# Using the lognorm package

# 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.