Coefficients of a power-law transformed Inverse Pareto distribution
invpareto_plt(xmax = 5, k = 1.5, a = 1, b = 1, inv = FALSE)Scale and shape of the Inverse Pareto distribution, defaults to 5 and 1.5 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 pinvpareto(3,k=2,xmax=5) coeff = invpareto_plt(xmax=5,k=2,a=5,b=7)$coefficients pinvpareto(5*3^7,k=coeff[["k"]],xmax=coeff[["xmax"]])
pinvpareto(5*0.9^7,k=2,xmax=5) coeff = invpareto_plt(xmax=5,k=2,a=5,b=7, inv=TRUE)$coefficients pinvpareto(0.9,k=coeff[["k"]],xmax=coeff[["xmax"]])
If the random variable x is Inverse Pareto-distributed with scale xmin and shape k, then the power-law transformed variable
$$ y = ax^b $$
is Inverse Pareto distributed with scale \( ( \frac{xmin}{a})^{\frac{1}{b}} \) and shape \(b*k\).