A version of transmuted generalized Rayleigh distribution
Published 2015-05-21
Keywords
- Generalized Rayleigh distribution,
- transmuted generalized Rayleigh distribution,
- quadratic rank transmutation map
How to Cite
Abstract
Statistical analysis procedures’s quality depends on the proper use of the probability distributions. For that reason, many probability distributions have been generalized. For example, Vodă in [13] introduced the generalized Rayleigh distribution, a model widely used in reliability analysis. In this article, we introduce an extension of the generalized Rayleigh distribution using the quadratic rank transmutation map studied by Shaw and Buckley in [12]. We study the main properties of this new distribution. Statistical inference studies are done. A real data application is shown. Finally, the main conclusions of this paper are presented.
To cite this article: Y.A. Iriarte, J.M. Astorga, Una versión de la distribución Rayleigh generalizada transmutada, Rev. Integr. Temas Mat. 33 (2015), no. 1, 83-95.Downloads
References
- Akaike H., “A new look at the statistical model identification. System identification and time-series analysis”, IEEE Trans. Automatic Control. 19 (1974), 716-723.
- Andrews D.F. and Herzberg A.M., Data: a collection of problems from many fields for the student and research worker, Springer, New York, 1985.
- Aryal G.R. and Tsokos C.P., “On the transmuted extreme value distribution with application”, Nonlinear Anal. 71 (2009), no. 12, 1401-1407.
- Aryal G.R. and Tsokos C.P., “Transmuted Weibull distribution: a generalization of the Weibull probability distribution”, Eur. J. Pure Appl. Math. 4 (2011), no. 2, 89-102.
- Bekker A. and Roux J.J.J., “Reliability characteristics of the Maxwell distribution: a Bayes estimation study”, Comm. Statist. Theory Methods. 34 (2005), no.11, 2169-2178.
- Hogg R.V. and Tanis E.A., Probability and statistical inference, Macmillan Publishing, New York, 1993.
- Johnson N.L., Kotz S. and Balakrishnan N., Continuous univariate distributions, John Wiley & Sons, Inc., New York, 1994.
- Merovci F., “Transmuted Rayleigh distribution”, Aust. J. Stat. 42 (2013), no. 1, 21-31.
- Merovci F., “Transmuted Generalized Rayleigh Distribution”, J. Stat. Appl. Prob. 3 (2014), no. 1, 9-20.
- R Development Core Team R., “A language and environment for statistical computing”, R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org (2013).
- Schwarz G., “Estimating the dimension of a model”, Ann. Statist. 6 (1978), no. 2, 461-464.
- Shaw W. and Buckley I., “The alchemy of probability distributions: beyond gramcharlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map”, IMA Primera Conferencia sobre Finanzas Computacionales, Cornell University, http://arxiv.org/abs/0901.0434 (2007).
- Vodă VG., “Inferential procedures on a generalized Rayleigh variate I”, Apl. Mat. 21 (1976), no. 6, 395-412.