R version 3.0.3 (2014-03-06) -- "Warm Puppy"
Copyright (C) 2014 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64 (64-bit)
> # simple data demonstration using continuous Uniform; for discrete calculations see "Shoe Shopping" link
> true = runif(10000, 99, 101)
> var(true)
[1] 0.3343414
> 4/12 # uniform variance
[1] 0.3333333
> err1 = runif(10000, -1, 1) # error (or wobble) in measuring the amount of change
> obs1 = true + err1
> var(err1)
[1] 0.3317162
> var(obs1)
[1] 0.6500566
> rel1 = var(true)/var(obs1)
> rel1
[1] 0.5143266
> # calc quantity for reliability is of course .5 even though measurement is pretty good here
> err2 = runif(10000, -2, 2)
> obs2 = true + err2
> rel2 = var(true)/var(obs2)
> rel2
[1] 0.2003544
> # u(-2,2) has variance 16/12 so reliability is 4/20 even with pretty good measurement
> ################ using both time 1 and time 2 errors
> trueDiff = runif(100000, 99, 101) # would get you closer to calc values
>
### maybe of interest http://cran.r-project.org/web/views/Distributions.html CRAN Task View: Probability Distributions
also for discrete triangular (sum of unif) http://cran.r-project.org/web/packages/TRIANG/TRIANG.pdf