Coefficients of a power-law transformed Fr<U+00E9>chet distribution
frechet_plt(shape = 1.5, scale = 0.5, a = 1, b = 1, inv = FALSE)Scale and shape of the Fr<U+00E9>chet distribution, defaults to 1.5 and 0.5 respectively.
constant and power of power-law transformation, defaults to 1 and 1 respectively.
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 a named list containing
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"]])
If the random variable x is Fr<U+00E9>chet distributed with scale shape and shape scale, then the power-law transformed variable
$$ y = ax^b $$
is Fr<U+00E9>chet distributed with scale \( \left( \frac{scale}{a}\right)^{\frac{1}{b}} \) and shape \(b*k\).