distributionsrd (version 0.0.6)

lnorm_plt: Log Normal coefficients of power-law transformed log normal

Description

Coefficients of a power-law transformed log normal distribution

Usage

lnorm_plt(meanlog = 0, sdlog = 1, a = 1, b = 1, inv = FALSE)

Arguments

meanlog, sdlog

mean and standard deviation of the log normal distributed variable, defaults to 0 and 1 respectively.

a, b

constant and power of power-law transformation, defaults to 1 and 1 respectively.

inv

logical indicating whether coefficients of the outcome variable of the power-law transformation should be returned (FALSE) or whether coefficients of the input variable being power-law transformed should be returned (TRUE). Defaults to FALSE.

Value

Returns a named list containing

coefficients

Named vector of coefficients

## Comparing probabilites of power-law transformed transformed variables plnorm(3,meanlog=-0.5,sdlog=0.5) coeff = lnorm_plt(meanlog=-0.5,sdlog=0.5,a=5,b=7)$coefficients plnorm(5*3^7,meanlog=coeff[["meanlog"]],sdlog=coeff[["sdlog"]])

plnorm(5*0.8^7,meanlog=-0.5,sdlog=0.5) coeff = lnorm_plt(meanlog=-0.5,sdlog=0.5,a=5,b=7,inv=TRUE)$coefficients plnorm(0.8,meanlog=coeff[["meanlog"]],sdlog=coeff[["sdlog"]])

## Comparing the first moments and sample means of power-law transformed variables for large enough samples x = rlnorm(1e5,meanlog=-0.5,sdlog=0.5) coeff = lnorm_plt(meanlog=-0.5,sdlog=0.5,a=2,b=0.5)$coefficients y = rlnorm(1e5,meanlog=coeff[["meanlog"]],sdlog=coeff[["sdlog"]]) mean(2*x^0.5) mean(y) mlnorm(r=1,meanlog=coeff[["meanlog"]],sdlog=coeff[["sdlog"]],lower.tail=FALSE)

Details

If the random variable y is log normally distributed with mean meanlog and standard deviation sdlog, then the power-law transformed variable

$$y=a{x}^b$$

is log normally distributed with mean $\frac{meanlog-ln(a)}{b}$ and standard deviation $\frac{sdlog}{b}$.