simEd (version 2.0.1)

sdTPS: Standard Deviation of Time-Persistent Statistics (TPS)

Description

Computes the sample standard deviation of a time-persistent function.

Usage

sdTPS(times = NULL, numbers = NULL)

Value

the sample standard deviation of the time-persistent function provided

Arguments

times

A numeric vector of non-decreasing time observations

numbers

A numeric vector containing the values of the time-persistent statistic between the time observation

Author

Barry Lawson (),
Larry Leemis (),
Vadim Kudlay ()

Details

The lengths of \code{times} and \code{numbers} either must be
the same, or \code{times} may have one more entry than \code{numbers}
(interval endpoints vs. interval counts). The sample variance is the
area under the square of the step-function created by the values in
\code{numbers} between the first and last element in \code{times} divided
by the length of the observation period, less the square of the sample mean.
The sample standard deviation is the square root of the sample variance.

Examples

 times  <- c(1,2,3,4,5)
 counts <- c(1,2,1,1,2)
 meanTPS(times, counts)
 sdTPS(times, counts)

 output <- ssq(seed = 54321, maxTime = 100, saveServerStatus = TRUE)
 utilization <- meanTPS(output$serverStatusT, output$serverStatusN)
 sdServerStatus <- sdTPS(output$serverStatusT, output$serverStatusN)

 # compute and graphically display mean and sd of number in system vs time
 output <- ssq(maxArrivals = 60, seed = 54321, saveAllStats = TRUE)
 plot(output$numInSystemT, output$numInSystemN, type = "s", bty = "l",
    las = 1, xlab = "time", ylab = "number in system")
 meanSys <- meanTPS(output$numInSystemT, output$numInSystemN)
 sdSys   <- sdTPS(output$numInSystemT, output$numInSystemN)
 abline(h = meanSys, lty = "solid", col = "red", lwd = 2)
 abline(h = c(meanSys - sdSys, meanSys + sdSys),
    lty = "dashed", col = "red", lwd = 2)