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ORDERINGS OF FINITE MIXTURE MODELS WITH LOCATION-SCALE DISTRIBUTED COMPONENTS

Published online by Cambridge University Press:  14 September 2020

Ghobad Barmalzan Open the ORCID record for Ghobad Barmalzan [Opens in a new window] ,
Sajad Kosari  and
Narayanaswamy Balakrishnan
Ghobad Barmalzan
Affiliation:
Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran E-mail: ghobad.barmalzan@gmail.com
Sajad Kosari
Affiliation:
Department of Mathematics, University of Zabol, Sistan and Baluchestan, Iran
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, OntarioL8S 4L8, Canada
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Abstract

In this paper, we consider finite mixture models with components having distributions from the location-scale family. We then discuss the usual stochastic order and the reversed hazard rate order of such finite mixture models under some majorization conditions on location, scale and mixing probabilities as model parameters.

Keywords

finite mixture modelslocation parameterslocation-scale distributionmultivariate chain majorization orderreversed hazard rate orderscale parametersusual stochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 2 , April 2022 , pp. 461 - 481
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Amini-Seresht, E. & Zhang, Y. (2017). Stochastic comparisons on two finite mixture models. Operations Research Letters 45: 475–480.CrossRefGoogle Scholar
Balakrishnan, N., Haidari, A. & Masoumifard, K. (2015). Stochastic comparisons of series and parallelsystems with generalized exponential components. IEEE Transactions on Reliability 64: 333–348.CrossRefGoogle Scholar
Castillo, E., Hadi, A.S., Balakrishnan, N. & Sarabia, J.M. (2005). Extreme value and related models with applications in engineering and science. Hoboken, NJ: John Wiley & Sons.Google Scholar
Cha, J.H. & Finkelstein, M. (2013). The failure rate dynamics in heterogeneous populations. Reliability Engineering and System Safety 112: 120–128.CrossRefGoogle Scholar
Everitt, B.S. & Hand, D.J. (1981). Finite mixture distributions. London: Chapman and Hall.CrossRefGoogle Scholar
Finkelstein, M. (2008). Failure rate modeling for reliability and risk. London: Springer.Google Scholar
Finkelstein, M. & Esaulova, V. (2006). On mixture failure rate ordering. Communications in Statistics – Theory and Methods 35: 1943–1955.CrossRefGoogle Scholar
Franco, M., Balakrishnan, N., Kundu, D., & Vivo, J.M. (2014). Generalized mixtures of Weibull components. Test 23: 515–535.CrossRefGoogle Scholar
Hazra, N.K. & Finkelstein, M. (2018). On stochastic comparisons of finite mixtures for some semiparametric families of distributions. Test 27: 988–1006.CrossRefGoogle Scholar
Hosking, J.R.M. & Wallis, J.R. (1997). Regional frequency analysis: An approach based on L-moment. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Johnson, N.L., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distributions, 2nd ed., vol. 1. New York: John Wiley & Sons.Google Scholar
Johnson, N.L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, 2nd ed., vol. 2. New York: John Wiley & Sons.Google Scholar
Khaledi, B.E, Farsinezhad, S., & Kochar, S.C. (2011). Stochastic comparisons of order statistics in the scale model. Journal of Statistical Planning and Inference 141: 276–286.CrossRefGoogle Scholar
Marshall, A.W. & Olkin, I. (2007). Life Distributions. New York: Springer.Google Scholar
Marshall, A.W., Olkin, I., & Arnold, B.C. (2011). Inequalities: theory of majorization and its applications, 2nd ed. New York: Springer.CrossRefGoogle Scholar
Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. New York: John Wiley & Sons.Google Scholar
Navarro, J. & Hernandez, P.J. (2004). How to obtain bathtub-shaped failure rate models from normal mixtures. Probability in the Engineering and Informational Sciences 18: 511–531.CrossRefGoogle Scholar
Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
Titterington, D.M., Smith, A.F.M., & Makov, U.E. (1985). Statistical analysis of finite mixture distributions. Chichester: John Wiley & Sons.Google Scholar