Filidor VİLCA, Diego I. GALLARDO, Héctor W. GÖRMEZ, Jimmy REYES

Modi ed slash Birnbaum-Saunders distribution

In this paper, we introduce an extension for the Birnbaum-Saunders(BS) distribution based on the modied slash (MS) distribution proposedby [12]. This new family of BS type distributions is obtainedby replacing the usual normal distribution with the quotient of twoindependent random variables, one being a normal distribution in thenumerator and the power of a exponential of parameter equal to two atthe denominator. The resulting distribution is an extension of the BSdistribution that has greater kurtosis values than the usual BS distributionand the slash Birnbaum-Saunders (SBS) distribution (see [7]).Moments and some properties are derived for the new distribution.Also, we draw inferences by the method of moments and maximumlikelihood. A real data application is presented where the model ttingis implemented by using maximum likelihood estimation producingbetter results than the classic BS model and slash BS model.

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Vilca, F. and Leiva, V. A new fatigue life model based on family of skew-elliptical distributions, Communications in Statistics: Theory and Methods, 35, 229-244, 2006.
Severini, T.A. Likelihood functions for inference in the presence of a nuisance parameter, Biometrika, 85, 507-522, 1998.
Rieck, J.R. and Nedelman, J.R. A log-linear model for the Birnbaum-Saunders distribution, Technometrics, 33, 51-60, 1991.
Reyes, J., Gómez, H. W. and Bolfarine, H. Modied slash distribution, Statistics, 47, 929- 941, 2013.
Lin, T.I., Lee, J.C. and Hsieh, W.J. Robust mixture modeling using the skew t distribution, Stat. Comput., 17, 81-92, 2007.
Leiva, V., Barros, M., Paula, G. A. and Sanhueza, A. Generalized Birnbaum-Saunders distribution applied to air pollutant concentration, Environmetrics, 19, 235-249, 2008.
Lee, S.Y. and Xu, L. Inffuence analyses of nonlinear mixed-effects models, Comput. Statist. Data Anal., 45, 321-341, 2004.
Ng, H.K.T., Kundu, D. and Balakrishnan, N. Modiffed moment estimation for the twoparameter Birnbaum-Saunders distribution, Comput. Statist. Data Anal., 43, 283-298, 2003.
Gómez, H.W.; Olivares-Pacheco, J.F. and Bolfarine, H. An Extension of the Generalized Birnbaun-Saunders Distribution, Statistics and Probability Letters, 79, 331-338, 2009.
Díaz-García, J. A. and Leiva, V. A new family of life distributions based on elliptically contoured distributions, Journal of Statistical Planning and Inference, 128, 445-457, 2005.
Chen, G. and Balakrishnan, N. A general purpose approximate goodness-of-t test, Journal of Quality Technology, 27, 154-161, 1995.
Birnbaum, Z.W. and Saunders, S.C. Estimation for a family of life distributions with applications to fatigue, Journal of Applied Probability, 6, 328-347, 1969b.
Birnbaum, Z.W. and Saunders, S.C. A New Family of Life Distributions, Journal of Applied Probability, 6, 319-327, 1969a.
Balakrishnan, N., Leiva, V., Sanhueza, A. and Vilca, F. Estimation in the BirnbaumSaunders distribution based on scale-mixture of normals and the EM-algorithm, Statistics and Operations Research Transactions, 33, 171-192, 2009.
Akaike, H. A new look at the statistical model identiffcation, IEEE Transactions on Automatic Control, 19, 716-723, 1974.

Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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