Computes (analytically)
point estimates and (by Monte Carlo)
confidence intervals (CI) for μ and σ
(Gaussian items) from sample sums alone.
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, apart from an adjustable scale factor.
Simulates N (trials) sets of samples
of size T, each with (generally) unequal nt,
with t (t = 1..T) elements (as in the Table above,
where T = 4), in order to compute “exact”
confidence intervals. Many (analytical) point estimates are computed,
and their (simulated) behavior leads to the confidence intervals.
Example data can be created
(or using this Excel.xlsm,
with a UDF, no macros) and inserted (copy-paste)
in the Table textarea, above. Other suggested data:
(a) equal size, T = 4 samples (n ≡ 20;
total items, 80; average size ≡ 20; scale, 0.0140);
(b) "industrial" unequal 50, T = 50 samples
(144 ≤ n ≤ 1296; total items, 43632; average size, 873;
scale, 0.002);
(c) "industrial" unequal 25, T = 25 samples
(432 ≤ n ≤ 1296; total items, 21672; average size, 867;
scale, 0.0032)
In industry, the sample sizes are usually
unequal (different customers' orders, often multiples of 72,
pallet), so the real (simulated) curve, f (with
unequal n), and the candidate, 'cand', curves obviously
do not match. An open question is whether
a candidate n exists for that purpose
(proposed: arithmetic mean of the n s). For the default data,
the average n (25) makes the curves for the mean coincide.
Same for variance, but a rule for the scale has not been
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. |
