# LogNormal: Create a LogNormal distribution In distributions3: Probability Distributions as S3 Objects

 LogNormal R Documentation

## Create a LogNormal distribution

### Description

A random variable created by exponentiating a Normal() distribution. Taking the log of LogNormal data returns in Normal() data.

### Usage

LogNormal(log_mu = 0, log_sigma = 1)


### Arguments

 log_mu The location parameter, written μ in textbooks. Can be any real number. Defaults to 0. log_sigma The scale parameter, written σ in textbooks. Can be any positive real number. Defaults to 1.

### Details

We recommend reading this documentation on https://alexpghayes.github.io/distributions3/, where the math will render with additional detail and much greater clarity.

In the following, let X be a LogNormal random variable with success probability p = p.

Support: R^+

Mean: \exp(μ + σ^2/2)

Variance: [\exp(σ^2)-1]\exp(2μ+σ^2)

Probability density function (p.d.f):

f(x) = \frac{1}{x σ √{2 π}} \exp (-\frac{(\log x - μ)^2}{2 σ^2})

Cumulative distribution function (c.d.f):

F(x) = \frac{1}{2} + \frac{1}{2√{pi}}\int_{-x}^x e^{-t^2} dt

Moment generating function (m.g.f): Undefined.

### Value

A LogNormal object.

Other continuous distributions: Beta(), Cauchy(), ChiSquare(), Erlang(), Exponential(), FisherF(), Frechet(), GEV(), GP(), Gamma(), Gumbel(), Logistic(), Normal(), RevWeibull(), StudentsT(), Tukey(), Uniform(), Weibull()

### Examples


set.seed(27)

X <- LogNormal(0.3, 2)
X

random(X, 10)

pdf(X, 2)
log_pdf(X, 2)

cdf(X, 4)
quantile(X, 0.7)


distributions3 documentation built on Sept. 7, 2022, 5:07 p.m.