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)

log_mu | The location parameter, written \(\mu\) in textbooks.
Can be any real number. Defaults to |
---|---|

log_sigma | The scale parameter, written \(\sigma\) in textbooks.
Can be any positive real number. Defaults to |

A `LogNormal`

object.

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`

#> Lognormal distribution (log_mu = 0.3, log_sigma = 2)#> [1] 61.21089083 13.32648994 0.29256703 0.07317767 0.15153514 2.43630473 #> [7] 1.36857751 13.66478070 96.47421603 2.17208867#> [1] 0.09782712#> [1] -2.324553#> [1] 0.7064858#> [1] 3.852803