| 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 \left( \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"]])