distributionsrd (version 0.0.6)

leftparetolognormal_plt: Left-Pareto Lognormal coefficients of power-law transformed Left-Pareto Lognormal

Description

Coefficients of a power-law transformed Left-Pareto Lognormal distribution

Usage

leftparetolognormal_plt(
  shape1 = 1.5,
  meanlog = -0.5,
  sdlog = 0.5,
  a = 1,
  b = 1,
  inv = FALSE
)

Arguments

shape1, meanlog, sdlog

Shapes, mean and variance of the Left-Pareto Lognormal distribution 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 y is Left-Pareto Lognormal distributed with mean meanlog and standard deviation sdlog, then the power-law transformed variable

$$ y = ax^b $$

is Left-Pareto Lognormal distributed with \( shape1*b, \frac{meanlog-log(a)}{b}, \frac{sdlog}{b} \).

Examples

# NOT RUN {
## Comparing probabilites of power-law transformed transformed variables
pleftparetolognormal(3, shape1 = 1.5, meanlog = -0.5, sdlog = 0.5)
coeff <- leftparetolognormal_plt(shape1 = 1.5, meanlog = -0.5, sdlog = 0.5,
a = 5, b = 7)$coefficients
pleftparetolognormal(5 * 3^7, shape1 = coeff[["shape1"]], meanlog = coeff[["meanlog"]],
sdlog = coeff[["sdlog"]])

pleftparetolognormal(5 * 0.9^7, shape1 = 1.5, meanlog = -0.5, sdlog = 0.5)
coeff <- leftparetolognormal_plt(shape1 = 1.5, meanlog = -0.5, sdlog = 0.5, a = 5, b = 7,
inv = TRUE)$coefficients
pleftparetolognormal(0.9, shape1 = coeff[["shape1"]], meanlog = coeff[["meanlog"]],
 sdlog = coeff[["sdlog"]])
# }