qStat {Renext} | R Documentation |
Quantiles of a test statistic
Description
Quantile of a test statistic.
Usage
qStat(p, n,
type = c("Greenwood", "Jackson", "logLRGPD", "logLRLomax",
"logLRGEV", "logLRFrechet"),
outNorm = FALSE)
Arguments
p |
Numeric vector of probabilities. Very small values ( |
n |
Sample size. |
type |
The type of statistic, see Details. |
outNorm |
Logical. If |
Details
The function provides an approximation of the distribution for several statistics.
For
"Greenwood"
, the statistic is Greenwood's statistic. The distribution is that of the squared coefficient of variationof a sample of size
n
from the exponential distribution as computed byCV2
.For
"Jackson"
, the statistic is Jackson's statistic, seeJackson
.For
"logLRGPD"
and"logLRLomax"
, the statistic is the log of the likelihood ratio of a sample from the exponential distribution. The log-likelihoods are for an exponential distribution compared to a GPD with non-zero shape, or to a GPD with positive shape (equivalently, a Lomax distribution).For
"logLRGEV"
and"logLRFrechet"
, the statistic is the log of the likelihood ratio of a sample from the Gumbel distribution. The log-likelihoods are for a Gumbel distribution compared to a GEV with non-zero shape, or to a GEV with positive shape (equivalently, a Fréchet distribution).
The log of Likelihood Ratios are multiplied by 2
, so that they
compare to a chi-square statistic with one degree of freedom.
Value
A vector of quantiles.
Note
The precision of the result given is limited, and is about two-digits. This function is not intended to be used as such and is only provided for information.
Author(s)
Yves Deville
Examples
res <- qStat(n = 40, type = "Greenwood")
plot(res$q, res$p, type = "o")