pareto_plt {distributionsrd} | R Documentation |

## Pareto coefficients after power-law transformation

### Description

Coefficients of a power-law transformed Pareto distribution

### Usage

```
pareto_plt(xmin = 1, k = 2, a = 1, b = 1, inv = FALSE)
```

### Arguments

`xmin` , `k` |
Scale and shape of the Pareto distribution, defaults to 1 and 2 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 x is Pareto-distributed with scale xmin and shape k, then the power-law transformed variable

` y = ax^b `

is Pareto distributed with scale ` ( \frac{xmin}{a})^{\frac{1}{b}} `

and shape `b*k`

.

### Value

Returns a named list containing

- coefficients
Named vector of coefficients

### Examples

```
## Comparing probabilites of power-law transformed transformed variables
ppareto(3, k = 2, xmin = 2)
coeff <- pareto_plt(xmin = 2, k = 2, a = 5, b = 7)$coefficients
ppareto(5 * 3^7, k = coeff[["k"]], xmin = coeff[["xmin"]])
ppareto(5 * 0.9^7, k = 2, xmin = 2)
coeff <- pareto_plt(xmin = 2, k = 2, a = 5, b = 7, inv = TRUE)$coefficients
ppareto(0.9, k = coeff[["k"]], xmin = coeff[["xmin"]])
## Comparing the first moments and sample means of power-law transformed variables for
#large enough samples
x <- rpareto(1e5, k = 2, xmin = 2)
coeff <- pareto_plt(xmin = 2, k = 2, a = 2, b = 0.5)$coefficients
y <- rpareto(1e5, k = coeff[["k"]], xmin = coeff[["xmin"]])
mean(2 * x^0.5)
mean(y)
mpareto(r = 1, k = coeff[["k"]], xmin = coeff[["xmin"]], lower.tail = FALSE)
```

[Package

*distributionsrd*version 0.0.6 Index]