nnspat (version 0.1.2)

bvnorm.pdf: pdf of the Bivariate Normal Distribution

Description

Computes the value of the probability density function (i.e., density) of the bivariate normal distribution at the specified point X, with mean mu and standard deviations of the first and second components being \(s_1\) and \(s_2\) (denoted as s1 and s2 in the arguments of the function, respectively) and correlation between them being rho (i.e., the covariance matrix is \(\Sigma=S\) where \(S_{11}=s_1^2\), \(S_{22}=s_2^2\), \(S_{12}=S_{21}=s_1 s_2 rho\)).

Usage

bvnorm.pdf(X, mu = c(0, 0), s1 = 1, s2 = 1, rho = 0)

Value

The value of the probability density function (i.e., density) of the bivariate normal distribution at the specified point X, with mean mu and standard deviations of the first and second components being \(s_1\)

and \(s_2\) and correlation between them being rho.

Arguments

X

A set of 2D points of size \(n\) (i.e an \(n \times 2\) matrix or array) at which the density of the bivariate normal distribution is to be computed.

mu

A \(1 \times 2\) vector of real numbers representing the mean of the bivariate normal distribution, default=\((0,0)\).

s1, s2

The standard deviations of the first and second components of the bivariate normal distribution, with default is 1 for both

rho

The correlation between the first and second components of the bivariate normal distribution with default=0.

Author

Elvan Ceyhan

See Also

mvrnorm

Examples

mu<-c(0,0)
s1<-1
s2<-1
rho<-.5

n<-5
Xp<-cbind(runif(n),runif(n))
bvnorm.pdf(Xp,mu,s1,s2,rho)