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From chi2 to gamma
Illustrates a pseudo-chi square statistic.
2024.Jul.03 20:39:51
T, n N. of loads and their (equal) sample size. •
μ, σ Gaussian parameters (mean, standard deviation). •
Trials Monte Carlo trials.
Points, seed     N. of graph points, RNG seed. •
Show values Show the graph coordinates.

Simulates samples of size T, each containing a set of n ≥ 1 elements.

For n = 1, the case reduces to classical samples of size T, ruled by Student's with T − 1  degrees of freedom, and chi-squared distributions. For n > 1, it is still a Student's, and a gamma with α = (T − 1) ⁄ 2 and β = 2 ⁄ n  (μ = α β = (T − 1) ⁄ n, and σ = βα) .

Draws plots for (0) the Gaussian, (1) the Student's, and (2) the chi-squared and gamma.

References: Plate: BagChi2Gamma

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

• Keisan Online Calculator: Gamma distribution Calculator (Casio Computer Co., Ltd.).

• 1561-08-25: Lansberge, Johan Philip van († 1632-12-08).

 
 
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Created: 2019-08-25 — Last modified: 2019-10-06