lmom (version 1.1)

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))

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).

Value

• cdfln3 gives the distribution function; qualn3 gives the quantile function.

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 $$y=(\log(x-\zeta)-\mu)/\sigma$$ and $\Phi(y)$ is the distribution function of the standard normal distribution.

See Also

cdfgno for the generalized normal distribution, a more general form of the three-parameter lognormal distribution. qlnorm for the standard Rversion of the two-parameter lognormal distribution.

Examples

# 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), c(0,0,1))
# 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)))