189
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Role of concomitants of order statistics in determining parent bivariate distributions

&
Pages 7976-7997 | Received 04 Aug 2014, Accepted 16 Mar 2016, Published online: 28 Apr 2017

References

  • Al-Hussaini, E.K. (1991). A characterization of the Burr type XII distribution. Appl. Math. Lett. 4:59–61.
  • Arnold, B.C., Balakrishnan, N., Nagaraja, H.N. (1992). A First Course in Order Statistics. New York: John Wiley and Sons.
  • Bairamov, I., Kotz, S., Bekci, M. (2000). New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics. J. Appl. Stat. 28:521–536.
  • Balakrishnan, N., Lai, C.D. (2009). Continuous Bivariate Distributions. New York: Springer.
  • Balasubramanian, K., Beg, M.I. (1997). Concomitant of order statistics in Morgenstern type bivariate exponential distributions. J. Appl. Stat. 5:233–245.
  • Balasubramanian, K., Beg, M.I. (1998). Concomitants of order statistics in Gumbel’s bivariate exponential distribution. Sankhya B 60:399–406.
  • Barlow, R.E., Proschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. New York: Holt, Rinehart and Winston.
  • Bateman, H. (1954). Tables of Integral Transforms. New York: Mc Graw-Hill.
  • Bayramoglu, I., Eryilmaz, S. (2015). Order statistics of dependent sequences consisting of two different sets of exchangeable variables. J. Comput. Appl. Math. 286:1–6.
  • Bayramoglu, I., Kemalbag, G. (2013). Some novel discrete distributions under fourfold sampling schemes and conditional bivariate order statistics. J. Comput. Appl. Math. 248:1–14.
  • Beerends, R.J., Morsche, J.C., Vanden Berg, J.C., Vande Vrie, E.M. (2003). Fourier and Laplace Transforms. Cambridge: Cambridge University Press.
  • Begum, A.A., Khan, A.H. (2000). Concomitants of order statistics from Marshall and Olkin bivariate Weibull distribution. Calcutta Stat. Assoc. Bull. 50:65–70.
  • Bhattacharya, P.K. (1984). Induced order statistics: Theory and applications. In: Krishnaiah, P.R., Sen, P.K., eds. Hand Book of Statistics (vol. 4, pp. 383–403). Amsterdam: North Holland.
  • Burrows, P.M. (1972). Expected selection differentials for directional selection. Biometrics 28:1091–1100.
  • Burrows, P.M. (1975). Variances of selection differentials in normal samples. Biometrics 31:125–133.
  • Chacko, M., Thomas, P.Y. (2004). Estimation of a parameter of Morgenstern type bivariate uniform distribution based on concomitants of order statistics and concomitants of record values. J. Kerala Stat. Assoc. 15:13–26.
  • Chacko, M., Thomas, P.Y. (2008). Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling. Ann. Inst. Stat. Math. 60:301–318.
  • Chacko, M., Thomas, P.Y. (2009). Estimation of parameters of Morgenstern type bivariate logistic distribution by ranked set sampling. J. Indian Soc. Agric. Stat. 63:77–83.
  • Chacko, M., Thomas, P.Y. (2011). Estimation of parameter of Morgenstern type bivariate exponential distribution using concomitants of order statistics. Stat. Methodol. 8:363–376.
  • Chen, Z., Bai, Z., Sinha, B.K. (2004). Ranked Set Sampling, Theory and Applications. Lecture Notes in Statistics. New York: Springer.
  • Chou, W.C., Huang, W.J. (2003). A note on characterizations of the bivariate gamma distribution. J. Stat. Plann. Inference. doi:10.1016/j.jspi.2003.09.034.
  • David, H.A. (1973). Concomitants of order statistics. Bull. Int. Stat. Inst. 45:295–300.
  • David, H.A., Nagaraja, H.N. (1998). Concomitants of order statistics. In: Balakrishnan, N., Rao, C.R., eds. Handbook of Statistics (vol. 16, pp. 487–513). Amsterdam The Netherlands: North-Holland.
  • David, H.A., Nagaraja, H.N. (2003). Order Statistics. Third Edition. New York: John Wiley and Sons.
  • Domma, F., Giordano, S. (2016). Concomitants of m-generalized order statistics from generalized Farlie-Gumbel-Morgenstern distribution family. J. Comput. Appl. Math. 294:413–435.
  • Ebrahimi, N., Zahedi, H. (1989). Testing for bivariate Gumbel against new better than used in expectation. Commun. Stat. - Theory Methods 18:1357–1371.
  • Eryilmaz, S. (2013). On the sums of distributions of order statistics from exchangeable random variables. J. Comput. Appl. Math. 253:204–207.
  • Johnson, N.L., Kotz, S. (1972). Continuous Multivariate Distributions. New York: John Wiley.
