Design of experiments and Laplace transform: Difference between pages
(Difference between pages)
Content deleted Content added
mNo edit summary |
m Automated conversion |
||
| Line 1: | Line 1: | ||
The '''Laplace transform''' of a [[function]] ''f''(''t'') defined for all [[real number|real numbers]] ''t'' ≥ 0 is the function ''F''(''s''), defined by: |
|||
The first statistician to considera methodology for the design of experiments was [[Sir Ronald A. Fisher]]. He described how to test the hypothesis that a certain lady could distinguish by flavor alone whether the milk or the tea was first placed in the cup. This sounds like a frivolous application, but in fact, it allowed him to illustrate the most important ideas of experimental design. |
|||
: ''F''(''s'') = ∫<sub>0</sub><sup>∞</sup> ''e''<sup>-''st''</sup> ''f''(''t'') d''t'' |
|||
'''Design of experiments''' was built on the foundation of the [[ANOVA|analysis of variance]], a collection of models in which the observed variance is partitioned into components due to different factors which are estimated and/or tested. |
|||
The Laplace transform ''F''(''s'') typically exists for all real numbers ''s'' > ''a'', where ''a'' is a constant which depends on the growth behavior of ''f''(''t''). |
|||
Developments of the theory of [[linear model]]s have encompassed and surpassed the cases that concerned early writers. Today, the theory rests on advanced topics in [[Abstract Algebra|abstract algebra]] and [[combinatorics]]. |
|||
See also: [[Fourier transform]], [[transfer function]], [[linear dynamic system]]. |
|||
: [[planning statistical research]] -- [[survey sampling]] |
|||
back to [[Statistics]] -- [[statistical theory]] |
|||
Links: |
|||
*[http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Fisher.html R. A. Fisher] |
|||
Revision as of 01:53, 29 January 2002
The Laplace transform of a function f(t) defined for all real numbers t ≥ 0 is the function F(s), defined by:
- F(s) = ∫0∞ e-st f(t) dt
The Laplace transform F(s) typically exists for all real numbers s > a, where a is a constant which depends on the growth behavior of f(t).
See also: Fourier transform, transfer function, linear dynamic system.