The goal of QQreflimits is to provide routines for finding reference limits using, where appropriate, QQ methodology. All use a data vector X of cases from the reference population. The default is to get the central 95% reference range of the population, namely the 2.5 and 97.5 percentiles.
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In some settings we want the 99% range.
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Sometimes we want only one of these limits – for example the upper 95% point.
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Along with the reference limit, we want a confidence interval which, for historical reasons, is typically at 90% confidence. A full analysis provides six numbers:
- the upper and the lower reference limits, and
- each of their confidence intervals.
Installation
You can install the development version of QQreflimits like so:
install.packages("QQreflimits") # once available on CRAN
Example
This is a basic example which shows you how to solve a common problem:
library(QQreflimits) # parameters mu <- 40 sigma <- 10 n <- 120 # identifying winsoring wins <- trunc(n/40) # replicable randomization set.seed(1069) X <- mu + sigma*rnorm(n) # replicable randomization with heavy tails set.seed(1069) HT <- mu + sigma * rt(n, 5) # visual settings par(mfrow=c(2,2)) par(oma=c(0,0,2,0)) # plot to compare base <- QQnorm(X, main="Base normal", showsum=TRUE) title("Illustrating QQnorm with para_limits", outer=TRUE) basew <- QQnorm(X, main="Winsorized", winsor=wins, showsum=TRUE) ht <- QQnorm(HT, main="Heavy tail", showsum=TRUE) htw <- QQnorm(HT, main="Winsorized", winsor=wins, showsum=TRUE)
# evaluate and review norm_results <- para_limits(mean(X), sd(X), n) norm_results #> $lower #> [1] 20.21278 17.57878 22.84678 #> #> $upper #> [1] 60.44854 57.81454 63.08255 #> #> $effn #> [1] 120 # evaluate and review with tails tailed_results <- para_limits(htw$intercept, htw$slope, n, winsor=wins) tailed_results #> $lower #> ns[QQrange] ns[QQrange] #> 19.14649 16.25381 22.03916 #> #> $upper #> ns[QQrange] ns[QQrange] #> 61.35614 58.46346 64.24881 #> #> $effn #> [1] 109.5