weibull_plt {distributionsrd} | R Documentation |

## Weibull coefficients of power-law transformed Weibull

### Description

Coefficients of a power-law transformed Weibull distribution

### Usage

```
weibull_plt(scale = 1, shape = 2, a = 1, b = 1, inv = FALSE)
```

### Arguments

`shape` , `scale` |
shape and scale of the distribution with default values of 2 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 y is Weibull distributed with mean meanlog and standard deviation sdlog, then the power-law transformed variable

` y = ax^b `

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

and shape `b*shape`

.

### Value

Returns a named list containing

- coefficients
Named vector of coefficients

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

pweibull(5*0.8^7,shape=2,scale=1) coeff = weibull_plt(shape=2,scale=1,a=5,b=7,inv=TRUE)$coefficients pweibull(0.8,shape=coeff[["shape"]],scale=coeff[["scale"]])

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

*distributionsrd*version 0.0.6 Index]