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.

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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