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Properties of the LogNormal distribution

The LogNormal distribution can be characterized by the exponent of its parameters:

  • exp(μ): the median
  • exp(σ): the multiplicative standard deviation $\sigma^*$.

Function σstar returns the multiplicative standard deviation.

A distribution can be specified by taking the log of median and $\sigma^*$

d = LogNormal(log(2), log(1.2))
σstar(d) == 1.2

Alternatively the distribution can be specified by its mean and $\sigma^*$ using type Σstar

d = fit(LogNormal, 2, Σstar(1.2))
(mean(d), σstar(d)) == (2, 1.2)

Detailed API

LogNormals.σstar — Method
σstar(d)

Get the multiplicative standard deviation of LogNormal distribution d.

Arguments

  • d: The type of distribution to fit

Examples

d = LogNormal(2,log(1.2))
σstar(d) == 1.2
source
StatsBase.fit — Method
fit(D, mean, σstar)

Fit a statistical distribution of type D to mean and multiplicative standard deviation.

Arguments

  • D: The type of distribution to fit
  • mean: The moments of the distribution
  • σstar::Σstar: The multiplicative standard deviation

See also σstar, Σstar.

Examples

d = fit(LogNormal, 2, Σstar(1.1));
(mean(d), σstar(d)) == (2, 1.1)
source
LogNormals.Σstar — Type
Σstar

Represent the multiplicative standard deviation of a LogNormal distribution.

Supports dispatch of fit. Invoking the type as a function returns its single value.

Examples

a = Σstar(4.2)
a() == 4.2
source