Table of contents for Stochastic orders / Moshe Shaked, J. George Shanthikumar.


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Univariate Stochastic Orders       .          . .      . . . . .  3
LA   The Usual Stochastic Ord  .  .           .    .....        3
L.A     Definition and equivalent conditions .             3
LA,2 A characterization by construction on the samei
probability space  .   .       .     .   ....  ..
i A.A  3  Closure properties  . . . .  .   .   .  . .  . . .
LAA. Furtther characterizations and properties ..... ..    8
"A. 5 Sonle properties in reliability theory ....          5
1.0 .The Hazard Rate Order     .     .     ...  .   .......  .  10
I.B.  Defi nitio   and equvaen conditions  . . . . . . .  . . .  1
1.B.2 The relation between the. hazard rate and the usual
stoch astic orders .. .                   ....      18
i.3B. 3 AClosiire properties and sorne characterizations ... .  11
1.13.4 Comnparison of order statistics .  ... .  ...  .  . 31
1,13.5 Some propertlies in reliabilit theory . .  ..    . 35
l.1.6 The reversed hazard order       . . . .  . . .  . .  36
I. C The Likelihood Ratio Order ..         ..   .........       2
1  .  D efinition  .... . ...          . .    .. .  ..    42
1.C 2 The relation betvveen the likelihood ratio and the
hazard and reversed hazard orders  ... . .     . . .43
l.C 3I Some proplrties and characterizations  .   .  . .  4
1C. I Shifted likelihood rat io orders .. ... .   ..   . .66
i.i  Tie Convolution Order   ......               .   .... .  . . .  70
CL E             . .  .  .  .                . . .   ....  .  .  71
SM     n R  idual Life Orders                                    81
2. A The Mean Residual Life Order  . . . .     .           . . 81
2A . i  Definition               ..   ....          ..    81
2.A.2 The relation between tilthe mean residual life and somet
other stioc'hastic order s ...         . .83
2. A3   Some closure properties ... .    .      .   . .  . 86
2 .             . . . . . . . ..  .. . . . . . . . . . . .. . .  . . . . . .. .
2.2 l     irdsm     twen 7-          1 1-,  reidh LIr
wir  wom( aher  hm                   ....  .  .   9 56
: 2.B.4  P   1       (05
-3 Univari'                    .   . .  .  .  .  . 1   .
, 1   D  inti  n   e   i a  n   dii ns  .  ............. . 109
3\ (.nwd    iti  iz-,u t 1cad  W  A . can w- cidor  .... . . . . 1  . . .  . 133
i,,A  S
3.B T A,5  i ve  r    ...  ..  .. . .. . (  . ... . .. . . . .. . ......  .  0,
3.11 .2  D ii n .  ,\nr[  ii iva en  e  . . .  ,  .  ,  . .  .  . . .  .  ....  . .  ......... ....... 63
3(   0 7. 14 - Ex we As  ke:lth.11  05 0 %.  . .  . . .  . . . ,. . . .  .. .  . . . . .  163,
3 ,(4,2  1" i m l: j  ,  ,  ,  ,  .,  I  .  .  . I  .  .  .  .  .  .  10 ;
K4. R ,  A bS o dill p oj '> r  e .. ...  .  ...  ..  . , . .  .. ... .  . ..  .  . .  ...... 17  !
itJF  (  NJ l1T0icaf-                          . .   . . . .   17i
40  Thlie Mohamhum  Al(sime anod TIOU wom CNIMcIDe, Owlems . . . . . .  5 181
4.,A.3 i D M ArOn  :Wd  w Ayniv ir (11 hioun  . .  . . . . . . . . . .  101
42A.3 Andivionn Owtv A! v the Ainrenwip; Rw,x osdl
i. '!.e   i;e^s ii  i  rA.i de W ri.vi lwo y  tA  . . ... ... ,. ...  19 7
4,  1 A i A  Im pu1rk ir's  ,]   e ,c, T  .  ...  .  .(..... . 203
40.0  F   m  i I      r .  .  .  ..... ... . . ..I.  .  I  .  ,  2 i,
. . .3   S o - c       s  . . . . . . . . .  . . . . . . . .  . . . . . .  2  2
" llhe 1iaplacic 'rinsform and Rea da  Orders   2.. 33
5,A  The I apiace 'Trah.sfo.rm d.r                          233
.A,I Dehikhtions and rquivalen coww tions-               233
5A.2 Closure a   other properties            .    . . .235
5A.-.-
5.B11  DeAi.tions an'd eqiuivalet conditions 1 . . . .   .
5.B.2 Closure rop    es                    .        . . .16
50.3 RSlationship to other s,ochastic orders ....  ..... 249
S3  ilMitvariacte Stocha tic Orders                    .    . .. 265
-6, A   NottionPe nk,d (Prrehlimiiaiies       ,265
6.B         al M  A    ate StAsi Order l                  . .  6
h.  )3,I T11 lfjOilCt  0111  (1K1nl 


Library of Congress subject headings for this publication: Stochastic orders