Published

2021-07-12

Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling

Estimación bayesiana de la distribución de Rayleigh bivariada de tipo Morgenstern utilizando algunos tipos de muestreo por conjuntos clasificados

DOI:

https://doi.org/10.15446/rce.v44n2.87825

Keywords:

Bayesian estimation, Concomitant ranked set sampling, Extreme ranked set sampling, Maximum ranked set sampling and Rayleigh distribution (en)
Estimación bayesiana, muestreo conjunto concomitante clasificado, muestreo conjunto extremo clasificado, muestreo conjunto máximo clasificado y distribución de Rayleigh (es)

Downloads

Authors

  • Mehdi Basikhasteh Department of Statistics, Persian Gulf University, Bushehr 75169, Iran
  • Fazlollah Lak Department of Statistics, Persian Gulf University, Bushehr 75169, Iran
  • Saeid Tahmasebi Department of Statistics, Persian Gulf University, Bushehr 75169, Iran

In this paper we consider Bayesian estimation based on bivariate ranked set sample, in which units are ranked based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We obtain Bayes estimator for the scale parameter of the study variate Y, when (X, Y ) follows a Morgenstern type bivariate Rayleigh distribution. The Bayes estimators are considered based on bivari-ate ranked set sampling, extreme ranked set sampling and maximum ranked set sampling with unequal sample. The accuracy of estimation methods in this paper is illustrated using simulation study. Finally, a real data set is analyzed.

En este artículo consideramos la estimación bayesiana basada en una muestra de conjuntos clasificados bivariados, en la que las unidades se clasifican según las mediciones realizadas en una variable auxiliar X fácil y exactamente medible que se correlaciona con la variable de estudio Y. Obtuvimos el estimador de Bayes para el parámetro de escala de la variante de estudio Y, cuando (X, Y ) sigue una distribución de Rayleigh bivariada de tipo Morgenstern. Los estimadores de Bayes se consideran basados en un muestreo conjunto bivariado, un muestreo conjunto extremo clasificado y un muestreo conjunto máximo clasificado con muestra desigual. La precisión de los métodos de estimación en este documento se ilustra mediante el estudio de simulación. Finalmente, se analiza un conjunto de datos real.

References

Al-Saleh, M. F. & Al-Ananbeh, A. M. (2005), ‘Estimating the Correlation Coefficient in a Bivariate Normal Distribution Using Moving Extreme Ranked Set Sampling With a Concomitant Variable’, Journal of the Korean Statistical Society 34(2), 125–140.

Al-Saleh, M. F. & Al-Ananbeh, A. M. (2007), ‘Estimation of the Means of the Bivariate Normal Using Moving Extreme Ranked Set Sampling With Concomitant Variable’, Statistical Papers 48(2), 179–195. DOI: https://doi.org/10.1007/s00362-006-0325-8

Al-Saleh, M. F. & Diab, Y. A. (2009), ‘Estimation of the Parameters of Downton’s Bivariate Exponential Distribution Using Ranked Set Sampling Scheme’, Journal of Statistical Planning and Inference 139(2), 277–286. DOI: https://doi.org/10.1016/j.jspi.2008.04.021

Bairamov, I. & Bekci, M. (1999), ‘Concomitant of Order Statistics in FGM Type Bivariate Uniform Distributions’, Istatistik, Journal of the Turkish Statistical Association 2(2), 135–144.

Balasubramanian, K. & Beg, M. I. (1997), ‘Concomitants of Order Statistics in Morgenstern Type Bivariate Exponential Distribution’, Journal of Applied Statistical Science 54(4), 233–245.

Bernardo, JM., S. A. (1994), Bayesian Theory, Wiley, New York. DOI: https://doi.org/10.1002/9780470316870

Chacko, M. (2017), ‘Bayesian Estimation Based on Ranked Set Sample from Morgenstern Type Bivariate Exponential Distribution When Ranking is Imperfect’, Metrika 80, 333–349. DOI: https://doi.org/10.1007/s00184-016-0607-7

Chacko, M. & Thomas, P. Y. (2008), ‘Estimation of a Parameter of Morgenstern Type Bivariate Exponential Distribution by Ranked Set Sampling’, Annals of the Institute of Statistical Mathematics 60(2), 301–318. DOI: https://doi.org/10.1007/s10463-006-0088-y

Chacko, M. & Thomas, P. Y. (2011), ‘Estimation of Parameter of Morgenstern Type Bivariate Exponential Distribution Using Concomitants of Order Statistics’, Statistical Methodology 8(4), 363–376. DOI: https://doi.org/10.1016/j.stamet.2011.02.004

