frechet_plt {distributionsrd} R Documentation

## Fréchet coefficients after power-law transformation

### Description

Coefficients of a power-law transformed Fréchet distribution

### Usage

frechet_plt(shape = 1.5, scale = 0.5, a = 1, b = 1, inv = FALSE)


### Arguments

 shape, scale Scale and shape of the Fréchet distribution, defaults to 1.5 and 0.5 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.

### Details

If the random variable x is Fréchet distributed with scale shape and shape scale, then the power-law transformed variable

y = ax^b

is Fréchet distributed with scale ≤ft( \frac{scale}{a}\right)^{\frac{1}{b}} and shape b*k.

### Value

Returns a named list containing

coefficients

Named vector of coefficients

## Comparing probabilites of power-law transformed transformed variables pfrechet(3,shape=2,scale=1) coeff = frechet_plt(shape=2,scale=1,a=5,b=7)$coefficients pfrechet(5*3^7,shape=coeff[["shape"]],scale=coeff[["scale"]]) pfrechet(5*0.8^7,shape=2,scale=1) coeff = frechet_plt(shape=2,scale=1,a=5,b=7,inv=TRUE)$coefficients pfrechet(0.8,shape=coeff[["shape"]],scale=coeff[["scale"]])

[Package distributionsrd version 0.0.6 Index]