Yıl: 2021 Cilt: 70 Sayı: 2 Sayfa Aralığı: 1055 - 1064 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.942909 İndeks Tarihi: 29-07-2022

On bivariate extension of the univariate transmuted distribution family

Öz:
The aim of this study is to examine the bivariate transmuted distributions in the literature and to propose alternative distribution. The method is based on mixing distributions of pairs of order statistics of a sample of size two. Some of proposed distributions allow both negative and positive Pearson correlations with admissible range between pairs of random variates. The results of the study gain importance in terms of eliminating or completing the missing aspects of the bivariate transmuted distributions existing in the literature.
Anahtar Kelime: Bivariate extension tranmuted distribution bivariate distribution Spearman’s Rho dependence

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Alizadeh, M., Merovci, F., Hamedani, G. G., Generalized transmuted family of distributions: properties and applications, Hacettepe Journal of Mathematics and Statistics, 46 (2017), 645–667.
  • [2] Asadian, N., Amini, M., Bozorgnia, A., Some concepts of negative dependence for bivariate distributions with applications, Journal of Mathematical Extension, 4 (1) (2009), 43–59.
  • [3] Baker, R., An order-statistics-based method for constructing multivariate distributions with fixed marginals, Journal of Multivariate Analysis, 99 (10) (2008), 2312–2327, https://dx.doi.org/10.1016/j.jmva.2008.02.019.
  • [4] Bakouch, H. S., Jamal, F., Chesneau, C., Nasir, A., A new transmuted family of distributions: Properties and estimation with applications, working paper or preprint, Sept. 2017.
  • [5] Barlow, R. E., Proschan, F., Statistical theory of reliability and life testing: probability models, Tech. rep., Florida State Univ Tallahassee, 1975, https://dx.doi.org/10.2307/1268641.
  • [6] Bekçi, M., Yılmaz, M., Construction of bivariate distribution by mixing positively dependent and negatively dependent distributions, International Journal of Statistics and Applications, 9 (4) (2015), 122–1127, https://dx.doi.org/10.5923/j.statistics.20190904.04.
  • [7] Bourguignon, M., Ghosh, I., Cordeiro, G. M., General results for the transmuted family of distributions and new models, Journal of Probability and Statistics, 2016 (2016), https://dx.doi.org/10.1155/2016/7208425.
  • [8] Dolati, A., Ubeda-Flores, M., Constructing copulas by means of pairs of order statistics, Kybernetika, 45 (6) (2009), 992–1002.
  • [9] Farlie, D. J. G., The performance of some correlation coefficients for a general bivariate distribution, Biometrika, 47 (3/4) (1960), 307–323, https://dx.doi.org/10.2307/2333302.
  • [10] Gumbel, E. J., Bivariate exponential distributions, Journal of the American Statistical Association, 55 (292) (1960), 698–707, https://dx.doi.org/10.1080/01621459.1960.10483368.
  • [11] Merovci, F., Alizadeh, M., Hamedani, G. G., Another generalized transmuted family of distributions:properties and applications, Austrian Journal of Statistics, 45 (3) (Jun. 2016), 71–93, https://dx.doi.org/10.17713/ajs.v45i3.109.
  • [12] Merovci, F., Alizadeh, M., Yousof, H. M., Hamedani, G. G., The exponentiated transmuted-g family of distributions: theory and applications, Communications in Statistics - Theory and Methods, 46 (21) (2017), 10800–10822, https://dx.doi.org/10.1080/03610926.2016.1248782.
  • [13] Mirhoseini, S., Dolati, A., Amini, M., On a class of distributions generated by stochastic mixture of the extreme order statistics of a sample of size two, arXiv preprint arXiv:1904.04287 (2019).
  • [14] Mirhosseini, S. M., Amini, M., Dolati, A., On a general structure of the bivariate fgm type distributions, Applications of Mathematics, 60 (1) (2015), 91–108, https://dx.doi.org/10.1007/s10492-015-0086-6.
  • [15] Oluyede, B. O., On local dependence and stochastic inequalities with applications to contingency tables, Applied mathematics and computation, 151 (3) (2004), 801–813, https://dx.doi.org/10.1016/s0096-3003(03)00537-x.