D’Este, G. (1981), ‘A Morgenstern-Type Bivariate Gamma Distribution’, Biometrika 68(1), 339–340. DOI: https://doi.org/10.1093/biomet/68.1.339

Eskandarzadeh, M., Di Crescenzo, A. & Tahmasebi, S. (2018), ‘Measures of Information for Maximum Ranked Set Sampling With Unequal Samples’, Communications in Statistics - Theory and Methods 49(19), 4692–4692. DOI: https://doi.org/10.1080/03610926.2018.1445857

Farlie, D. J. G. (1960), ‘The Performance of Some Correlation Coefficients for a General Bivariate Distribution’, Biometrika 47(3/4), 307–323. DOI: https://doi.org/10.1093/biomet/47.3-4.307

Gumbel, E. J. (1960a), ‘Bivariate Exponential Distributions’, Journal of the American Statistical Association 55(292), 698–707. DOI: https://doi.org/10.1080/01621459.1960.10483368

Gumbel, E. J. (1960b), ‘Bivariate Logistic Distributions’, Journal of the American Statistical Association 56(294), 335–349. DOI: https://doi.org/10.1080/01621459.1961.10482117

Lam, K., Sinha, B. K. & Wu, Z. (1994), ‘Estimation of Parameters in a TwoParameter Exponential Distribution Using Ranked Set Sample’, Annals of the Institute of Statistical Mathematics 46(4), 723–736. DOI: https://doi.org/10.1007/BF00773478

McIntyre, G. A. (1952), ‘A Method for Unbiased Selective Sampling Using Ranked Sets’, Australian Journal of Agricultural Research 3(4), 385–390. DOI: https://doi.org/10.1071/AR9520385

Morgenstern, D. (1956), ‘A Method for Unbiased Selective Sampling Using Ranked Sets’, Einfache beispiele zweidimensionaler verteilungen 8(1), 234–235.

Owen, O. E., Kavle, E., Owen, R. S., Polansky, M., Caprio, S., Mozzoli, M. A., Kendrick, Z. V., Bushman, M. & Boden, G. (1986), ‘A Reappraisal of Caloric Requirements in Healthy Women’, The American Journal of Clinical Nutrition 44(1), 1–19. DOI: https://doi.org/10.1093/ajcn/44.1.1

Samawi, H. M., Ahmed, M. S. & Abu-Dayyeh, W. (1996), ‘Estimating the Population Mean Using Extreme Ranked Set Sampling’, Biometrical Journal 38(5), 577–586. DOI: https://doi.org/10.1002/bimj.4710380506

Scaria, J. & Nair, N. U. (1999), ‘On Concomitants of Order Statistics from Morgenstern Family’, Biometrical Journal 41(4), 483–489. DOI: https://doi.org/10.1002/(SICI)1521-4036(199907)41:4<483::AID-BIMJ483>3.0.CO;2-2

Singh, H. P. & Mehta.V (2015), ‘Estimation of Scale Parameter of a Morgenstern Type Bivariate Uniform Distribution Using Censored Ranked Set Samples’, Model Assisted Statistics and Applications 10(2), 139–489. DOI: https://doi.org/10.3233/MAS-140315

Stokes, S. L. (1977), ‘Ranked Set Sampling With Concomitant Variables’, Communications in Statistics - Theory and Methods 6(12), 1207–1211. DOI: https://doi.org/10.1080/03610927708827563

Stokes, S. L. (1980), ‘Inferences on the Correlation Coefficient in Bivariate Normal Populations from Ranked Set Samples’, Journal of the American Statistical Association 75(372), 989–995. DOI: https://doi.org/10.1080/01621459.1980.10477584

Stokes, S. L. (1995), ‘Parametric Ranked Set Sampling’, Annals of the Institute of Statistical Mathematics 47(3), 465–482.

Tahmasebi, S., Eskandarzadeh, M. & Almaspoor, Z. (2017), ‘Inferences on a Scale Parameter of Bivariate Rayleigh Distribution by Ranked Set Sampling’, Pak.j.stat.oper.res. XIII(1), 1–16. DOI: https://doi.org/10.18187/pjsor.v13i1.1453

Tahmasebi, S. & Jafari, A. A. (2014), ‘Estimators for the Parameter Mean of Morgenstern Type Bivariate Generalized Exponential Distribution Using Ranked Set Sampling’, Statistics and Operations Research Transactions 38(2), 161–180.

