Continuous Multivariate Distributions, Volume 1: Models and Applications

By R. Strawderman. 2001

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View Paper: https://www.semanticscholar.org/paper/7f6dfbf1652b919fc998c43171b8805c0d62dc6c

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Citations in the corpus

Multivariate Symmetry and Asymmetry (2006, background): “Among spherically symmetric distributions are not only multivariate normal distributions with covariance matrices of form σ 2 I d , but also, for example, certain cases of standard multivariate t and logistic distributions (see [34], pp. 34 and 573).”
Bayesian structured additive distributional regression for multivariate responses (2015, methodology): “We assume that Σ is strictly positive definite, so that the density of y is defined as p.y1, : : : , yD/= 1√{.2π/D det.Σ/} exp { −1 2 .y −μ/′Σ−1.y −μ/ } : The multivariate normal distribution has several practically and theoretically attractive properties; see for example Kotz et al. (2005).”
Some positive dependence stochastic orders (2006, neutral): “…the a’s (whose number is ∑n i=2 ( n i ) = 2n−n−1) are suitable parameters which satisfy the constraints 1 + ∑ 1≤i1<i2≤n εa1εa2ai1i2 + ∑ 1≤i1<i2<a3≤n εa1εa2εa3ai1i2i3 + · · ·+ ε1ε2 · · · εna12···n ≥ 0, 9 with εi = ±1, i = 1, 2, . . . , n; see, for example, Kotz, Balakrishnan, and Johnson (2000).”
Optimal Portfolio Allocation under Higher Moments (2006, neutral): “…obtained by direct optimization of the expected utility, and r̂p the optimal portfolio return from a given ap- 13In the normal case, all co-skewness are equal to zero, while co-kurtosis are given by iiii = 3, iijj = 1:125, iiij = 0:75, and iijk = 0:375, for i 6= j 6= k 6= l;see Kotz et al. (2000).”
Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence (2007, methodology): “3 in Nelsen (2006), we may assume that X has a centered elliptically contoured distribution with stochastic representation as given in formula (20).”
Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis (2007, background): “The family of densities in (4) belongs to the Sarmanov class of densities (see Kotz et al., 2000, Chapter 44, for more details and further references).”
Matrix Variate Distributions for Probabilistic Structural Dynamics (2007, methodology): “If we consider the special case whenG is a one-dimensional matrix (that is a scalar), then from Theorem 3, we obtain that G becomes an 2 random variable with p degrees of freedom [33].”
Multivariate Survival Modelling: A Unified Approach with Copulas (2001, background): “It is defined by ρ (T1, T2) = cov (T1, T2) √ var (T1) var (T2) (99) with cov (T1, T2) = ∫ ∞ 0 ∫ ∞ 0 (S (t1, t2)− S1 (t1)S2 (t2)) dt1 dt2 (100) and var (Tn) = 2 ∫ ∞ 0 tSn (t) dt− [∫ ∞ 0 Sn (t) dt ]2 (101) The Pearson correlation is an appropriate measure of the dependence when the random variables ha”
Consistent inference in fixed-effects stochastic frontier models (2017, methodology): “Following Gouriéroux & Monfort (1991), under the regularity conditions ensuring the large sample properties of the MMLE, the resulting marginal maximum simulated likelihood estimator (MMSLE) is consistent and asymptotically equivalent to the MMLE as n→∞ and G→∞ with √ n/G→ 0.12 It then follows that”
Exponential behavior in the presence of dependence in risk theory (2006, background): “Other bivariate distributions that lead to polynomial equations of low order for ω include Freund’s bivariate exponential distribution (order three) and the bivariate gamma of Cheriyan and Ramabhadran (order two) (see [9] for their definitions).”
The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks (2011, methodology): “We refer the reader to Kotz et al. (2000) for a general account on FGM distribution functions, and to Tang and Vernic (2007) and Cossette et al. (2008) for applications of FGM distribution functions to risk theory.”
SKEW-NORMALITY IN STOCHASTIC FRONTIER ANALYSIS (2003, neutral): “where: C−1 = Φq (0; ν, ∆ + DΣD′) , (12) where φp (· ; μ, Σ) and Φp (· ; μ, Σ) denote the p.”