leftparetolognormal_plt {distributionsrd} | R Documentation |
Coefficients of a power-law transformed Left-Pareto Lognormal distribution
leftparetolognormal_plt( shape1 = 1.5, meanlog = -0.5, sdlog = 0.5, a = 1, b = 1, inv = FALSE )
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. |
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} .
Returns a named list containing
Named vector of coefficients
## 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"]])