Renext (version 3.1-4)

pGreenwood1: Probability that the Greenwood's statistic is smaller than one

Description

Probability that the Greenwood's statistic is smaller than one.

Usage

pGreenwood1(n)

Value

Probability that the Greenwood's statistic is smaller than one. For a random sample of an exponential distribution with size \(n\), this is the probability that the coefficient of variation is less than one, or the probability that the ML estimate of the GPD shape parameter

\(\xi\) is negative.

Arguments

n

Sample size.

Author

Yves Deville

Details

The probability was computed by using the approximation of the quantile function of the Greenwood's statistic returned by qStat. The result is found by interpolating the distribution function for \(x = 1\).

Examples

n <- 8:500
plot(n, pGreenwood1(n), type = "l", col = "orangered", lwd = 2,
     log ="x", ylim =c(0.5, 0.7), main = "slow convergence to 0.5")
grid() ; abline(h = 0.5, col = "SpringGreen")