The logit-Normal distribution

Density, distribution, and quantile functions for the logit-normal distribution: the distribution of plogis(z) where z is normal with mean mu and standard deviation sigma. It is the natural marginal for a covariate reported as a proportion on (0, 1), such as percent body surface area.

Usage

dlogitnorm(x, mu = 0, sigma = 1, log = FALSE, ..., mean, sd)

plogitnorm(q, mu = 0, sigma = 1, ..., mean, sd)

qlogitnorm(p, mu = 0, sigma = 1, ..., mean, sd)

Arguments

x, q

Vector of quantiles, in (0, 1).

mu, sigma

Location and scale, on the logit scale.

log

Return the log density. Positional, as in stats::dnorm().

...

For plogitnorm() and qlogitnorm(), passed to the underlying stats normal function (stats::pnorm(), stats::qnorm()), so lower.tail and log.p work as usual. dlogitnorm() builds its density from stats::dnorm() and a Jacobian rather than delegating, so it has nothing to forward and refuses anything passed here; in its signature ... serves only to keep mean and sd from matching positionally.

mean, sd

Mean and standard deviation on the (0, 1) scale, overriding mu and sigma when both are supplied.

p

Vector of probabilities.

Value

A numeric vector.

Details

For convenience the distribution may be given by its mean and sd on the natural (0, 1) scale instead of mu and sigma on the logit scale. There is no closed form for that reparameterization, so mu and sigma are found numerically; supply mu / sigma directly if you have them.

See also

distr(), add_integration(), GammaDist

Examples

qlogitnorm(0.5, mean = 0.34, sd = 0.19)
#> [1] 0.310708