# cdfln3: Three-parameter lognormal distribution In lmom: L-Moments

 cdfln3 R Documentation

## 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).

### 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.

### 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.

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)))


lmom documentation built on Aug. 29, 2023, 9:07 a.m.