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Sums of unequal size samples: estimation
Estimates the parameters, from sums of unequal size samples.
2024.Jul.03 20:34:22
T =     nn N. of loads and their (unequal) sample sizes. •
μ, σ Gaussian parameters (mean, standard deviation). •
prob % Confidence level. •
Points, seed         N. of graph points, RNG seed. •
xmax Max. x (adjustable) for variab. graph. •
Show values Show the graph coordinates.

Simulates T loads, each containing a random (uniform) size, n, of items, in the interval given.

The items are generated as Gaussian, with the given μ, σ.

For the parameters μ and σ, with n the (conservative) global minimum of the sizes, point estimation is done based on ML, and confidence intervals are computed, respectively: by the Student's distribution procedure, with (T − 1) n degrees of freedom; and by a gamma distribution procedure ("parallel" to χ²) with α = (T − 1) ⁄ 2 and β = 2 ⁄ n .

Draws plots for (1) the Student's statistic, and (2) the chi-squared and gamma statistics.

References: Plate: bagsumuneqpeci

• Wikipedia: Gamma distribution. Here: k = α and θ = β .

• 1819-08-30: Serret, Joseph Alfred († 1885-03-02).

 
 
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Created: 2019-08-30 — Last modified: 2020-05-15