  • [16] Rezaei, S., Marvasty, A. K., Nadarajah, S., Alizadeh, M., A new exponentiated class of distributions: Properties and applications, Communications in Statistics - Theory and Methods, 46 (12) (2017), 6054–6073, https://dx.doi.org/10.1080/03610926.2015.1116579.
  • [17] Rüschendorf, L., Construction of multivariate distributions with given marginals, Annals of the Institute of Statistical Mathematics, 37 (2) (1985), 225–233, https://dx.doi.org/10.1007/bf02481093.
  • [18] Sarabia, J. M., Raja, A. V., Asha, G., Bivariate distributions with transmuted conditionals: models and applications, Communications in Statistics - Theory and Methods, 49 (1) (2020), 221–242, https://dx.doi.org/10.1080/03610926.2018.1536785.
  • [19] Schweizer, B., Wolff, E. F., On nonparametric measures of dependence for random variables, The Annals of Statistics, 9 (4) (1981), 879 – 885, https://dx.doi.org/10.1214/aos/1176345528.
  • [20] Shaw, W. T., Buckley, I. R. C., The alchemy of probability distributions: beyond GramCharlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, ArXiv e-prints (Jan. 2009).
  • [21] Unözkan, H., Yılmaz, M., Construction of continuous bivariate distribution by trans- muting dependent distribution, Cumhuriyet Science Journal, 40 (4) (2019), 860–866, https://dx.doi.org/10.17776/csj.618236.
APA YILMAZ M, UNOZKAN H (2021). On bivariate extension of the univariate transmuted distribution family. , 1055 - 1064. 10.31801/cfsuasmas.942909
Chicago YILMAZ MEHMET,UNOZKAN HUSEYIN On bivariate extension of the univariate transmuted distribution family. (2021): 1055 - 1064. 10.31801/cfsuasmas.942909
MLA YILMAZ MEHMET,UNOZKAN HUSEYIN On bivariate extension of the univariate transmuted distribution family. , 2021, ss.1055 - 1064. 10.31801/cfsuasmas.942909
AMA YILMAZ M,UNOZKAN H On bivariate extension of the univariate transmuted distribution family. . 2021; 1055 - 1064. 10.31801/cfsuasmas.942909
Vancouver YILMAZ M,UNOZKAN H On bivariate extension of the univariate transmuted distribution family. . 2021; 1055 - 1064. 10.31801/cfsuasmas.942909
IEEE YILMAZ M,UNOZKAN H "On bivariate extension of the univariate transmuted distribution family." , ss.1055 - 1064, 2021. 10.31801/cfsuasmas.942909
ISNAD YILMAZ, MEHMET - UNOZKAN, HUSEYIN. "On bivariate extension of the univariate transmuted distribution family". (2021), 1055-1064. https://doi.org/10.31801/cfsuasmas.942909
APA YILMAZ M, UNOZKAN H (2021). On bivariate extension of the univariate transmuted distribution family. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 70(2), 1055 - 1064. 10.31801/cfsuasmas.942909
Chicago YILMAZ MEHMET,UNOZKAN HUSEYIN On bivariate extension of the univariate transmuted distribution family. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 70, no.2 (2021): 1055 - 1064. 10.31801/cfsuasmas.942909
MLA YILMAZ MEHMET,UNOZKAN HUSEYIN On bivariate extension of the univariate transmuted distribution family. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.70, no.2, 2021, ss.1055 - 1064. 10.31801/cfsuasmas.942909
AMA YILMAZ M,UNOZKAN H On bivariate extension of the univariate transmuted distribution family. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2021; 70(2): 1055 - 1064. 10.31801/cfsuasmas.942909
Vancouver YILMAZ M,UNOZKAN H On bivariate extension of the univariate transmuted distribution family. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2021; 70(2): 1055 - 1064. 10.31801/cfsuasmas.942909
IEEE YILMAZ M,UNOZKAN H "On bivariate extension of the univariate transmuted distribution family." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 70, ss.1055 - 1064, 2021. 10.31801/cfsuasmas.942909
ISNAD YILMAZ, MEHMET - UNOZKAN, HUSEYIN. "On bivariate extension of the univariate transmuted distribution family". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 70/2 (2021), 1055-1064. https://doi.org/10.31801/cfsuasmas.942909