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

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.

Value

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

Note

The functions expect the distribution parameters in a vector, rather than as separate arguments as in the standard R distribution functions pnorm, qnorm, etc.

See Also

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

qlnorm for the standard R version 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))
# 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)))

Results