  • Johnson, N.L., Kotz, S., Balakrishnan, N. (1994). Continuous Univariate Distributions, vol. 1, Second edition. New York: John Wiley.
  • Johnson, N.L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions, vol. 2, Second edition. New York: John Wiley.
  • Kundu, D., Raqab, M.Z. (2012). Bayesian inference and prediction of order statistics for type II censored Weibull distribution. J. Stat. Plann. Inference 142:41–47.
  • Lai, C.D. (1978). Morgenstern’s bivariate distribution and its application to point processes. J. Math. Anal. Appl. 65:247–256.
  • Lesitha, G., Thomas, P.Y. (2013). Estimation of the scale parameter of a log-logistic distribution. Metrika 76:427–448.
  • Nagaraja, H.N. (1981). Some finite sample results for the selection differential. Ann. Inst. Stat. Math. 33:437–448.
  • Nagaraja, H.N. (1982). Some asymptotic results for the induced selection differential. J. Appl. Probab. 19:253–261.
  • Nair, K.R.M., Nair, N.U. (1988). On characterizing the bivariate exponential and geometric distributions. Ann. Inst. Stat. Math. 40:267–271.
  • Navarro, J., Ruiz, J.M. (2004). A characterization of the multivariate normal distribution by using the hazard gradient. Ann. Inst. Stat. Math. 56:361–367.
  • Pal, S., Murthy, G.S.R. (2003). An application of Gumbel’s bivariate exponential distribution in estimation of warranty cost of motor cycles. Int. J. Qual. Reliab. Manage. 20:488–502.
  • Philip, A., Thomas, P.Y. (2015). On concomitants of order statistics arising from the extended Farlie-Gumbel-Morgenstern bivariate logistic distribution and its application in estimation. Stat. Methodol. 25:59–73.
  • Rao, C.R., Shanbhag, D.N. (1998). Recent approaches to characterizations based on order statistics and record values. In: Balakrishnan, N., Rao, C.R., eds. Handbook of Statistics (vol. 16, pp. 231–256). Amsterdam: North-Holland.
  • Rodriguez, R.N. (1977). A guide to the Burr type XII distributions. Biometrika 64:129–134.
  • Rohatgi, V.K., Saleh, A.K.E. (2001). An Introduction to Probability and Statistics, 2nd edition. New York: John Wiley and Sons.
  • Rychlik, T. (2001). Mean-variance bounds for order statistics from dependent DFR, IFR, DFRA and IFRA samples. J. Stat. Plann. Inference 92:21–38.
  • Scaria, J., Nair, N.U. (1999). On concomitants of order statistics from Morgenstern family. Biomet. J. 41:483–489.
  • Scaria, J., Nair, N.U. (2005). Distribution of the maximum of concomitants of selected order statistics from the Morgenstern family. J. Appl. Stat. Sci. 14:251–262.
  • Scaria, J., Nair, N.U. (2008). Distribution of extremes of rth concomitant from the Morgenstern family. Stat. Pap. 49:109–119.
  • Scaria, J., Thomas, B. (2014). Second order concomitants from the Morgenstern family of distributions. J. Appl. Stat. Sci. 21:63–76.
  • Stokes, S.L. (1977). Ranked set sampling with concomitant variables. Commun. Stat. - Theory Methods 6:1207–1211.
  • Suresh, R.P. (1993). Some asymptotic results for the induced percentile selection differential. Sankhya A 55:120–129.
  • Tahmasebi, S., Behboodian, J. (2012). Information properties for concomitants of order statistics in Farlie-Gumbel-Morgenstern (FGM) family. Commun. Stat. - Theory Methods 41:1954–1968.
  • Thomas, P.Y., Veena, T.G. (2011). On an application of concomitants of order statistics in characterizing a family of bivariate distributions. Commun. Stat. - Theory Methods 40:1445–1452.
  • Veena, T.G., Thomas, P.Y. (2008). Characterizations of bivariate distributions by properties of concomitants of order statistics. Stat. Prob. Lett. 78:3350–3354.
  • Veena, T.G., Thomas, P.Y. (2015). Application of concomitants of order statistics of independent non-identically distributed random variables in estimation. Commun. Stat. - Theory Methods 44:2530–2545.
  • Yang, S.S. (1977). General distribution theory of concomitants of order statistics. Ann. Stat. 5:996–1002.
  • Yorubulut, S., Gebizlioglu, O.L. (2013). Bivariate Pseudo-Gompertz distribution and concomitants of its order statistics. J. Comput. Appl. Math. 247:68–83.
  • Zimmer, W.J., Keats, J.B., Wang, F.K. (1998). The Burr XII distribution in reliability analyiss. J. Qual. Technol. 30:386–394.

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.