scholarly journals Quantification of pattern recognition quality by multivariate normal distribution functions

2008 ◽  
Vol 48 (3) ◽  
pp. 209-217
Author(s):  
P. Serapinas
Keyword(s):  
Pattern Recognition ◽  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Distribution Functions ◽  
Multivariate Normal ◽  
Recognition Quality

scholarly journals Calculations Involving the Multivariate Normal and Multivariate t Distributions with and without Truncation

2018 ◽  
Vol 18 (4) ◽  
pp. 826-843
Author(s):  
Michael J. Grayling ◽  
Adrian P. Mander
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Distribution Functions ◽  
Multivariate Normal ◽  
Random Vectors ◽  
Multivariate T Distribution ◽  
T Distribution ◽  
Multivariate T

In this article, we present a set of commands and Mata functions to evaluate different distributional quantities of the multivariate normal distribution and a particular type of noncentral multivariate t distribution. Specifically, their densities, distribution functions, equicoordinate quantiles, and pseudo–random vectors can be computed efficiently, in either the absence or the presence of variable truncation.

Upper bounds for the probability of a union by multitrees

2001 ◽  
Vol 33 (2) ◽  
pp. 437-452 ◽  
Author(s):  
József Bukszár
Keyword(s):  
Graph Theory ◽  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Multivariate Normal ◽  
Common Generalization

The problem of finding bounds for P(A1 ∪ ⋯ ∪ An) based on P(Ak1 ∩ ⋯ ∩ Aki) (1 ≤ k1 < ⋯ < ki ≤ n, i = 1,…,d) goes back to Boole (1854), (1868) and Bonferroni (1937). In this paper upper bounds are presented using methods in graph theory. The main theorem is a common generalization of the earlier results of Hunter, Worsley and recent results of Prékopa and the author. Algorithms are given to compute bounds. Examples for bounding values of multivariate normal distribution functions are presented.

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