application of empirical distribution functions for decision making & statistical estimation of...
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Presentation for PDMU-2013TRANSCRIPT
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APPLICATION OF EMPIRICAL DISTRIBUTION FUNCTIONS FOR DECISION
MAKING Bakhrushin V.E., Dudko I.O., Ignakhina M.A.
STATISTICAL ESTIMATION OF THE DIFFERENTIAL RELATIONSHIPS
Bakhrushin V.E.
Classic Private University, [email protected]
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Empirical distribution function
Distribution function contains the most complete information about sample statistical properties.
Empirical distribution function at large n is approximately equal to the theoretical distribution function.
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Correlation coefficients of 2011 EIE tests tasks
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EIE mean results for software engineering applicants in 2012
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SJR rating of countries publication activity in 1996 –
2011
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Party of regions results at the 2007 elections
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Difference between ERF and TRF for R random values generator
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Correlation of Lillieforse criterion calculated values
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Critical values, calculated by Monte-Carlo method
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The method of differential relation estimation
( ) ( )( )'1 2f x F f x=
( )( ) ( )( ) ( )
11 2 1
1j 1 j 1 1 j 1 1 j j j 1
y f x ;
y y f x f x x x / 2; j 2,...,n,− − −
=
= + + − =
d 1 2K (y , f )
1 2R(y , f )
- nonlinear relation;
- linear relation
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Model linear differential relation
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Differential relation between internal friction and elastic modulus of Nb-N
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Differential relation between internal friction and elastic modulus of Nb-N
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R script for estimation of differential bond
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( ) 11 152 ε++= xxf ( ) 22
2 25 ε+−+= xxxf
1502 ,R = 960,Kd =
Model differential relation
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( ) ( )1 1 2 2f x 1/ x ; f x ln(x)= + ε = + ε2R 0,880= dK 0,989=
Model differential relation
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Publications1.Бахрушин В.Е. Проблемы идентификации моделей распределения случайных величин с применением современного программного обеспечения // Успехи современного естествознания. – 2011. – № 11. – С. 50 – 54. 2.Бахрушин В.Є. Статистичний аналіз університетських рейтингів // Освіта і управління. – 2011. – № 1. – С. 7 – 12.3.Бахрушин В.Є., Ігнахіна М.О. Застосування емпіричних функцій розподілу в дослідженні соціально-економічних систем // Складні системи і процеси. – 2012. – № 1. – С. 103 - 111 4.Бахрушин В.Є. Критерій для перевірки гіпотези про наявність зв'язку типу // Складні системи і процеси. – 2010, № 1. – С. 3 – 5. 5.Бахрушин В.Е. Статистический анализ дифференциальных связей в колебательных системах // Фундаментальные физико-математические проблемы и моделирование технико-технологических систем: Ежегодный сборник научных трудов, вып. 14. Труды второй международной конференции Моделирование нелинейных процессов и систем / Под ред. Л.А. Уваровой. – М.: Янус-К, 2011. – С. 57 – 62.