dist.Log.Normal.Precision {LaplacesDemon} | R Documentation |

## Log-Normal Distribution: Precision Parameterization

### Description

These functions provide the density, distribution function, quantile
function, and random generation for the univariate log-normal
distribution with mean `\mu`

and precision `\tau`

.

### Usage

```
dlnormp(x, mu, tau=NULL, var=NULL, log=FALSE)
plnormp(q, mu, tau, lower.tail=TRUE, log.p=FALSE)
qlnormp(p, mu, tau, lower.tail=TRUE, log.p=FALSE)
rlnormp(n, mu, tau=NULL, var=NULL)
```

### Arguments

`x` , `q` |
These are each a vector of quantiles. |

`p` |
This is a vector of probabilities. |

`n` |
This is the number of observations, which must be a positive integer that has length 1. |

`mu` |
This is the mean parameter |

`tau` |
This is the precision parameter |

`var` |
This is the variance parameter, which must be positive. Tau and var cannot be used together |

`log` , `log.p` |
Logical. If |

`lower.tail` |
Logical. If |

### Details

Application: Continuous Univariate

Density:

`p(\theta) = \sqrt{\frac{\tau}{2\pi}} \frac{1}{\theta} \exp(-\frac{\tau}{2} (\log(\theta - \mu))^2)`

Inventor: Carl Friedrich Gauss or Abraham De Moivre

Notation 1:

`\theta \sim \mathrm{Log-}\mathcal{N}(\mu, \tau^{-1})`

Notation 2:

`p(\theta) = \mathrm{Log-}\mathcal{N}(\theta | \mu, \tau^{-1})`

Parameter 1: mean parameter

`\mu`

Parameter 2: precision parameter

`\tau > 0`

Mean:

`E(\theta) = \exp(\mu + \tau^{-1} / 2)`

Variance:

`var(\theta) = (\exp(\tau^{-1}) - 1)\exp(2\mu + \tau^{-1})`

Mode:

`mode(\theta) = \exp(\mu - \tau^{-1})`

The log-normal distribution, also called the Galton distribution, is
applied to a variable whose logarithm is normally-distributed. The
distribution is usually parameterized with mean and variance, or in
Bayesian inference, with mean and precision, where precision is the
inverse of the variance. In contrast, `Base R`

parameterizes the
log-normal distribution with the mean and standard deviation. These
functions provide the precision parameterization for convenience and
familiarity.

A flat distribution is obtained in the limit as
`\tau \rightarrow 0`

.

These functions are similar to those in `base R`

.

### Value

`dlnormp`

gives the density,
`plnormp`

gives the distribution function,
`qlnormp`

gives the quantile function, and
`rlnormp`

generates random deviates.

### Author(s)

Statisticat, LLC. software@bayesian-inference.com

### See Also

`dnorm`

,
`dnormp`

,
`dnormv`

, and
`prec2var`

.

### Examples

```
library(LaplacesDemon)
x <- dlnormp(1,0,1)
x <- plnormp(1,0,1)
x <- qlnormp(0.5,0,1)
x <- rlnormp(100,0,1)
#Plot Probability Functions
x <- seq(from=0.1, to=3, by=0.01)
plot(x, dlnormp(x,0,0.1), ylim=c(0,1), type="l", main="Probability Function",
ylab="density", col="red")
lines(x, dlnormp(x,0,1), type="l", col="green")
lines(x, dlnormp(x,0,5), type="l", col="blue")
legend(2, 0.9, expression(paste(mu==0, ", ", tau==0.1),
paste(mu==0, ", ", tau==1), paste(mu==0, ", ", tau==5)),
lty=c(1,1,1), col=c("red","green","blue"))
```

*LaplacesDemon*version 16.1.6 Index]