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Ahad Jamalizadeh,H. Mahmoodian,A. Pourdarvish,N. Balakrishnan 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.2
In this paper, by considering a (k + n)-dimensional random vector XT , YT T , X ∈ Rk and Y ∈ Rn, having a multivariate elliptical distribution, we derive the exact distribution of AX + LY (n), where A ∈ Rp×k, L ∈ Rp×n, and Y(n) = Y(1), Y(2), . . . , Y(n)T denotes the vector of order statistics from Y. Next, we discuss the distribution of aTX+bY(r), for r = 1, . . . ,n, a =(a1, . . . , ak)T ∈ Rk and b ∈ R. We show that these distributions can be expressed as mixtures of multivariate unified skew-elliptical distributions. Finally, we illustrate an application of the established results to stock fund evaluation.
Mehrdad Naderi,Alireza Arabpour,Tsung-I Lin,Ahad Jamalizadeh 한국통계학회 2017 Journal of the Korean Statistical Society Vol.46 No.3
This paper presents a new extension of nonlinear regression models constructed by assuming the normal mean–variance mixture of Birnbaum–Saunders distribution for the unobserved error terms. A computationally analytical EM-type algorithm is developed for computing maximum likelihood estimates. The observed information matrix is derived for obtaining the asymptotic standard errors of parameter estimates. The practical utility of the methodology is illustrated through both simulated and real data sets.
A robust class of multivariate fatigue distributions based on normal mean-variance mixture model
Sasaei Mahsa,Pourmousa Reza,Balakrishnan Narayanaswamy,Jamalizadeh Ahad 한국통계학회 2021 Journal of the Korean Statistical Society Vol.50 No.1
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.