pareto_plt {distributionsrd} | R Documentation |
Coefficients of a power-law transformed Pareto distribution
pareto_plt(xmin = 1, k = 2, a = 1, b = 1, inv = FALSE)
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. |
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.
Returns a named list containing
Named vector of coefficients
## 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)