| |||||||

μ |
Length, width, height (etc.) means. • | ||||||

σ |
Respective standard deviations. • | ||||||

Ρ(capital ρ) |
Correlation matrix. • | ||||||

p_{low}, p_{upp} |
Quantiles. • | ||||||

N, .seed |
10 ^ |
N. of items ("lot size"), random no. gener.
seed. • | |||||

tol, klass | Tolerance, n. of histogram classes. • | ||||||

Show values | Shows the coordinates of the graph. • | ||||||

Simulates, via Monte Carlo,
the (possibly hyper) In order to simulate correlated variables, compute (here, for Gaussians):
*Covariance matrix*,**C**('cov_mat' in the results), as*c*=_{ij}*σ*,_{i}σ_{j}ρ_{ij}*i*,*j*= 1..*n*;- Vector
**g**= Φ^{inv}(**r**), with**r**a uniform random vector; - Vector
**d**=**L**_{C}**g**, with**L**_{C}= Chol(**C**), such that**C**=**L**_{C}**L**_{C}^{T}(not the 'L D L' Cholesky factorization); and - Vector
**x**=**μ**+**d**.
The Cholesky decomposition can be independently computed in this same site. ( From the quantiles,
(
Some theoretical values and the simulated results are given, and a plot is shown for the (simulated) 'pdf' and 'cdf'. Other suggested data: correlation34. | |||||||

References: |
Plate: CorrelatedBrick | ||||||

• Google: "parallelepiped" • Rowland, Todd and Weisstein, Eric W. "Parallelepiped." From MathWorld--A Wolfram Web Resource. • Wikipedia "Cuboid ("brick") (rectangular —). • Google: simulation correlated variables; generating correlated random variables using cholesky decomposition • Google: Cholesky decomposition (Cholesky factorization) • Haugh, Martin, The Monte Carlo framework, .... • 1909-08-15: Krylov, Aleksey Nikolaevich
(Алекс |

http://web.tecnico.ulisboa.pt/~mcasquilho/compute/or/Fx-correlatedBricks.phpCreated: 2017-08-15 — Last modified: 2017-09-27 |