Oracle Corporation et al v. SAP AG et al

Filing 836

Declaration of Scott W. Cowan in Support of 835 Memorandum in Opposition, filed bySAP AG, SAP America Inc, Tomorrownow Inc. (Attachments: # 1 Exhibit A, # 2 Exhibit B, # 3 Exhibit C, # 4 Exhibit D, # 5 Exhibit E, # 6 Exhibit F, # 7 Exhibit G, # 8 Exhibit H, # 9 Exhibit I, # 10 Exhibit J, # 11 Exhibit K, # 12 Exhibit L, # 13 Exhibit M, # 14 Exhibit N, # 15 Exhibit O, # 16 Exhibit P, # 17 Exhibit Q)(Related document(s) 835 ) (Froyd, Jane) (Filed on 9/9/2010)

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Oracle Corporation et al v. SAP AG et al Doc. 836 Att. 5 EXHIBIT E Dockets.Justia.com OXFORD DIC:TIONARY OF STATISTICAL TERMS EDITOR YADOLAH DODGE Unil'ersit} O/NClichfitcl, Switzerland EIlITOHL\L B O \ 1 I 1 l SII{ D AV I D CO X Nuffield College, Unil'ersity o f Ox j i mI, UK DAN I EI , CO M MEN GES Institute o j P u b l i c Health and f)e/eloJ!lT/enL France A 1 V I ' H O ] ' ; Y D A V I S O N Swiss Federal Institllteoj'Tcchnolog}, Su'itzerland P A T T Y SO 1 , 0 M 0 N Unit'ersity ojAdelaide, Australia S U Z A N W I L S O N Australian National University, Australia OXFORD UNIVERSITY PRESS OXFORD UNIVERSITY PRESS Great Clarendon Street, Oxford OX2 6 D P Oxford University Press is a department of the University of Oxford. It furthers the University's objeetive of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Bangkok Buenos Aires Cape TOWIl Chennai Dar es Salaam Delhi Hong Kong Istanhul Karachi Kolkata Kuala Lumpur Madrid Melhoume Mexico City Mumbai Nairobi Sao Paulo Shanghai Taipei Tokyo TOTOnto Oxford is a r e g i s t e w d trade mark of Oxford University Press in the UK and certain other countries P u b l i s h e d in t h e United S t a t e s by Oxford University Press Inc., New York © International Statistical Institute The moral rights of the a u t h o r have been asserted Database right Oxford University Press (maker) First p u b l i s h e d 2 0 0 3 First p u b l i s h e d i n p a p e r b a c k 2 0 0 6 All r i g h t s r e s e r v e d . 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Enquiries c o n c e r n i n g r e p r o d u c t i o n o u t s i d e t h e s c o p e o f t h e a b o v e s h o u l d b e s e n t t o t h e Rights D e p a r t m e n t , O x f o r d U n i v e r s i t y Press, a t t h e a d d r e s s a b o v e You m u s t n o t c i r c u l a t e t h i s b o o k i n a n y o t h e r b i n d i n g o r c o v e r and you must impose the same condition on any acquirer British Library C a t a l o g u i n g i n P u b l i c a t i o n D a t a Data available l i b r a r y o f Congress Cataloging i n Publication D a t a Data available P r i n t e d i n G r e a t Britain on add·free paper by Biddies Ltd, King's Lynn ISBN 0 - 1 9 - 8 5 0 9 9 4 - 4 ISBN 0 - 1 9 - 9 2 0 6 1 3 - 9 (Pbk.) 978-0-19-850994-3 9 7 8 - 0 - 1 9 - 9 2 0 6 1 3 - 1 (Pbk.) 1 3 5 7 9 10 8 6 4 2 O n e possible o b j target language i t h e words a r e i n t t h e function o f a a r e i n c u r r e n t us a n d t h e r a p i d an t h e l a t e r definiti( Looking a t t h s u p p o r t from UJ' I n s t i t u t e (lSI), c lished. 