distributions3 (version 0.1.2)

# LogNormal: 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 $$\mu$$ in textbooks. Can be any real number. Defaults to 0.

log_sigma

The scale parameter, written $$\sigma$$ in textbooks. Can be any positive real number. Defaults to 1.

## Value

A LogNormal object.

## 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: $$\exp(\mu + \sigma^2/2)$$

Variance: $$[\exp(\sigma^2)-1]\exp(2\mu+\sigma^2)$$

Probability density function (p.d.f):

$$f(x) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp \left(-\frac{(\log x - \mu)^2}{2 \sigma^2} \right)$$

Cumulative distribution function (c.d.f):

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

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

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

## Examples

Run this code
# NOT RUN {
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)

# }


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