doubleparetolognormal_plt function

Double-Pareto Lognormal coefficients of power-law transformed Double-Pareto Lognormal

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

doubleparetolognormal_plt(
  shape1 = 1.5,
  shape2 = 1.5,
  meanlog = -0.5,
  sdlog = 0.5,
  a = 1,
  b = 1,
  inv = FALSE
)

Arguments

• shape1, shape2, meanlog, sdlog: Shapes, mean and variance of the Double-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.

Returns

Returns a named list containing

• coefficients: Named vector of coefficients

Comparing probabilites of power-law transformed transformed variables pdoubleparetolognormal(3,shape1 = 1.5, shape2 = 3, meanlog = -0.5, sdlog = 0.5) coeff = doubleparetolognormal_plt(shape1 = 1.5, shape2 = 3, meanlog = -0.5, sdlog = 0.5,a=5,b=7)$coefficients pdoubleparetolognormal(5*3^7,shape1=coeff[["shape1"]],shape2=coeff[["shape2"]],meanlog=coeff[["meanlog"]],sdlog=coeff[["sdlog"]])

pdoubleparetolognormal(5*0.9^7,shape1 = 1.5, shape2 = 3, meanlog = -0.5, sdlog = 0.5) coeff = doubleparetolognormal_plt(shape1 = 1.5, shape2 = 3, meanlog = -0.5, sdlog = 0.5,a=5,b=7, inv=TRUE)$coefficients pdoubleparetolognormal(0.9,shape1=coeff[["shape1"]],shape2=coeff[["shape2"]],meanlog=coeff[["meanlog"]],sdlog=coeff[["sdlog"]])

Details

If the random variable y is Double-Pareto Lognormal distributed with mean meanlog and standard deviation sdlog, then the power-law transformed variable

is Double-Pareto Lognormal distributed with $shape1*b, \frac{meanlog-log(a)}{b}, \frac{sdlog}{b}, shape2*b$.