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T h e d i s t i n c t i o n is i m p o r t a n t in a l l o m e t r y , a n d e x t e n d s by a n a l o g y t o variables of o t h e r typs, a s in f a c t o r a n a l y s i s . s i z e o f a r e g i o n o r t e s t In t h e t h e o r y of t e s t i n g s t a t i s t i c a l h y p o t h e s e s , t h e size o f a c r i t i c a l r e g i o n is a m e a s u r e o f p r o b a b i l i t y a n d is t h e s a m e as probabilih o f a n a - e r r o r o r e r r o r o f t h e f i r s t k i n d . F o r c o m p o s i t e h y p o t h e s e s it has s o m e t i m e s b e e n used t o d e n o t e t h e l i m i t s o f t h e a - e r r o r where n o s i m i l a r r e g i o n s exist. s k e w d i s t r i b u t i o n A d i s t r i b u t i o n which is n o t s y m m e t r i c a l ; a d i s t r i b u t i o n for w h i c h a m e a s u r e o f s k e w n e s s h a s s o m e v a l u e o t h e r t h a n zero. s k e w - n o r m a l d i s t r i b u t i o n A skew d i s t r i b u t i o n o b t a i n e d by c o n d i t i o n i n g on p o s i t i v i t y o f o n e c o m p o n e n t o f a b i v a r i a t e n o r m a l variable. s k e w r e g r e s s i o n A n o b s o l e t e t e r m for c u r v i l i n e a r r e g r e s s i o n . s k e w n e s s A s y m m e t r y , in r e l a t i o n t o a f r e q u e n c y d i s t r i b u t i o n o r a measure of that. a s y m m e t r y . I f a u n i m o d a l d i s t r i b u t i o n h a s a l o n g e r tail e x t e n d i n g towards lower values o f t h e v a r i a b l e i t is s a i d t o h a v e n e g a t i v e skewness; in t h e cont.rary case, p o s i t i v e skewness. s k i p f r e e p r o c e s s A t e r m p r o p o s e d by Keilson (1962) for a class o f r a n d o m wal w h e r e i n p a s s i n g f r o m X l t o X 2 > X l all i n t e r v e n i n g s t a t e s m u s t b e e n c o u n t e r e d at. l e a s t once. As s t a t e d t h e p r o c e s s would b e p o s i t i v e s k i p free; t h e opposite m o d e , n e g a t i v e s k i p free, r e q u i r e s t h e p a s s a g e f r o m X 2 t o X l < X z . S k i t o v i c h - D a r m o i s t h e o r e m T h i s s t a t e s ( D a r m o i s , 1953; Skitovich, 1954), t h a t i f ai, b;, i = 1, . . . , n, a r e c o n s t a n t coefficients a n d X l , . . . , X " a r e independ e n t , b u t n o t necessarily i d e n t i c a l l y d i s t r i b u t e d , s c a l a r r a n d o m variables, then if and L b i Xi i=] " a r e i n d e p e n d e n t , i t follows t h a t t h e r a n d o m v a r i a b l e s for which a j b j normal. =1= 0 a r e all s l a s h d i s t r i b u t i o n A h e a v y - t a i l e d d i s t r i b u t i o n used in r o b u s t n e s s s t u d i e s and o b t a i n e d from division of a n o r m a l by a n i n d e p e n d e n t u n i f o r m r a n d o m variable. s l i p p a g e t e s t A significance t e s t of k s a m p l e s i n which t.he h y p o t h e s i s is onE' of h o m o g e n e i t y in t h e m e a n s , as a g a i n s t t h e a l t e r n a t i v e t h a t o n e m e m b e r o r set of m e m b e r s ha'i ' s l i p p e d ' away from t h e o t h e r s . F o r e x a m p l e , where t h e samples a r e o b s e r v a t i o n s o n a n i n d u s t r i a l process a t successive t i m e p o i n t s a n d i t is s u s p e c t e d t h a t t h e m a g n i t u d e o f t h e v a r i a b l e is s y s t e m a t i c a l l y moving away f r o m t h e i n t e n d e d value. s l o p e r a t i o a s s a y A g e n e r a l c l a s s o f biological a s s a y w h e r e t h e d o s e - r e s p o n s e l i n e s for t h e s t a n d a r d t e s t s t i m u l i a r e n o t i n t h e f o r m o f t w o p a r a l l e l r e g r e s s i o n 376

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