## Engineer's Book

Engineers – Telecoms – Physics – Teaching – Methods

## Khi² Tests – 04 – Probabilities Densities – Mathematics or Engineering ?

Written By: Jean-Paul Cipria - Mar• 10•17

Khi2 – Densities and Probabilities – Ref. [CIPRIA-2017]

How Agile, Scrum, Programs Developpements can be more Innovative ? For example how to display Khi² Densities ? How to calculate Right Probabilities with just Simpson Algorithm ? Why we can do with this Development Method ?

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Created :2017-03-10 12:46:01. – Modified : 2017-05-15 10:41:33.

Difficult ! Master Level.

Expériences En Construction.

# Do we use Mathematics or Physicists Equations ?

## Engineers, do you understand what you write ?

Ref. [CIPRIA-2107] : Are methods to use equations in algorithm simplify or not understanding ? And how understanding  help engineering, scrum or agile development in high level technologies ?

## Evidences ?

Matlab Program Example First Step DEMINING :

% Khi² Probability.
% -------------------------------
% Seemingly Simple Equations with NOT Understanding parameters :
% ---------------------------------------------
Khi2 = power(b,-a).*power(x,a-1).*exp(-x/b)./gamma(a);


End of Matlab Example

# Do we use K. Pearson Equations then ?

## First Part : do we understand khi² physical phenomenon ?

Physical phenomenon for khi² is the … probability or (repartition function for mathematician).

Khi2 – Results by K. Pearson  [PEARSON-1900] – © JP Cipria – 2017.

## Second part : do we compare with K. Pearson Tabulation Values ?

We compare for K. Pearson $n^{\prime}=7$ and $\chi^2=6$ then $Probabilities(\chi^2>P)=0.423190$ at your left hand in the following drawing and we read for the same values at you right hand with Matlab plotting

Kearson and Khi² Probabilities Comparisons – © JP Cipria – 2017.

# Do we use rules for High Technical Scientific Algorithms ?

## Simpliest functions ?

• Gamma function ? Don’t use it. You don’t know anything on this « codage » function.
• FFT, filter, delay-group functions ? Don’t use it. If you are an engineer then they don’t « agree » with your expectations.

## Object Programmation ?

• Object Programmation : Don’t use, DON’T use, DON’T USE ! Use O.P. for Sciences is a fault. Then you are all in fault 😉 ! Heavy, Complex, Difficult, Inadapted for 70% of Engineer’s Minds Types (See HP), Need three days to display « Hello » : Exemple with Android … long list …

LA ZApplication – Android-Screenshot

• Mouse-over without solicited customer action : Don’t …
• Simulink : Use with extremely precautionsssssssss … but … don’t use in a first time !

## Others booooh functions ?

• Goto : …. Don’t …
• Loop without a watchdog : Don’t …

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… Following … 10/03/2017

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# References

• [PEARSON-1900] : PEARSON, Karl. « On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. » Philos. Magazine, 5th Series 50 157–175., Reprinted in Karl Pearson’s Early Statistical Papers (1948) 339–357 Cambridge Univ. Press., 1900.
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• [CIPRIA-2017] : CIPRIA, Jean-Paul – « Parts of PhD Annexes . » – 2017.
• Matlab files :
• Khi² Probabilities and Densities Algorithms : khi2_Gamma_2017_03_10_2.m
• Khi² Model/Measurements Fittings : Khi2_Exponentielle_2017_02_24.m
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Jean-Paul Cipria
10/03/2017

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