invpareto_plt {distributionsrd} R Documentation

## Inverse Pareto coefficients after power-law transformation

### Description

Coefficients of a power-law transformed Inverse Pareto distribution

### Usage

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.

### Details

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.

### Value

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"]])

[Package distributionsrd version 0.0.6 Index]