cnormal: Complex Normal Distribution

In config-i1/complex: Time Series Analysis and Forecasting Using Complex Variables

Complex Normal Distribution

Description

Density, cumulative distribution, quantile functions and random number generation for the Complex Normal distribution.

Usage

dcnorm(q, mu = 0, sigma2 = 1, varsigma2 = 0, log = FALSE, ...)

pcnorm(lower = -Inf, upper = Inf, mu = 0, sigma2 = 1, varsigma2 = 0,
  ...)

qcnorm(p, mu = 0, sigma2 = 1, varsigma2 = 0, ...)

rcnorm(n = 1, mu = 0, sigma2 = 1, varsigma2 = 0, ...)

Arguments

q	vector of quantiles.
mu	vector of location parameters (means).
sigma2	vector of conjugate variances.
varsigma2	vector of direct variances.
log	if TRUE, then probabilities are returned in logarithms.
...	Other parameters passed to the mvtnorm functions.
lower	complex number of lower limits of length n.
upper	complex number of upper limits of length n.
p	vector of probabilities.
n	number of observations. Should be a single number.

Details

Complex Normal distribution is a special case of a multivariate normal distribution, which is parametrised using direct and conjugate variances instead of the covariance matrix.

These functions are just wrappers for the functions from the mvtnorm package.

Note that sigma2 and varsigma2 are the conjugate and direct variances, not the standard deviations!

Both pcnorm and qcnorm are returned for the lower tail of the distribution.

All the functions are defined for non-negative values only.

Value

Depending on the function, various things are returned (usually either vector or scalar):

• dcnorm returns the density function values for the provided parameters, based on Mvnorm function.

• pcnorm returns the values of the cumulative function for the provided parameters, based on pmvnorm function.

• qcnorm returns quantiles of the distribution, based on qmvnorm function.

• rcnorm returns a vector of random variables generated from the Complex Normal distribution, based on Mvnorm function.

Author(s)

Ivan Svetunkov, [e-mail]

Examples

dcnorm(89+90i, 100+100i, 2, 1+1i)
pcnorm(90+90i, 110+110i, 100+100i, 2, 1+1i)
qcnorm(0.95, 100+100i, 2, 1+1i)
rcnorm(1000, 100+100i, 2, 1+1i)

config-i1/complex documentation built on Oct. 9, 2024, 3:04 p.m.