15_PD_normal: Normal Distributions

In bivariate: Bivariate Probability Distributions

Description

Bivariate and trivariate normal distributions.

Usage

#normal bivariate (PDF and CDF), sd/cor
nbvpdf (mean.X=0, mean.Y=0, sd.X=1, sd.Y=1, cor=0)
nbvcdf (mean.X=0, mean.Y=0, sd.X=1, sd.Y=1, cor=0)

#normal bivariate (PDF and CDF), var/cov
nbvpdf.2 (mean.X=0, mean.Y=0, var.X=1, var.Y=1, cov=0)
nbvcdf.2 (mean.X=0, mean.Y=0, var.X=1, var.Y=1, cov=0)

#normal trivariate (PDF only)
ntvpdf (mean.X=0, mean.Y=0, mean.Z=0,
    sd.X=1, sd.Y=1, sd.Z=1,
    cor.XY=0, cor.XZ=0, cor.YZ=0)
ntvpdf.2 (mean.X=0, mean.Y=0, mean.Z=0,
    var.X=1, var.Y=1, var.Z=1,
    cov.XY=0, cov.XZ=0, cov.YZ=0)

Arguments

mean.X, mean.Y, mean.Z	Numeric values, giving the means of X, Y and Z.
sd.X, sd.Y, sd.Z	Positive numeric values, giving the standard deviations of X, Y and Z.
var.X, var.Y, var.Z	Positive numeric values, giving the variances of X, Y and Z.
cor	Numeric value, giving the correlation between X and Y.
cov	Numeric value, giving the covariance between X and Y.
cor.XY, cor.XZ, cor.YZ	Numeric values, giving the pairwise correlations between X, Y and Z.
cov.XY, cov.XZ, cov.YZ	Numeric values, giving the pairwise covariances between X, Y and Z.

Details

Note that the resulting covariance matrix needs to be a positive definite matrix.
Also, in the bivariate case, both sd/variance parameters need to be positive, and the absolute correlation needs to be less than one.

Note that the misc3d package needs to be installed and loaded, in order to plot the trivariate normal distribution.

Value

Self-referencing S4-based function objects.

Refer to Function Objects.

References

Refer to the vignette for an overview, references, theoretical background and better examples.

See Also

Uniform
For uniform distributions.

Binomial, Poisson and Categorical
For other probability distributions of discrete random variables.

Bimodal, Dirichlet and Nonparametric
For other probability distributions of continuous random variables.

Main Plotting Functions

Random Numbers
For bivariate and trivariate normal random numbers.

Density Matrices

Examples

f <- nbvpdf ()

plot (f)
f (0, 0)

bivariate documentation built on April 11, 2021, 9:06 a.m.