Studies the estimation
of Gaussian parameters from unequal size samples when
sums only are known (not the individual item values).
The samples are assumed to come from
a (common) Gaussian population for which the distribution parameters,
μ and σ, are to be estimated.
Above, the "sample sums" have been arbitrarily preferred,
but the "sample averages" (later computed by the program)
might be a suitable alternative.
The problem is very frequent in industry,
a typical example being the following. A fertilizer factory sells
its product in sacks of 50 kg that leave the factory
in the customers' trucks. Each truck is weighed on exit for control. Thus, e.g.,
trucks with 200 sacks weigh about 10000 kg,
trucks with 300 sacks weigh about 15000 kg, etc.. From these data,
an estimation of μ ≅ 50 kg
is obvious. What about σ ?
The base data are from another, similar case:
4 (closed) packets of biscuits, with nominal weight of 200 g
and contaning "about" 36 biscuits each.
(Tolerance is for the inversion of the
Gaussian distribution.)
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• Dunnett, C. W., 1980,
"Pairwise multiple comparisons in the homogeneous variance, unequal
sample size case", Journal of the American Statistical Association,
vol. 75, issue 372, pp 789–795 (doi: 10.1080/01621459.1980.10477551).
(Preview)
•
NIST: Weighted variance
← Dataplot
← Stat. Eng.ing Division
← Information Technology
Lab.
• Parra Frutos, Isabel, 2013,
"Testing homogeneity of variances with unequal sample sizes",
Computational Statistics,
28:1269–1297.pdf (DOI 10.1007/s00180-012-0353-x).
(.pdf)
• Ramsey, Philip H.,
Patricia P. Ramsey, 2008,
"Power of pairwise comparisons in the equal variance
and unequal sample size case",
British Journal of Statistical Psychology, 61,
115–131 (DOI:10.1348/000711006X153051).
(.pdf)
• Rao, Poduri S. R. S, 2012,
"Estimation of the best linear unbiased predictor for the mean
with unequal sample sizes", Statistical Methodology, vol. 9,
pp 515–519 (doi:10.1016/j.stamet.2012.02.001). (|.pdf|)
• Spjøtvoll, Emil,
Michael R. Stoline, 1973,
"An Extension of the T-Method of multiple comparison
to include the cases with unequal sample sizes",
Journal of the American Statistical Association, 68(344),
December, pp 975–978. (|.pdf|)
• Wikipedia: Weighted
arithmetic mean
• 1601-08-17: Fermat, Pierre de (1665-01-12). |
