LogitNormal function

Logit Normal Distribution

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

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.

Returns

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.

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.

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)

References

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

See Also

Distributions

Author(s)

Ivan Svetunkov, ivan@svetunkov.com