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

## Description

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

## Usage

 1 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}{xσ√{2π}}\exp(-\frac{(\log x - μ)^2}{2σ^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, Exponential, FisherF, Gamma, Logistic, Normal, StudentsT, Tukey, Uniform, Weibull
  1 2 3 4 5 6 7 8 9 10 11 12 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)