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

1 2 |

`x` |
Vector of quantiles. |

`f` |
Vector of probabilities. |

`para` |
Numeric vector containing the parameters of the distribution,
in the order |

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.

`cdfln3`

gives the distribution function;
`qualn3`

gives the quantile function.

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
# 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)))
``` |

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