178
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

An absolutely continuous bivariate Topp–Leone distribution: A useful model on a bounded domain

Pages 9726-9742 | Received 26 May 2015, Accepted 22 Jul 2016, Published online: 20 Jun 2017

References

  • Al-Zahrani, B. (2012). Goodness-of-fit for the Topp-Leone distribution with unknown parameters. Appl. Math. Sci. 6:6355–6363.
  • Balakrishnan, N., Lai, C. (2009). Continuous Bivariate Distributions. 2nd Ed. New York: Springer.
  • Barreto-Souza, W., Lemonte, A.J. (2013). Bivariate Kumaraswamy distribution: properties and a new method to generate bivariate classes. Statistics 47:1321–1342.
  • Bayoud, H.A. (2016). Admissible minimax estimators for the shape parameter of Topp-Leone distribution. Commun. Stat. Theory Methods 45:71–82.
  • Byrd, R.H., Lu, P., Nocedal, J., Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16:11901208.
  • Eugene, N., Lee, C., Famoye, F. (2002). Beta-normal distribution and its applications. Commun. Stat. Theory Methods 31:497–512.
  • Genç, A.İ. (2012). Moments of order statistics of Topp-Leone distribution. Stat. Pap. 53:117–131.
  • Genç, A.İ. (2013). Estimation of P(X > Y) with Topp-Leone distribution. J. Stat. Comput. Simul. 83:326–339.
  • Ghitany, M.E., Kotz, S., Xie, M. (2005). On some reliability measures and their stochastic orderings for the Topp-Leone distribution. J. Appl. Stat. 32:715–722.
  • Ghitany, M.E. (2007). Asymptotic distribution of order statistics from the Topp-Leone distribution. Int. J. Appl. Math. 20:371–376.
  • Gradshteyn, I.S., Ryzhik, I.M. (2007). Table of Integrals, Series, and Products. 7th ed. San Diego: Academic Press.
  • Johnson, N.L., Kotz, S. (1975). A vector multivariate hazard rate. J. Multivariate Anal. 5:53–66.
  • Kotz, S., Van Dorp, J.R. (2004). Beyond Beta- Other Continuous Families of Distributions with Bounded Support and Applications. Singapore: World Scientific.
  • Kotz, S., Nadarajah, S. (2006). J-shaped distribution, Topp and Leone’s. In: Encylopedia of Statistical Sciences (2nd Ed., Vol. 6, p. 3786). Hoboken, New Jersey: Wiley.
  • Kundu, D., Dey, A.K. (2009). Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm. Comput. Stat. Data Anal. 53:956–965.
  • Kundu, D., Gupta, R.D. (2009). Bivariate generalized exponential distribution. J. Multivariate Anal. 100:581–593.
  • Kundu, D., Gupta, R.D. (2011). Absolute continuous bivariate generalized exponential distribution. Adv. Stat. Anal. 95:169–185.
  • Lehmann, E.L. (1953). The power of rank test. Ann. Math. Stat. 24:23–42.
  • Mardia, K.V. (1962). Multivariate Pareto distribution. Ann. Math. Stat. 24:23–42.
  • Meintanis, S.G. (2007). Test of fit for Marshall-Olkin distributions with applications. J. Stat. Plann. Inference 137:3954–3963.
  • MirMostafaee, S.M.T.K. (2014). On the moments of order statistics coming from the Topp-Leone distribution. Stat. Probab. Lett. 95:85–91.
  • Nadarajah, S., Kotz, S. (2003). Moments of some J-shaped distributions. J. Appl. Stat. 30:311–317.
  • Nadarajah, S., Kotz, S. (2006). The exponentiated type distributions. Acta Appl. Math. 92:97–111.
  • R Core Team. (2014). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available at: http://www.R-project.org/.
  • Topp, C.W., Leone, F.C. (1955). A family of J-shaped frequency functions. JASA 50:209–219.
  • Vicari, D., Van Dorp, J.R., Kotz, S. (2008). Two-sided generalized Topp and Leone (TS-GTL) distributions. J. Appl. Stat. 35:1115–1129.
  • Wolfram Research, Inc. (2012). Mathematica, Version 9.0, Champaign, IL.
  • Zghoul, A.A. (2010). Order statistics from a family of J-shaped distributions. Metron LXVIII:127–136.

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.