Tahmasebi, S. & Jafari, A. A. (2015a), ‘A Review on Unbiased Estimators of a Parameter from Morgenstern Type Bivariate Gamma Distribution Using Ranked Set Sampling’, Azerbaijan Journal of Mathematics 5(2), 3–12.

Tahmasebi, S. & Jafari, A. A. (2015b), ‘Concomitants of Order Statistics and Record Values from Morgenstern Type Bivariate Generalized Exponential Distribution’, Bulletin of the Malaysian Mathematical Sciences Society 38(4), 1411–1423. DOI: https://doi.org/10.1007/s40840-014-0087-8

Tahmasebi, S. & Jafari, A. A. (2017), ‘Estimation of a Scale Parameter of Morgenstern Type Bivariate Uniform Distribution by Ranked Set Sampling’, Journal of Data Science 10, 129–141. DOI: https://doi.org/10.6339/JDS.201201_10(1).0009

Tahmasebi, S., Jafari, A. A. & Ahsanullah, M. (2017), ‘Reliability Characteristics of Bivariate Rayleigh Distribution and Concomitants of Its Order Statistics and Record Values’, Studia Scientiarum Mathematicarum Hungarica 54(2), 151–170. DOI: https://doi.org/10.1556/012.2017.54.2.1359

How to Cite

APA

Basikhasteh, M., Lak, F. & Tahmasebi, S. (2021). Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling. Revista Colombiana de Estadística, 44(2), 279–296. https://doi.org/10.15446/rce.v44n2.87825

ACM

[1]
Basikhasteh, M., Lak, F. and Tahmasebi, S. 2021. Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling. Revista Colombiana de Estadística. 44, 2 (Jul. 2021), 279–296. DOI:https://doi.org/10.15446/rce.v44n2.87825.

ACS

(1)
Basikhasteh, M.; Lak, F.; Tahmasebi, S. Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling. Rev. colomb. estad. 2021, 44, 279-296.

ABNT

BASIKHASTEH, M.; LAK, F.; TAHMASEBI, S. Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling. Revista Colombiana de Estadística, [S. l.], v. 44, n. 2, p. 279–296, 2021. DOI: 10.15446/rce.v44n2.87825. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/87825. Acesso em: 11 nov. 2025.

Chicago

Basikhasteh, Mehdi, Fazlollah Lak, and Saeid Tahmasebi. 2021. “Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling”. Revista Colombiana De Estadística 44 (2):279-96. https://doi.org/10.15446/rce.v44n2.87825.

Harvard

Basikhasteh, M., Lak, F. and Tahmasebi, S. (2021) “Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling”, Revista Colombiana de Estadística, 44(2), pp. 279–296. doi: 10.15446/rce.v44n2.87825.

IEEE

[1]
M. Basikhasteh, F. Lak, and S. Tahmasebi, “Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling”, Rev. colomb. estad., vol. 44, no. 2, pp. 279–296, Jul. 2021.

MLA

Basikhasteh, M., F. Lak, and S. Tahmasebi. “Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling”. Revista Colombiana de Estadística, vol. 44, no. 2, July 2021, pp. 279-96, doi:10.15446/rce.v44n2.87825.

Turabian

Basikhasteh, Mehdi, Fazlollah Lak, and Saeid Tahmasebi. “Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling”. Revista Colombiana de Estadística 44, no. 2 (July 12, 2021): 279–296. Accessed November 11, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/87825.

Vancouver

1.
Basikhasteh M, Lak F, Tahmasebi S. Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling. Rev. colomb. estad. [Internet]. 2021 Jul. 12 [cited 2025 Nov. 11];44(2):279-96. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/87825

Download Citation

CrossRef Cited-by

CrossRef citations3

1. Dmytro Perepolkin, Erik Lindström, Ullrika Sahlin. (2025). Quantile-Parameterized Distributions for Expert Knowledge Elicitation. Decision Analysis, 22(3), p.169. https://doi.org/10.1287/deca.2024.0219.

2. Manoj Chacko, Varghese George. (2024). Extropy properties of ranked set sample when ranking is not perfect. Communications in Statistics - Theory and Methods, 53(9), p.3187. https://doi.org/10.1080/03610926.2022.2150825.

3. Rohan D. Koshti, Kirtee K. Kamalja. (2024). A review on concomitants of order statistics and its application in parameter estimation under ranked set sampling. Journal of the Korean Statistical Society, 53(1), p.65. https://doi.org/10.1007/s42952-023-00235-2.

Dimensions

PlumX

Article abstract page views

302

Downloads

Download data is not yet available.

License

Copyright (c) 2021 Revista Colombiana de Estadística

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).