Distribution

Shape by multiplicative standard deviation

Density distributions of lognormal distributions (lines) get closer to normal density shaded area) as multiplicative standard deviation \(\sigma^*\) decreases down to 1.2 for same \(\mu^* = 1\).

Density, distribution function, quantile function and random generation

Are already provided with the base stats package. See ?dlnorm.

Expected value, Variance, Mode, and Median

getLognormMode(mu = 0.6,sigma = 0.5)

## [1] 1.419068

getLognormMedian(mu = 0.6,sigma = 0.5)

## [1] 1.822119

(theta <- getLognormMoments(mu = 0.6,sigma = 0.5))

##          mean      var        cv
## [1,] 2.064731 1.210833 0.5329404

Mode < Median < Mean for the right-skewed distribution.

The return type of getLognormMoments is a matrix.

Parameter Estimation from moments

moments <- cbind(mean = c(1,1), var = c(0.2, 0.3)^2 )
(theta <- getParmsLognormForMoments( moments[,1], moments[,2]))

##               mu     sigma
## [1,] -0.01961036 0.1980422
## [2,] -0.04308885 0.2935604

The larger the spread, the more skewed is the distribution, here both with an expected value of one.

Using the lognorm package

Distribution

Shape by multiplicative standard deviation

Density, distribution function, quantile function and random generation

Expected value, Variance, Mode, and Median

Parameter Estimation from moments