A robust class of multivariate fatigue distributions based on normal mean-variance mixture model

다국어 초록 (Multilingual Abstract)

The Birnbaum–Saunders (BS) distribution, introduced in 1969, is a popular univariate fatigue life distribution which has been widely used to model right-skewed lifetime and reliability data. In this paper, a new class of generalized multivariate BS distributions is proposed based on mean-variance mixture models to accommodate strongly skewed and heavy tailed multivariate lifetime data. Some special cases of this class as well as their properties are then discussed. We present a hierarchical representation which facilitates an efficient EM-type algorithm for the computation of maximum likelihood estimates. Empirical results from a simulation study and real data analyses show that this class of distributions outperforms many existing extensions of the BS distribution in modeling lifetime data.

참고문헌 (Reference)

1 Mohammadi, K., "Use of Birnbaum–Saunders distribution for estimating wind speed and wind power probability distributions : A review" 143 : 109-122, 2017

2 Good, I. J., "The population frequencies of species and the estimation of population parameters" 40 (40): 237-260, 1953

3 Azzalini, A., "The multivariate skew-normal distribution" 83 (83): 715-726, 1996

4 Gomes, M. I., "The extreme value Birnbaum–Saunders model and its moments and application in biometry" 49 (49): 81-94, 2012

5 Böhning, D., "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family" 46 (46): 373-388, 1994

6 Hannan, E. J., "The determination of the order of an autoregression" B41 (B41): 190-195, 1979

7 Liu, C., "The ECME algorithm : A simple extension of EM and ECM with faster monotone convergence" 81 (81): 633-648, 1994

8 Marchant, C., "Robust multivariate control charts based on Birnbaum–Saunders distributions" 88 (88): 182-202, 2018

9 McNeil, A., "Quantitative risk management: Concepts. Techniques and tools" Princeton University Press 2005

10 Desmond, A. F., "On the relationship between two fatigue-life models" 35 (35): 167-169, 1986

11 Aitken, A. C., "On Bernoulli’s numerical solution of algebraic equations" 46 : 623-634, 1926

12 Mehrdad Naderi, "Nonlinear regression models based on the normal mean–variance mixture of Birnbaum–Saunders distribution" 한국통계학회 46 (46): 476-485, 2017

13 Vilca, F., "Multivariate skew normal generalized hyperbolic distribution and its properties" 128 : 73-85, 2014

14 Naderi, M., "Multivariate normal mean-variance mixture distribution based on Lindley distribution" 47 (47): 1179-1192, 2018

15 Pourmousa, R., "Multivariate normal mean-variance mixture distribution based on Birnbaum–Saunders distribution" 85 (85): 2736-2749, 2015

16 Jamalizadeh, A., "Multivariate Birnbaum–Saunders distribution based on multivariate skew normal distribution" 45 : 1-20, 2015

17 Mehrdad Naderi, "Modeling right-skewed financial data streams: A likelihood inference based on the generalized Birnbaum–Saunders mixture model" Elsevier BV 376 : 125109-, 2020

18 Bozdogan, H., "Model selection and Akaike’s information criterion(AIC) : The general theory and its analytical extensions" 52 (52): 345-370, 1987

19 Lindsay, B., "Mixture models : Theory. Geometry and applications" Institute of Mathematical Statistics 1995

20 Balakrishnan, N., "Mixture inverse Gaussian distribution and its transformations, moments and applications" 43 : 91-104, 2009

21 Dempster, A. P., "Maximum likelihood from incomplete data via the EM algorithm" 39 : 1-22, 1977

22 Meng, X. L., "Maximum likelihood estimation via the ECM algorithm : A general framework" 80 (80): 267-278, 1993

23 Lindley, D. V., "Introduction to probability and statistics from a Bayesian viewpoint. Part II: Inference" Cambridge University Press 1965

24 Barndorf-Nielsen, O., "Infnite divisibility of the hyperbolic and generalized inverse Gaussian distributions" 38 (38): 309-311, 1977

25 Kundu, D., "Generalized multivariate Birnbaum–Saunders distributions and related inferential issues" 116 : 230-244, 2013

26 Barros, M., "Generalized Tobit models : Diagnostics and application in econometrics" 45 : 145-167, 2018

27 Punzo, A., "Fitting insurance and economic data with outliers : A fexible approach based on fnite mixtures of contaminated gamma distributions" 45 (45): 2563-2584, 2018

28 Louis, T. A., "Finding the observed information when using the EM algorithm" B44 (B44): 226-233, 1982

29 Lindley, D. V., "Fiducial distributions and Bayes theo" B20 : 102-107, 1958

30 Birnbaum, Z. W., "Estimation for a family of life distributions with applications to fatigue" 6 : 328-347, 1969

31 Schwarz, G., "Estimating the dimension of a model" 6 (6): 461-464, 1978

32 Jamalizadeh, A., "Discussion of Birnbaum–Saunders distribution : A review of models, analysis, and applications" 35 : 82-89, 2019

33 Marchant, C., "Diagnostics in multivariate generalized Birnbaum–Saunders regression models" 43 (43): 2829-2849, 2016

34 Hashemi, F., "Clustering right-skewed data stream via Birnbaum–Saunders mixture models : A fexible approach based on fuzzy clustering algorithm" 82 : 105539-, 2019

35 Kundu, D., "Bivariate Birnbaum–Saunders distribution and associated inference" 101 : 113-125, 2010

36 Balakrishnan, N., "Birnbaum–Saunders distribution : A review of models, analysis, and applications" 35 : 4-132, 2019

37 Johnson, R. A., "Applied Multivariate Statistical Analysis" Prentice Hall 1999

38 Sclove, L. S., "Application of model-selection criteria to some problems in multivariate analysis" 52 (52): 333-343, 1987

39 Blæsild, P., "And related distributions, with an application to Johannsen’s bean data" 68 : 251-263, 1981

40 Arslan, O., "An alternative multivariate skew Laplace distribution : Properties and estimation" 51 (51): 865-887, 2010

41 Ahmed, S. E., "A truncated version of the Birnbaum–Saunders distribution with an application in fnancial risk" 26 : 293-311, 2010

42 Romeiro, R. G., "A robust multivariate Birnbaum–Saunders distribution : EM estimation" 52 (52): 321-344, 2018

43 Vilca, F., "A robust extension of the bivariate Birnbaum–Saunders distribution and associated inference" 124 : 418-435, 2014

44 Naderi, M., "A novel mixture model using the multivariate normal mean-variance mixture of Birnbaum–Saunders distribution and its application to extrasolar planets" 171 : 126-138, 2019

45 Saulo, H., "A nonparametric method for estimating asymmetric densities based on skewed Birnbaum–Saunders distributions applied to environmental data" 27 (27): 1479-1491, 2013

46 Birnbaum, Z. W., "A new family of life distributions" 6 : 319-327, 1969

47 Leiva, V., "A length-biased version of the Birnbaum–Saunders distribution with application in water quality" 23 (23): 299-307, 2009

48 Akaike, H., "2nd international symposium on information theory" Akademiai Kiado 267-281, 1973