leftparetolognormal_plt {distributionsrd} R Documentation

## 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.

### 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} .

### Value

Returns a named list containing

coefficients

Named vector of coefficients

### Examples


## 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"]])


[Package distributionsrd version 0.0.6 Index]