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

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. 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):

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

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, Exponential, FisherF, Gamma, Logistic, Normal, StudentsT, Tukey, Uniform, Weibull

## Examples


set.seed(27)

X <- LogNormal(0.3, 2)
X#> Lognormal distribution (log_mu = 0.3, log_sigma = 2)
random(X, 10)#>  [1] 61.21089083 13.32648994  0.29256703  0.07317767  0.15153514  2.43630473
#>  [7]  1.36857751 13.66478070 96.47421603  2.17208867
pdf(X, 2)#> [1] 0.09782712log_pdf(X, 2)#> [1] -2.324553
cdf(X, 4)#> [1] 0.7064858quantile(X, 0.7)#> [1] 3.852803