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

 LNORM3 R Documentation

## Three-Parameter Lognormal Distribution

### 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

```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

```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)
```

FAdist documentation built on March 18, 2022, 5:24 p.m.