doubleparetolognormal_plt {distributionsrd} | R Documentation |

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

### Description

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

### Usage

```
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. |

### Details

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

` y = ax^b `

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

.

### Value

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"]])

*distributionsrd*version 0.0.6 Index]