Log-Normal Distribution — Log-Normal • anyFit

Three-parameter Log-Normal distribution with location $\mu$, scale $\beta$, and shape $\sigma$. The distribution is lower-bounded at $\mu$ and arises when the logarithm of $x - \mu$ follows a Normal distribution. Density, distribution, quantile, and random generation functions are provided via the FAdist package. Fitting is performed via closed-form L-moments through pelln3; an optional fixed lower bound is supported.

The probability density function is: $$f(x) = \frac{1}{(x-\mu) \sigma \sqrt{2\pi}} \exp\left(-\frac{\left(\ln\left(\frac{x-\mu}{\beta}\right)\right)^2}{2\sigma^2}\right), \quad x > \mu$$ where:

$\mu$ — location parameter (location)
$\beta$ — scale parameter (scale)
$\sigma$ — shape parameter (shape)

Usage

dlognorm(x, location = 0, scale, shape)

plognorm(q, location = 0, scale, shape)

qlognorm(p, location = 0, scale, shape)

rlognorm(n, location = 0, scale, shape)

Arguments

x, q: vector of quantiles.
location: location parameter.
scale: scale parameter.
shape: shape parameter.
p: vector of probabilities.
n: number of observations. If length(n) > 1, the length is taken as the number required.