ptailw {distTails}

TailW Probability Function

Description

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

F(x,\alpha,\beta,\nu)=1-\exp(-\alpha(x+\nu)^\beta+\alpha\nu^\beta).

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.

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")