frechet_plt function

Fréchet coefficients after power-law transformation

Coefficients of a power-law transformed Fréchet distribution

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.

Returns

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"]])

Details

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

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