. H. Hafez, A. S. Eldeeb, A flexible extension of pareto distribution: properties and applications, Comput. Intell. Neurosci., 2021 (2021), 9819200. https://doi.org/10.1155/2021/9819200 doi: 10.1155/2021/9819200
    [20] A. Z. Afify, A. M. Gemeay, N. M. Alfaer, G. M. Cordeiro, E. H. Hafez, Power-modified kies-exponential distribution: properties, classical and Bayesian inference with an application to engineering data, Entropy, 24 (2022), 883. https://doi.org/10.3390/e24070883
    [21] H. M. Alshanbari, A. M. Gemeay, A. A. A. H. El-Bagoury, S. K. Khosa, E. H. Hafez, A. H. Muse, A novel extension of Fréchet distribution: application on real data and simulation, Alex. Eng. J., 61 (2022), 7917–7938. https://doi.org/10.1016/j.aej.2022.01.013 doi: 10.1016/j.aej.2022.01.013
    [22] N. Alsadat, A. Ahmad, M. Jallal, A. M. Gemeay, M. A. Meraou, E. Hussam, et al., The novel Kumaraswamy power Frechet distribution with data analysis related to diverse scientific areas, Alex. Eng. J., 70 (2023), 651–664. https://doi.org/10.1016/j.aej.2023.03.003
    [23] G. Aryal, I. Elbatal, Kumaraswamy modified inverse Weibull distribution: theory and application, Appl. Math. Inf. Sci., 9 (2015), 651–660. http://doi.org/10.12785/amis/090213 doi: 10.12785/amis/090213
    [24] J. S. Hwang, G. D. Lin, Extensions of Muntz-Szasz theorem and applications, Analysis, 4 (1984). 143–160. https://doi.org/10.1524/anly.1984.4.12.143
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(547) PDF downloads(43) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(1)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog