Araştırma Makalesi
BibTex RIS Kaynak Göster

Estimation of Parameters of Morgenstern type Bivariate Lindley Distribution by Ranked Set Sampling

Yıl 2019, Cilt: 12 Sayı: 1, 25 - 34, 31.07.2019

Öz

In this work, we have discussed the problem of estimation of the
parameters of Morgenstern type bivariate Lindley distribution (MTBLDD) us-
ing ranked set sampling. We have proposed two estimators, namely an unbiased
estimator based on the Stoke's ranked set sample and the best linear unbiased
estimator (BLUE) based on the Stoke's ranked set sample. The efficiencies of
the BLUE with respect to the unbiased estimator are also evaluated in this work.

Kaynakça

  • [1] Barnett, V. and Moore, K. (1997): Best linear unbiased estimates in rankedset sampling with particular reference to imperfect ordering. Journal of Ap-plied Statistics, 24: 697-710.
  • [2] Chen, Z., Bai, Z. and Sinha, B. K. (2004): Lecture Notes in Statistics,Ranked Set Sampling: Theory and Applications, Springer, New York.
  • [3] Everitt, B.S. and Hande, D.J. (1981): Finite mixture distribution. Chapmanand Hall, London.
  • [4] Ghitany, M. E., Atieh, B. and Nadarajah, S. (2008): Lindley distributionand its applications. Mathematics and Computers in Simulation, 78(4): 493506.
  • [5] Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N. and Al-Enezi, L. J.(2013): Power Lindley distribution and associated inference. ComputationalStatistics and Data Analysis, 64: 20-33.
  • [6] Gomez, D. E. and Ojeda, E. C. (2011): The discrete Lindley distribution:Properties and applications. Journal of Statistical Computation and Simula-tion, 81(11): 1405-1416.
  • [7] Irshad, M. R. and Maya, R. (2017): Extended Version of Generalized LindleyDistribution. South African Statistical Journal, 51(1): 19-44.
  • [8] Lam, K., Sinha, B. K. and Wu, Z. (1994): Estimation of parameters in atwo-parameter exponential distribution using ranked set sample. Annals ofthe Institute of Statistical Mathematics, 46: 723-736.
  • [9] Lindley, D. V. (1958): Fiducial distributions and Bayes' theorem. Journalof the Royal Statistical Society, Series B, 20(1): 102107.
  • [10] Maya, R. and Irshad, M. R. (2017): Generalized Stacy-Lindley Mixturedistribution. Afrika Statistika, 12(3): 1447-1465.
  • [11] McIntyre, G. A. (1952): A method for unbiased selective sampling usingranked sets. Australian Journal of Agricultural Research, 3: 385-390.
  • [12] McLachlan, G. and Peel, D. (2000): Finite mixture models. Wiley, NewYork.
  • [13] Monsef, M. M. E. A. (2015). A new Lindley distribution with location pa-rameter. Communications in Statistics-Theory and Methods, 45(17): 5204-5219.
  • [14] Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen.Mittelingsblatt fur Mathematische Statistik, 8: 234-235.
  • [15] Nadarajah, S., Bakouch, H. and Tahmasbi, R. (2011): A generalized lindleydistribution. Sankhya B - Applied and Interdisciplinary Statistics, 73: 331-359.
  • [16] Nedjar, S. and Zehdoudi, H. (2016): On gamma Lindley distribution: Prop-erties and simulations. Journal of Computational and Applied Mathematics,298: 167-174.
  • [17] Scaria, J. and Nair, N. U. (1999): On concomitants of order statistics fromMorgenstern family. Biometrical Journal, 41: 483-489.
  • [18] Shibu, D. S. and Irshad, M. R. (2016): Extended New Generalized LindleyDistribution. Statistica, 42-56.
  • [19] Stokes, S. L. (1977): Ranked set sampling with concomitant variables.Communications in Statistics-Theory and Methods, 6: 1207-1211.
  • [20] Stokes, S. L. (1995): Parametric ranked set sampling. Annals of instituteof Statistical methods, 47: 465-482.
  • [21] Titterington, D.M. Smith, A.F.M. and Markov, U.E. (1985): Statisticalanalysis of nite mixture distributions. Wiley, NewYork.
  • [22] Vaidhyanathan, V. S and Varghese, A. S. (2016): Morgenstern type bivari-ate lindley Distribution. Statistics, Optimization and information Computing,4: 132-146.
  • [23] Zakerzadeh, H. and Dolati, A. (2009): Generalized Lindley distribution.Journal of Mathematical Extension, 3(2): 13-25.
Yıl 2019, Cilt: 12 Sayı: 1, 25 - 34, 31.07.2019

Öz

Kaynakça

  • [1] Barnett, V. and Moore, K. (1997): Best linear unbiased estimates in rankedset sampling with particular reference to imperfect ordering. Journal of Ap-plied Statistics, 24: 697-710.
  • [2] Chen, Z., Bai, Z. and Sinha, B. K. (2004): Lecture Notes in Statistics,Ranked Set Sampling: Theory and Applications, Springer, New York.
  • [3] Everitt, B.S. and Hande, D.J. (1981): Finite mixture distribution. Chapmanand Hall, London.
  • [4] Ghitany, M. E., Atieh, B. and Nadarajah, S. (2008): Lindley distributionand its applications. Mathematics and Computers in Simulation, 78(4): 493506.
  • [5] Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N. and Al-Enezi, L. J.(2013): Power Lindley distribution and associated inference. ComputationalStatistics and Data Analysis, 64: 20-33.
  • [6] Gomez, D. E. and Ojeda, E. C. (2011): The discrete Lindley distribution:Properties and applications. Journal of Statistical Computation and Simula-tion, 81(11): 1405-1416.
  • [7] Irshad, M. R. and Maya, R. (2017): Extended Version of Generalized LindleyDistribution. South African Statistical Journal, 51(1): 19-44.
  • [8] Lam, K., Sinha, B. K. and Wu, Z. (1994): Estimation of parameters in atwo-parameter exponential distribution using ranked set sample. Annals ofthe Institute of Statistical Mathematics, 46: 723-736.
  • [9] Lindley, D. V. (1958): Fiducial distributions and Bayes' theorem. Journalof the Royal Statistical Society, Series B, 20(1): 102107.
  • [10] Maya, R. and Irshad, M. R. (2017): Generalized Stacy-Lindley Mixturedistribution. Afrika Statistika, 12(3): 1447-1465.
  • [11] McIntyre, G. A. (1952): A method for unbiased selective sampling usingranked sets. Australian Journal of Agricultural Research, 3: 385-390.
  • [12] McLachlan, G. and Peel, D. (2000): Finite mixture models. Wiley, NewYork.
  • [13] Monsef, M. M. E. A. (2015). A new Lindley distribution with location pa-rameter. Communications in Statistics-Theory and Methods, 45(17): 5204-5219.
  • [14] Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen.Mittelingsblatt fur Mathematische Statistik, 8: 234-235.
  • [15] Nadarajah, S., Bakouch, H. and Tahmasbi, R. (2011): A generalized lindleydistribution. Sankhya B - Applied and Interdisciplinary Statistics, 73: 331-359.
  • [16] Nedjar, S. and Zehdoudi, H. (2016): On gamma Lindley distribution: Prop-erties and simulations. Journal of Computational and Applied Mathematics,298: 167-174.
  • [17] Scaria, J. and Nair, N. U. (1999): On concomitants of order statistics fromMorgenstern family. Biometrical Journal, 41: 483-489.
  • [18] Shibu, D. S. and Irshad, M. R. (2016): Extended New Generalized LindleyDistribution. Statistica, 42-56.
  • [19] Stokes, S. L. (1977): Ranked set sampling with concomitant variables.Communications in Statistics-Theory and Methods, 6: 1207-1211.
  • [20] Stokes, S. L. (1995): Parametric ranked set sampling. Annals of instituteof Statistical methods, 47: 465-482.
  • [21] Titterington, D.M. Smith, A.F.M. and Markov, U.E. (1985): Statisticalanalysis of nite mixture distributions. Wiley, NewYork.
  • [22] Vaidhyanathan, V. S and Varghese, A. S. (2016): Morgenstern type bivari-ate lindley Distribution. Statistics, Optimization and information Computing,4: 132-146.
  • [23] Zakerzadeh, H. and Dolati, A. (2009): Generalized Lindley distribution.Journal of Mathematical Extension, 3(2): 13-25.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

İrshad M R

Maya R Bu kişi benim

Shibu D.s Bu kişi benim

Yayımlanma Tarihi 31 Temmuz 2019
Kabul Tarihi 28 Kasım 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 1

Kaynak Göster

APA M R, İ., R, M., & D.s, S. (2019). Estimation of Parameters of Morgenstern type Bivariate Lindley Distribution by Ranked Set Sampling. Istatistik Journal of The Turkish Statistical Association, 12(1), 25-34.
AMA M R İ, R M, D.s S. Estimation of Parameters of Morgenstern type Bivariate Lindley Distribution by Ranked Set Sampling. IJTSA. Temmuz 2019;12(1):25-34.
Chicago M R, İrshad, Maya R, ve Shibu D.s. “Estimation of Parameters of Morgenstern Type Bivariate Lindley Distribution by Ranked Set Sampling”. Istatistik Journal of The Turkish Statistical Association 12, sy. 1 (Temmuz 2019): 25-34.
EndNote M R İ, R M, D.s S (01 Temmuz 2019) Estimation of Parameters of Morgenstern type Bivariate Lindley Distribution by Ranked Set Sampling. Istatistik Journal of The Turkish Statistical Association 12 1 25–34.
IEEE İ. M R, M. R, ve S. D.s, “Estimation of Parameters of Morgenstern type Bivariate Lindley Distribution by Ranked Set Sampling”, IJTSA, c. 12, sy. 1, ss. 25–34, 2019.
ISNAD M R, İrshad vd. “Estimation of Parameters of Morgenstern Type Bivariate Lindley Distribution by Ranked Set Sampling”. Istatistik Journal of The Turkish Statistical Association 12/1 (Temmuz 2019), 25-34.
JAMA M R İ, R M, D.s S. Estimation of Parameters of Morgenstern type Bivariate Lindley Distribution by Ranked Set Sampling. IJTSA. 2019;12:25–34.
MLA M R, İrshad vd. “Estimation of Parameters of Morgenstern Type Bivariate Lindley Distribution by Ranked Set Sampling”. Istatistik Journal of The Turkish Statistical Association, c. 12, sy. 1, 2019, ss. 25-34.
Vancouver M R İ, R M, D.s S. Estimation of Parameters of Morgenstern type Bivariate Lindley Distribution by Ranked Set Sampling. IJTSA. 2019;12(1):25-34.