On the concavity of multivariate probability distribution functions

被引：6
|
作者：
Prékopa, A [1 ]
机构：
[1] Rutgers Ctr Operat Res, RUTCOR, Piscataway, NJ 08854 USA
来源：
OPERATIONS RESEARCH LETTERS | 2001年 / 29卷 / 01期
关键词：
probability distribution; normal distribution; Dirichlet distribution; concavity; stochastic programming;
D O I：
10.1016/S0167-6377(01)00070-0
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariate probability distribution functions too. The result has important application, e.g., in probabilistic constrained stochastic programming problems. 2001 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：1 / 4
页数：4
相关论文
共 50 条
  • [1] DISTRIBUTION-FUNCTIONS AND LOG-CONCAVITY
    FINNER, H
    ROTERS, M
    [J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1993, 22 (08) : 2381 - 2396
  • [2] Monge property and bounding multivariate probability distribution functions with given marginals and covariances
    Hou, Xiaoling
    Prekopa, Andras
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2007, 18 (01) : 138 - 155
  • [3] Hierarchical Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution Functions
    Pambabay-Calero, Johny
    Bauz-Olvera, Sergio
    Nieto-Librero, Ana
    Sanchez-Garcia, Ana
    Galindo-Villardon, Puri
    [J]. MATHEMATICS, 2021, 9 (11)
  • [4] ON THE PROBABILITY FUNCTION IN A NORMAL MULTIVARIATE DISTRIBUTION
    VARMA, RS
    [J]. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1952, 5 (03): : 361 - 362
  • [5] On Computing the Multivariate Poisson Probability Distribution
    Cekyay, Bora
    Frenk, J. B. G.
    Javadi, Sonya
    [J]. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2023, 25 (03)
  • [6] Probability integrals of the multivariate t distribution
    Nadarajah, Saralees
    Kotz, Samuel
    [J]. INTERNATIONAL STATISTICAL REVIEW, 2008, 76 (01) : 58 - 88
  • [7] On Computing the Multivariate Poisson Probability Distribution
    Bora Çekyay
    J.B.G. Frenk
    Sonya Javadi
    [J]. Methodology and Computing in Applied Probability, 2023, 25
  • [8] On the Riesz estimation of multivariate probability density functions
    Reyes, Camilo
    Ossandon, Sebastian
    Barrientos, Mauricio
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (16) : 9248 - 9265
  • [9] THRESHOLD FOR LOG-CONCAVITY FOR PROBABILITY GENERATING FUNCTIONS AND ASSOCIATED MOMENT INEQUALITIES
    KEILSON, J
    [J]. ANNALS OF MATHEMATICAL STATISTICS, 1972, 43 (05): : 1702 - &
  • [10] Distribution functions of multivariate copulas
    Rodríguez-Lallena, JA
    Ubeda-Flores, M
    [J]. STATISTICS & PROBABILITY LETTERS, 2003, 64 (01) : 41 - 50
12345