|
Conjecture: from sums of
Exponentials Estimates μ
from unequal size sample sums of an
Exponential. |
|
|
| Sizes, sums |
|
Sizes and
sums. • |
| α, β |
(iff
α ∨ β = 0, see below) |
Gamma distribution parameters. • |
| β in, tol |
|
Interval for β (sensitive),
tolerance. • |
| Confidence level |
% |
Confidence level. • |
| Trials, seed |
|
Monte Carlo: trials, seed
(0: unrepeatable). • |
| Histogram classes |
|
N. of classes. • |
| x-limits |
|
Limits for the x-axis
(±i, ∞). • |
| Show values |
|
Show graph coordinates. |
From sums (alone)
of unequal size samples, with items distributed Exponentially,
finds, for μ: (analytical) point estimate; and
(Monte Carlo) confidence intervals.
Iff α = 0, then (conjecture)
α = Σnt.
Iff β = 0, then β is optimized (numerically,
with sensitive initial guesses).
Draws a graph for the
confidence interval. |
| References: |
Plate: ConjSumsExponentials |
• (Wikipedia) PHP (from Personal Home Page).
• (Wikipedia) Exponential distribution
• (Wikipedia) Logical symbols
(∨, ⊕: inclusive 'or', exclusive 'or').
• 1.3.6.4. Location and Scale Parameters (NIST, SEMATECH)
• CISTI'2023, 18.ª
Conferência Ibérica de Sistemas e Tecnologias de Informação
(18.th Iberian Conference on Information Systems and
Technologíes), Faro (Portugal), 21–24 June 2023.
• 1746-05-09: Monge, Gaspard
(†1818-07-28, 72 yrs.). |
