IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i1p1-11.html

Inferences on Weibull parameters with conventional type-I censoring

Author

Listed:
  • Joarder, Avijit
  • Krishna, Hare
  • Kundu, Debasis

Abstract

In this article we consider the statistical inferences of the unknown parameters of a Weibull distribution when the data are Type-I censored. It is well known that the maximum likelihood estimators do not always exist, and even when they exist, they do not have explicit expressions. We propose a simple fixed point type algorithm to compute the maximum likelihood estimators, when they exist. We also propose approximate maximum likelihood estimators of the unknown parameters, which have explicit forms. We construct the confidence intervals of the unknown parameters using asymptotic distribution and also by using the bootstrapping technique. Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters are also obtained under fairly general priors on the unknown parameters. The Bayes estimates cannot be obtained explicitly. We propose to use the Gibbs sampling technique to compute the Bayes estimates and also to construct the highest posterior density credible intervals. Different methods have been compared by Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.

Suggested Citation

  • Joarder, Avijit & Krishna, Hare & Kundu, Debasis, 2011. "Inferences on Weibull parameters with conventional type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 1-11, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:1-11
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00150-7
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tzong-Ru Tsai & Yuhlong Lio & Jyun-You Chiang & Yi-Jia Huang, 2022. "A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme," Mathematics, MDPI, vol. 10(21), pages 1-17, November.
    2. Tianyu Liu & Lulu Zhang & Guang Jin & Zhengqiang Pan, 2022. "Reliability Assessment of Heavily Censored Data Based on E-Bayesian Estimation," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
    3. Xiang Jia & Saralees Nadarajah & Bo Guo, 2020. "Inference on q-Weibull parameters," Statistical Papers, Springer, vol. 61(2), pages 575-593, April.
    4. Jia, Xiang & Wang, Dong & Jiang, Ping & Guo, Bo, 2016. "Inference on the reliability of Weibull distribution with multiply Type-I censored data," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 171-181.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Haitham M. Yousof & Hafida Goual & Walid Emam & Yusra Tashkandy & Morad Alizadeh & M. Masoom Ali & Mohamed Ibrahim, 2023. "An Alternative Model for Describing the Reliability Data: Applications, Assessment, and Goodness-of-Fit Validation Testing," Mathematics, MDPI, vol. 11(6), pages 1-26, March.
    2. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    3. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    4. Maha A Aldahlan & Farrukh Jamal & Christophe Chesneau & Ibrahim Elbatal & Mohammed Elgarhy, 2020. "Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-25, March.
    5. Roberts, Leigh A., 2015. "Distribution free testing of goodness of fit in a one dimensional parameter space," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 215-222.
    6. Haitham M. Yousof & Yusra Tashkandy & Walid Emam & M. Masoom Ali & Mohamed Ibrahim, 2023. "A New Reciprocal Weibull Extension for Modeling Extreme Values with Risk Analysis under Insurance Data," Mathematics, MDPI, vol. 11(4), pages 1-26, February.
    7. Aliyu Ismail Ishaq & Alfred Adewole Abiodun, 2020. "The Maxwell–Weibull Distribution in Modeling Lifetime Datasets," Annals of Data Science, Springer, vol. 7(4), pages 639-662, December.
    8. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-90, November.
    9. A. Shabani & M. Khaleghi Moghadam & A. Gholami & E. Moradi, 2018. "Exponentiated Power Lindley Logarithmic: Model, Properties and Applications," Annals of Data Science, Springer, vol. 5(4), pages 583-613, December.
    10. Sanku Dey & Vikas Kumar Sharma & Mhamed Mesfioui, 2017. "A New Extension of Weibull Distribution with Application to Lifetime Data," Annals of Data Science, Springer, vol. 4(1), pages 31-61, March.
    11. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    12. Ayman Alzaatreh & Mohammad A. Aljarrah & Michael Smithson & Saman Hanif Shahbaz & Muhammad Qaiser Shahbaz & Felix Famoye & Carl Lee, 2021. "Truncated Family of Distributions with Applications to Time and Cost to Start a Business," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 5-27, March.
    13. Mukhtar M. Salah & M. El-Morshedy & M. S. Eliwa & Haitham M. Yousof, 2020. "Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing," Mathematics, MDPI, vol. 8(11), pages 1-29, November.
    14. Morad Alizadeh & Ahmed Z. Afify & M. S. Eliwa & Sajid Ali, 2020. "The odd log-logistic Lindley-G family of distributions: properties, Bayesian and non-Bayesian estimation with applications," Computational Statistics, Springer, vol. 35(1), pages 281-308, March.
    15. Raid Al-Aqtash & Avishek Mallick & G.G. Hamedani & Mahmoud Aldeni, 2021. "On the Gumbel-Burr XII Distribution: Regression and Application," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(6), pages 1-31, December.
    16. Jukic, Dragan & Bensic, Mirta & Scitovski, Rudolf, 2008. "On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4502-4511, May.
    17. Ahmed Z. Afify & Haitham M. Yousof & Gauss M. Cordeiro & Edwin M. M. Ortega & Zohdy M. Nofal, 2016. "The Weibull Fréchet distribution and its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2608-2626, October.
    18. Rama Shanker, 2016. "Sujatha Distribution And Its Applications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 391-410, September.
    19. Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The [beta]-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1445-1461, March.
    20. Odom Conleth Chinazom & Nduka Ethelbert Chinaka & Ijomah Maxwell Azubuike, 2019. "The Marshall-Olkin Extended Weibull-Exponential Distribution: Properties and Applications," Journal of Asian Scientific Research, Asian Economic and Social Society, vol. 9(10), pages 158-172, October.

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:1-11. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.