In the case of an underlying Exponential variable, from given μ and sample sizes, computes the point estimate (PE) of μ ("recovers" μ) and confidence interval (CI) from sums of unequal size samples.

A reasonable initial guess for β is μ ⁄ (Σ_t n_t). These other data are suggested: 1 2 4 8 16, β = 0.4 (giving 0.48195); 1 2 4 8, β = 1. (0.99414). (The minimization has tolerance of 1.e-4 and 500 (max.) iterations, values which were not deemed of interest for the general user to change.)

This PHP front-end calls a Python master that uses Fortran 90 and 'gnuplot'. The main files are:  (a) P-ConjSimulSumsExponentials.php (this one); (b) ConjSimulSumsExponen.php, 'action' manager; (c) conjSimulSumsExponen.py, Python hub importing the following module and calling 'gnuplot'; and (d) user module from modSimul.f90, created through 'f2py3'. Advantage is taken from: PHP, for the web page construction; Python, as "glue"; Fortran, for numerical segment; and 'gnuplot', for plotting..

Draws graphs with the experimental and the theoretical curves. In summary:  the theoretical curve, as a conjecture, is a Gamma distribution with α = Σ_t n_t ;  and, as a proposal, its shape parameter (β) is obtained by adjusting to the simulated curve.

• (Wikipedia) PHP (from Personal Home Page). • (Wikipedia) Python (programming language). Python as glue. Using Python as glue.

• F2PY Users Guide and Reference Manual • (Wikipedia) Fortran (Fortran 90) • (Wikipedia) gnuplot.

• (Wikipedia) Gamma distribution • GAMMA.DIST function (Microsoft, Excel) • Gamma distribution Calculator (Keisan Casio)

• COMPSTAT'2022, 24.th International Conference on Computational Statistics (COMPSTAT 2022), Bologna (Italy), 23–26 August.

• Unicode symbol charts

• 1814-05-16: Silva, Daniel Augusto da (†1878-10-06, 64 yrs.).