invpareto_plt function

Inverse Pareto coefficients after power-law transformation

Coefficients of a power-law transformed Inverse Pareto distribution

invpareto_plt(xmax = 5, k = 1.5, a = 1, b = 1, inv = FALSE)

Arguments

• xmax, k: Scale and shape of the Inverse Pareto distribution, defaults to 5 and 1.5 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 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"]])

Details

If the random variable x is Inverse Pareto-distributed with scale xmin and shape k, then the power-law transformed variable

is Inverse Pareto distributed with scale $( \frac{xmin}{a})^{\frac{1}{b}}$ and shape $b*k$.