cdfln3: Three-parameter lognormal distribution

Description

Distribution function and quantile function of the three-parameter lognormal distribution.

Usage

cdfln3(x, para = c(0, 0, 1))
qualn3(f, para = c(0, 0, 1))

Value

cdfln3 gives the distribution function;

qualn3 gives the quantile function.

Arguments

x: Vector of quantiles.
f: Vector of probabilities.
para: Numeric vector containing the parameters of the distribution, in the order $\zeta, \mu, \sigma$ (lower bound, mean on log scale, standard deviation on log scale).

Details

The three-parameter lognormal distribution with lower bound $\zeta$, mean on log scale $\mu$, and standard deviation on log scale $\sigma$ has distribution function $$F(x)=\Phi(y),$$ $x>0$, where $$y=\lbrace\log(x - \zeta)-\mu\rbrace/\sigma$$ and $\Phi(y)$ is the distribution function of the standard normal distribution.

Examples

Run this code

# Random sample from three-parameter lognormal distribution
# with parameters zeta=0, mu=1, sigma=0.5.
qualn3(runif(100), c(0,1,0.5))

## Functions for the three-parameter lognormal distribution can
## also be used with the two-parameter lognormal distribution
# Generate a random sample from a standard lognormal distribution
xx <- qualn3(runif(50))
# Fit 2-parameter LN distribution
pelln3(samlmu(xx), bound=0)
# Fit 2-parameter LN distribution "in log space",
# i.e. fit normal distribution to log-transformed data
pelnor(samlmu(log(xx)))