535
Views
5
CrossRef citations to date
0
Altmetric
Research Article

Discrete Weibull distribution: different estimation methods under ranked set sampling and simple random sampling

ORCID Icon &
Pages 1740-1762 | Received 22 May 2021, Accepted 09 Nov 2021, Published online: 28 Nov 2021

References

  • Hinde J, Demétrio CG. Overdispersion: models and estimation. Comput Stat Data Anal. 1998;27(2):151–170.
  • Cameron AC, Trivedi PK. Regression analysis of count data. Vol. 53, New York: Cambridge University Press; 2013.
  • Rigby RA, Stasinopoulos MD, Heller GZ, et al. Distributions for modeling location, scale, and shape: using gamlss in r. Boca Raton, FL: CRC press; 2019.
  • Nakagawa T, Osaki S. The discrete Weibull distribution. IEEE Trans Reliab. 1975;24(5):300–301.
  • Chakraborty S, Chakravarty D. Discrete gamma distributions: properties and parameter estimations. Commun Stat-Theor Meth. 2012;41(18):3301–3324.
  • Krishna H, Pundir PS. Discrete burr and discrete pareto distributions. Stat Methodol. 2009;6(2):177–188.
  • Patriarca R, Hu T, Costantino F, et al. A system-approach for recoverable spare parts management using the discrete Weibull distribution. Sustainability. 2019;11(19):5180.
  • Peluso A, Vinciotti V, Yu K. Discrete Weibull generalized additive model: an application to count fertility data. J R Stat Soc: Ser C (Appl Stat). 2019;68(3):565–583.
  • Ali S, Zafar T, Shah I, et al. Cumulative conforming control chart assuming discrete Weibull distribution. IEEE Access. 2020;8:10123–10133.
  • Kundu D, Nekoukhou V. On bivariate discrete Weibull distribution. Commun Stat-Theor Meth. 2019;48(14):3464–3481.
  • Almalki SJ, Nadarajah S. Modifications of the Weibull distribution: A review. Reliab Eng Syst Saf. 2014;124:32–55.
  • Khan MA, Khalique A, Abouammoh A. On estimating parameters in a discrete Weibull distribution. IEEE Trans Reliab. 1989;38(3):348–350.
  • Barbiero A. A comparison of methods for estimating parameters of the type i discrete Weibull distribution. Stat Interface. 2016;9(2):203–212.
  • Barbiero A. Least-squares and minimum chi-square estimation in a discrete Weibull model. Commun Stat-Simul Comput. 2017;46(10):8028–8048.
  • Qian W, Chen W, He X. Parameter estimation for the pareto distribution based on ranked set sampling. Statistical Papers. 2019;62:395–417.
  • Taconeli CA, Bonat WH. On the performance of estimation methods under ranked set sampling. Comput Stat. 2020;35:1805–1826.
  • Pedroso VC, Taconeli CA, Giolo SR. Estimation based on ranked set sampling for the two-parameter birnbaum–saunders distribution. J Stat Comput Simul. 2021;91(2):316–333.
  • McIntyre G. A method for unbiased selective sampling, using ranked sets. Aust J Agric Res. 1952;3(4):385–390.
  • Takahasi K, Wakimoto K. On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann Inst Stat Math. 1968;20(1):1–31.
  • Dell T, Clutter J. Ranked set sampling theory with order statistics background. Biometrics. 1972;28:545–555.
  • Wolfe DA. Ranked set sampling: its relevance and impact on statistical inference. International scholarly research notices. 2012;2012.
  • Al-Omari AI, Bouza CN. Review of ranked set sampling: modifications and applications. Investigación Operacional. 2014;35(3):215–235.
  • Bouza-Herrera CN, Al-Omari AIF. Ranked set sampling: 65 years improving the accuracy in data gathering. Chennai, India: Academic Press; 2018.
  • Taconeli CA, Giolo SR. Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data. Comput Stat. 2020;35:1827–1851.
  • Arnold BC, Balakrishnan N, Nagaraja HN. A first course in order statistics. Philadelphia, PA: SIAM; 2008.
  • Zheng G, Al-Saleh MF. Modified maximum likelihood estimators based on ranked set samples. Ann Inst Stat Math. 2002;54(3):641–658.
  • Pearson K. X: on the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1900;50(302):157–175.
  • Cochran WG. The χ2 test of goodness of fit. Ann Math Stat. 1952;23:315–345.
  • Rolke W, Gongora CG. A chi-square goodness-of-fit test for continuous distributions against a known alternative. Comput Stat. 2020;36:1885–1900.
  • R Core Team. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2020. Available from: https://www.R-project.org/.
  • Barbiero A. DiscreteWeibull: Discrete Weibull distributions (type 1 and 3). 2015. R package version 1.1. Available from: https://CRAN.R-project.org/package=DiscreteWeibull.
  • Modarres R, Hui TP, Zheng G. Resampling methods for ranked set samples. Comput Stat Data Anal. 2006;51(2):1039–1050.
  • Croissant Y, Graves S. Ecdat: Data sets for econometrics. 2020. R package version 0.3-9; Available from: https://CRAN.R-project.org/package=Ecdat.
  • Rigby RA, Stasinopoulos DM. Generalized additive models for location, scale and shape, (with discussion). Appl Stat. 2005;54:507–554.
  • Hilbe JM. Count: Functions, data and code for count data. 2016. R package version 1.3.4. Available from: https://CRAN.R-project.org/package=COUNT.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.