CRV.computeCov: CRV.computeCov

In AlecuMihai/ContinuousRV: Create and Manipulate Continue Random Variables

Description

Determina covarianta pentru doua v.a. continue X, Y cu repartitia comuna 'double.fun'.

Usage

CRV.computeCov(X, Y, double.fun)

Arguments

X	v.a. continua construita utilizand ContinuousRV::CRV.
Y	v.a. continua construita utilizand ContinuousRV::CRV.
double.fun	Functie cu doua argumente - (x, y). - densitatea comuna a celor doua v.a.

Value

Cov(X, Y)

Note

Pentru determinarea covariantei se foloseste urmatoare metoda: inner.fun <- function(x, y) {
x * y * double.fun(x, y)
}

M_X_Y <- integrate(function(y) {
sapply(y, function(y) {
integrate(function(x) inner.fun(x, y), X@lo, X@hi)$value
})
}, Y@lo, Y@hi)$value

M_X <- CRV.computeEV(X)
M_Y <- CRV.computeEV(Y)

out <- M_X_Y - M_X * M_Y


unde M_X, M_Y, reprezinta media v.a. X, respectiv Y;

Examples

X <- CRV(fun = function(x){(2197/5412) * (x**2 + 3*x + 1)}, lo = 0, hi = 12/13)
Y <- CRV(fun = function(x) {20000/7708481 * (2 * x**3 - 2)}, lo = 1, hi = 53/10)
com <- function(x, y) {
x + y
}
CRV.computeCov(X = X, Y = Y, double.fun = com)

AlecuMihai/ContinuousRV documentation built on Dec. 17, 2021, 7:48 a.m.