qua.ostat | R Documentation |
This function computes a specified quantile by nonexceedance probability F
for the j
th-order statistic of a sample of size n
for a given distribution. Let the quantile function (inverse distribution) of the Beta distribution be
\mathrm{B}^{(-1)}(F,j,n-j+1) \mbox{,}
and let x(F,\Theta)
represent the quantile function of the given distribution and \Theta
represents a vector of distribution parameters. The quantile function of the distribution of the j
th-order statistic is
x(\mathrm{B}^{(-1)}(F,j,n-j+1),\Theta) \mbox{.}
qua.ostat(f,j,n,para=NULL)
f |
The nonexceedance probability |
j |
The |
n |
The sample size. |
para |
A distribution parameter list from a function such as |
The quantile of the distribution of the j
th-order statistic is returned.
W.H. Asquith
Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton, Fla.
lmom2par
, vec2par
gpa <- vec2par(c(100,500,0.5),type='gpa')
n <- 20 # the sample size
j <- 15 # the 15th order statistic
F <- 0.99 # the 99th percentile
theoOstat <- qua.ostat(F,j,n,gpa)
## Not run:
# Let us test this value against a brute force estimate.
Jth <- vector(mode = "numeric")
for(i in seq(1,10000)) {
Q <- sort(rlmomco(n,gpa))
Jth[i] <- Q[j]
}
bruteOstat <- quantile(Jth,F) # estimate by built-in function
theoOstat <- signif(theoOstat,digits=5)
bruteOstat <- signif(bruteOstat,digits=5)
cat(c("Theoretical=",theoOstat," Simulated=",bruteOstat,"\n"))
## End(Not run)
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