Probability that the Greenwood's statistic is smaller than one

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

Usage

pGreenwood1(n)

Arguments

n

Sample size.

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.

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 \(x = 1\).

Author

Yves Deville

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")