burr_plt {distributionsrd} | R Documentation |

## Burr coefficients after power-law transformation

### Description

Coefficients of a power-law transformed Burr distribution

### Usage

```
burr_plt(shape1 = 2, shape2 = 1, scale = 0.5, a = 1, b = 1, inv = FALSE)
```

### Arguments

`shape1` , `shape2` , `scale` |
Shape1, shape2 and scale of the Burr distribution, defaults to 2, 1 and 1 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 Burr distributed with scale shape and shape scale, then the power-law transformed variable

` y = ax^b `

is Burr distributed with shape1 `shape1`

, shape2 `b*shape2`

and scale ` ( \frac{scale}{a})^{\frac{1}{b}} `

.

### Value

Returns a named list containing

- coefficients
Named vector of coefficients

## Comparing probabilites of power-law transformed transformed variables pburr(3,shape1=2,shape2=3,scale=1) coeff = burr_plt(shape1=2,shape2=3,scale=1,a=5,b=7)$coefficients pburr(5*3^7,shape1=coeff[["shape1"]],shape2=coeff[["shape2"]],scale=coeff[["scale"]])

pburr(5*0.9^7,shape1=2,shape2=3,scale=1) coeff = burr_plt(shape1=2,shape2=3,scale=1,a=5,b=7, inv=TRUE)$coefficients pburr(0.9,shape1=coeff[["shape1"]],shape2=coeff[["shape2"]],scale=coeff[["scale"]])

## Comparing the first moments and sample means of power-law transformed variables for large enough samples x = rburr(1e5,shape1=2,shape2=3,scale=1) coeff = burr_plt(shape1=2,shape2=3,scale=1,a=2,b=0.5)$coefficients y = rburr(1e5,shape1=coeff[["shape1"]],shape2=coeff[["shape2"]],scale=coeff[["scale"]]) mean(2*x^0.5) mean(y) mburr(r=1,shape1=coeff[["shape1"]],shape2=coeff[["shape2"]],scale=coeff[["scale"]],lower.tail=FALSE)

*distributionsrd*version 0.0.6 Index]