×
Gomes, Antonio E.; Da-Silva, Cibele Q.; Cordeiro, Gauss M.; Ortega, Edwin M. M.

A new lifetime model: the Kumaraswamy generalized Rayleigh distribution. (English) Zbl 1453.62686

J. Stat. Comput. Simulation 84, No. 2, 290-309 (2014).
Summary: The generalized Rayleigh (GR) distribution [V. Gh. Vodă, Apl. Mat. 21, 395–419 (1976; Zbl 0362.62035)] has been applied in several areas such as health, agriculture, biology and other sciences. For the first time, we propose the Kumaraswamy GR (KwGR) distribution for analysing lifetime data. The new density function can be expressed as a mixture of GR density functions. Explicit formulae are derived for some of its statistical quantities. The density function of the order statistics can be expressed as a mixture of GR density functions. We also propose a linear log-KwGR regression model for analysing data with real support to extend some known regression models. The estimation of parameters is approached by maximum likelihood. The importance of the new models is illustrated in two real data sets.

Cited in 6 Documents

MSC:

62N05 Reliability and life testing
62E10 Characterization and structure theory of statistical distributions
62F10 Point estimation

Keywords:

Kumaraswamy distribution; information matrix; maximum likelihood; moment-generating function; Rayleigh distribution; reliability theory

Citations:

Zbl 0362.62035
Cite Review PDF
Full Text: DOI

References:

[1] V.G. Vodǎ, Inferential procedures on a generalized Rayleigh variate, I, Appl. Math. 21 (1976), pp. 395-412. [Google Scholar] · Zbl 0362.62035
[2] V.G. Vodǎ, Inferential procedures on a generalized Rayleigh variate, II, Appl. Math. 21 (1976), pp. 413-419. [Google Scholar] · Zbl 0362.62035
[3] N. Balakrishnan and S. Kocherlakota, On the double Weibull distribution: Order statistics and estimation, Sankhya 47 (1985), pp. 161-178. [Google Scholar] · Zbl 0594.62055
[4] J.G. Surles and W.J. Padgett, Inference for reliability and stress-strength for a scaled Burr type X distribution, Lifetime Data Anal. 7 (2001), pp. 187-200. doi: 10.1023/A:1011352923990[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 0984.62082
[5] D. Kundu and M.Z. Raqab, Generalized Rayleigh distribution: Different methods of estimation, Comput. Stat. Data Anal. 49 (2005), pp. 187-200. doi: 10.1016/j.csda.2004.05.008[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1429.62449
[6] S.F. Manesh and B.E. Khaledi, On the likelihood ratio order for convolutions of independent generalized Rayleigh random variables, Statist. Probab. Lett. 78 (2008), pp. 3139-3144. doi: 10.1016/j.spl.2008.05.035[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1154.60311
[7] H.A. Sartawi and M.S. Abu-Salih, Bayes prediction bounds for the Burr type X model, Comm. Statist. Theory Methods 20 (1991), pp. 2307-2330. doi: 10.1080/03610929108830633[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 0850.62288
[8] M.Z. Raqab, Order statistics from the Burr type X model, Comput. Math. Appl. 36 (1998), pp. 111-120. doi: 10.1016/S0898-1221(98)00143-6[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0933.62042
[9] J.G. Surles and W.J. Padgett, Inference for P(Y<X) in the Burr type X model, J. Appl. Statist. Sci. 7 (1998), pp. 225-238. [Google Scholar] · Zbl 0911.62092
[10] A. Bekker and J.J.J. Roux, Reliability characteristics of the Maxwell distribution: A Bayes estimation study, Comm. Statist. Theory Methods 34 (2005), pp. 2169-2178. doi: 10.1080/STA-200066424[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1081.62087
[11] R.V. Hogg and E.A. Tanis, Probability and Statistical Inference, Macmillan Publishing Co. Inc., New York, 1993. [Google Scholar] · Zbl 0732.62002
[12] P. Kumaraswamy, A generalized probability density function for double-bounded random processes, J. Hydrol. 46 (1980), pp. 79-88. doi: 10.1016/0022-1694(80)90036-0[Crossref], [Web of Science ®], [Google Scholar]
[13] G.M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883-898. doi: 10.1080/00949650903530745[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1219.62022
[14] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, San Diego, CA, 2000. [Google Scholar] · Zbl 0981.65001
[15] A.P. Prudnikov, Y.A. Brychkov, and O.I. Marichev, Integrals and Series, Gordon and Breach Science Publishers, New York, 1986. [Google Scholar] · Zbl 0606.33001
[16] G. Chen and N. Balakrishnan, A general purpose approximate goodness-of-fit test, J. Qual. Technol. 27 (1995), pp. 154-161. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[17] J.F. Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 2003. [Google Scholar] · Zbl 1015.62093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.