Computes (analytically)
point estimates (PE) and (by Monte Carlo)
confidence intervals (CI) for μ and σ
(Gaussian parameters) from sample sums alone. Here, the sums
are simulated from given μ and σ, thus expected
to be recovered.
As a conjecture, the average sample size
leads to: a Student's t with
n − 1
(nearest integer) degrees of freedom; and a chi-square with
T − 1 df, and, as a proposal, an adjustable
scale factor. This scale factor is optimized so that
the simulated and proposed curves "coincide".
Simulates N (trials)
sets of T samples, each with (generally) unequal
nt (t = 1..T) elements
(as in the Sizes above, T = 4), in order to compute
“exact” confidence intervals. Many (analytical) point estimates
are computed, and their (simulated) behavior leads to
the confidence intervals.
In industry, the sample sizes are usually
unequal (different customers' orders).
Two questions remain. The candidate n seems to be
the arithmetic mean of the n 's. For the default data,
the average n (25) makes the curves for the mean coincide.
For the variance, a rule for the scale was not found.
(For the basis problem, scale is 0.0135.)
Warning: large data sets may lead to excede
a typical (Web) time limit (~2 min) with error message
as '502 Bad Gateway'. Speed: ~400 million Gaussians/min.
Draws plots of:
the estimated value of μ; and
the estimated value of σ². | 
