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)

[Package distributionsrd version 0.0.6 Index]