Renext (version 3.0-0)

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)

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 $x = 1$.

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")