distributionsrd (version 0.0.6)

pareto_plt: Pareto coefficients after power-law transformation

Description

Coefficients of a power-law transformed Pareto distribution

Usage

pareto_plt(xmin = 1, k = 2, a = 1, b = 1, inv = FALSE)

Arguments

xmin, k

Scale and shape of the Pareto distribution, defaults to 1 and 2 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.

Value

Returns a named list containing

coefficients

Named vector of coefficients

Details

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

$$ y = ax^b $$

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

Examples

# NOT RUN {
## Comparing probabilites of power-law transformed transformed variables
ppareto(3, k = 2, xmin = 2)
coeff <- pareto_plt(xmin = 2, k = 2, a = 5, b = 7)$coefficients
ppareto(5 * 3^7, k = coeff[["k"]], xmin = coeff[["xmin"]])

ppareto(5 * 0.9^7, k = 2, xmin = 2)
coeff <- pareto_plt(xmin = 2, k = 2, a = 5, b = 7, inv = TRUE)$coefficients
ppareto(0.9, k = coeff[["k"]], xmin = coeff[["xmin"]])

## Comparing the first moments and sample means of power-law transformed variables for
#large enough samples
x <- rpareto(1e5, k = 2, xmin = 2)
coeff <- pareto_plt(xmin = 2, k = 2, a = 2, b = 0.5)$coefficients
y <- rpareto(1e5, k = coeff[["k"]], xmin = coeff[["xmin"]])
mean(2 * x^0.5)
mean(y)
mpareto(r = 1, k = coeff[["k"]], xmin = coeff[["xmin"]], lower.tail = FALSE)
# }