# LNORM3: Three-Parameter Lognormal Distribution In FAdist: Distributions that are Sometimes Used in Hydrology

## Description

Density, distribution function, quantile function and random generation for the 3-parameter lognormal distribution with shape, scale, and threshold (or shift) parameters equal to `shape`, `scale`, and `thres`, respectively.

## Usage

 ```1 2 3 4``` ```dlnorm3(x,shape=1,scale=1,thres=0,log=FALSE) plnorm3(q,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE) qlnorm3(p,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE) rlnorm3(n,shape=1,scale=1,thres=0) ```

## Arguments

 `x,q` vector of quantiles. `p` vector of probabilities. `n` number of observations. `shape` shape parameter. `scale` scale parameter. `thres` threshold (or shift) parameter. `log,log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

## Details

If Y is a random variable distributed according to a normal distribution (with location(mean) and scale(standard deviation) parameters), then X = exp(Y)+m has a 3-parameter lognormal distribution with shape and scale parameters corresponding to the scale and location parameteres of Y, respectively; and threshold parameter m.

## Value

`dlnorm3` gives the density, `plnorm3` gives the distribution function, `qlnorm3` gives the quantile function, and `rlnorm3` generates random deviates.

`dnorm`, `pnorm`, `qnorm`, `rnorm`, `dlnorm`, `plnorm`, `qlnorm`, `rlnorm`

## Examples

 ```1 2 3 4 5``` ```m <- 100 x <- rlnorm3(10,1,0,m) dlnorm3(x,1,0,m) dlnorm(x-m,0,1) dnorm(log(x-m),0,1)/(x-m) ```

### Example output

``` [1] 0.4845318 0.6322110 0.6180881 0.2435706 0.6035988 0.6114316 0.3524868
[8] 0.5289494 0.6025743 0.1423993
[1] 0.4845318 0.6322110 0.6180881 0.2435706 0.6035988 0.6114316 0.3524868
[8] 0.5289494 0.6025743 0.1423993
[1] 0.4845318 0.6322110 0.6180881 0.2435706 0.6035988 0.6114316 0.3524868
[8] 0.5289494 0.6025743 0.1423993
```

FAdist documentation built on April 17, 2020, 1:24 a.m.