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

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.

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 ξ is negative.

Author(s)

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")

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
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> library(Renext)
Loading required package: evd
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Renext/pGreenwood1.Rd_%03d_medium.png", width=480, height=480)
> ### Name: pGreenwood1
> ### Title: Probability that the Greenwood's statistic is smaller than one
> ### Aliases: pGreenwood1
> 
> ### ** 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")
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>