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"]])
```

*distributionsrd*version 0.0.6 Index]