ptailw: TailW Probability Function

In SergiVilardell/distributionTails: A Collection of Full Defined Distribution Tails

Description

This function computes the cumulative density function of the tailW with the input sample data.

F(x,α,β,ν)=1-\exp(-α(x+ν)^β+αν^β).

Usage

ptailw(x, threshold, scale, shape)

Arguments

x	Sample data.
threshold	Minimum value of the tail.
scale	Scale parameter.
shape	Shape parameter.

Value

Gives the distribution function of the TailW. The length of the result is determined by the length of x.

References

Vilardell, Sergi & Serra, Isabel & Abella, Jaume & del Castillo, Joan & Cazorla, Francisco. (2019). Software Timing Analysis for Complex Hardware with Survivability and Risk Analysis. 227-236. <doi:10.1109/ICCD46524.2019.00036>.

Examples

# Using the probability function to show the fitting.
samp <- rtailw(1000, 1, 2, 3)
emp_cdf <- ecdf(samp)(samp)
pars <- fittail(samp, dist = "TailW")
x_seq <- seq(min(samp), max(samp), length.out = 250)
p <- ptailw(x_seq, threshold = 1, scale = pars$scale, shape = pars$shape)
plot(samp, 1-emp_cdf, log = "y")
lines(x_seq, 1-p, col = "red")

SergiVilardell/distributionTails documentation built on Jan. 17, 2021, 8:44 a.m.