LogitNormal: Logit Normal Distribution

In config-i1/greybox: Toolbox for Model Building and Forecasting

Logit Normal Distribution

Description

Density, cumulative distribution, quantile functions and random number generation for the distribution that becomes normal after the Logit transformation.

Usage

dlogitnorm(q, mu = 0, sigma = 1, log = FALSE)

plogitnorm(q, mu = 0, sigma = 1)

qlogitnorm(p, mu = 0, sigma = 1)

rlogitnorm(n = 1, mu = 0, sigma = 1)

Arguments

q	vector of quantiles.
mu	vector of location parameters (means).
sigma	vector of scale parameters.
log	if TRUE, then probabilities are returned in logarithms.
p	vector of probabilities.
n	number of observations. Should be a single number.

Details

The distribution has the following density function:

f(y) = 1/(sqrt(2 pi) y (1-y)) exp(-(logit(y) -mu)^2 / (2 sigma^2))

where y is in (0, 1) and logit(y) =log(y/(1-y)).

Both plogitnorm and qlogitnorm are returned for the lower tail of the distribution.

All the functions are defined for the values between 0 and 1.

Value

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

• dlogitnorm returns the density function value for the provided parameters.

• plogitnorm returns the value of the cumulative function for the provided parameters.

• qlogitnorm returns quantiles of the distribution. Depending on what was provided in p, mu and sigma, this can be either a vector or a matrix, or an array.

• rlogitnorm returns a vector of random variables generated from the logitnorm distribution. Depending on what was provided in mu and sigma, this can be either a vector or a matrix or an array.

Author(s)

Ivan Svetunkov, [e-mail]

References

• Mead, R. (1965). A Generalised Logit-Normal Distribution. Biometrics, 21 (3), 721–732. doi: 10.2307/2528553

See Also

Distributions

Examples

x <- dlogitnorm(c(-1000:1000)/200, 0, 1)
plot(c(-1000:1000)/200, x, type="l")

x <- plogitnorm(c(-1000:1000)/200, 0, 1)
plot(c(-1000:1000)/200, x, type="l")

qlogitnorm(c(0.025,0.975), 0, c(1,2))

x <- rlogitnorm(1000, 0, 1)
hist(x)

config-i1/greybox documentation built on Dec. 12, 2024, 1:42 p.m.