weibull_plt function

Weibull coefficients of power-law transformed Weibull

Coefficients of a power-law transformed Weibull distribution

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.

Returns

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)

Details

If the random variable y is Weibull distributed with mean meanlog and standard deviation sdlog, then the power-law transformed variable

is Weibull distributed with scale $( \frac{scale}{a})^{\frac{1}{b}}$ and shape $b*shape$.