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Book

Probability and Statistical Models with Applications

Book

Probability and Statistical Models with Applications

DOI link for Probability and Statistical Models with Applications

Probability and Statistical Models with Applications book

Probability and Statistical Models with Applications

DOI link for Probability and Statistical Models with Applications

Probability and Statistical Models with Applications book

Edited ByCH. A. Charalambides, M.V. Koutras, N. Balakrishnan
Edition 1st Edition
First Published 2000
eBook Published 21 September 2000
Pub. Location New York
Imprint Chapman and Hall/CRC
DOI https://doi.org/10.1201/9781420036084
Pages 664
eBook ISBN 9780429126031
Subjects Engineering & Technology, Mathematics & Statistics
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Charalambides, C.A., Koutras, M.V., & Balakrishnan, N. (Eds.). (2000). Probability and Statistical Models with Applications (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781420036084

ABSTRACT

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probabili

TABLE OF CONTENTS

part |2 pages

PART I APPROXIMATION, O UNDS, AND NEQUALITIES

chapter |1 pages

Nonu niform Bomn ds in Pro ba

chapter |2 pages

H.Y . Clien

= 0) = = 1, ....n . W = Er=, = W E,"=, 2 + 1) = h(w) = . .}.

chapter |4 pages

Y. Chen

5 C" xp:[4(1 X-')Ejh(Z = 1,

chapter |1 pages

Y. C1w1

chapter |8 pages

Conclusion

chapter |5 pages

; the finict,ion

IX,,

chapter |17 pages

= < <

1 5 ,l 5 n,

chapter 3|2 pages

Applications of Compound Poisson Approximation .-I. U . Rurhotrr, 0. C:hr!j.scsaplaino~u, a ~ ~ d E:. Vu,qgclato~u

E. Vaggelatou 5 EOMOk7) + ElMl(L7) > 0 and for all bounded g N R. where ML(g) := + 1) &v(P,Q ) :=

chapter |3 pages

Ct2 ,

chapter |4 pages

p have the citnoi~ic;xlt lefinitioiis

= I,
ByZia re intleperident, which then easily gives

chapter |7 pages

< 2,1r~n,(4k 3)(1n

EI/17

chapter C|3 pages

l,rIM,C

:; S,

chapter 0|3 pages

E.

D. P.

chapter |5 pages

Colnpound Poisson Approximation for Sums of Depe12dent Raadorn Variables

..., are "weakly" dependent. S1lcl.1 problems

chapter 1|4 pages

)’. Markos V.

chapter Xi|2 pages

,, >

chapter X|2 pages

,t ,

, -- .;
ByXic an be altcrriatively

chapter |7 pages

( I ( )

+ C:?l this = P(x::~-l
ByC::-

chapter |4 pages

RHS as

chapter |6 pages

Ukified Variance ounds and a

chapter |7 pages

= ,,,

chapter X|6 pages

P apatiatoi

chapter |4 pages

Probability Inequalities

< Let t > 0. Using Hoeffding's
ByU;,is constructed using i.i.d. random variables. However; with

chapter |1 pages

= 1, =

< p < 1. Then as a special

chapter 11|4 pages

1

. , X . , oJ'(1,. . ,n). . Following the

chapter |11 pages

PART PROBABILITY STOCHASTIC

chapter |10 pages

H. Peria and Lai

chapter |4 pages

H.c le la Pcrla and Tze L

a := < > 0 such that bm/I'(I- a > 6. Sincc lirn,,, l/I'(l > 1; > rjS) 5
By:P (l

chapter 11|7 pages

la Pena a

= m,
By2 1) Iflight.

chapter |1 pages

Process

+ . =

chapter |2 pages

. S)

(fi, ,m ) (fi,. (6:m.

chapter |5 pages

for Boundary

. are independent, identically $?kl

chapter |3 pages

> 0, > a

chapter |2 pages

S.K orolyuk and K. Limnios

2 defined by the generator 1 ,5 2 which is uniformly ergodic in every class X 5 5 and PI &(z.

chapter |9 pages

S .K orolyuk K. Limnios

mJ2n= verage of SLOC > 0,g iven (9.2.3), in

chapter |7 pages

ueues with e termirrrist

chapter |16 pages

+ 1,

(2-tS (?],) l, = 0 > 1, n-1. > 1). By
By5 5 n

chapter 1|2 pages

' a,s.siliou

chapter |13 pages

H.T sakiriclou +

+ + s + m%, + m,,-] + m,.)] -t o (m,. + m,., = n.
Bym,+1,

chapter |5 pages

DISTRIBUTION , ARAGTERIZATIONS, AND APPLICATIONS

chapter X|13 pages

R ao, and h.

< cl,. (Oiie of the

chapter 13|2 pages

Bivariate Distributions Compatible or Nearly Compatible with Given Con di tion

chapter I|3 pages

,l).

chapter |17 pages

PPQ, thc

chapter |4 pages

Refinements of nctior~ls

. and let the arithmetic, geometric and

chapter |23 pages

MO,-

chapter |2 pages

First Bivariate Skew

chapter |3 pages

= and =

chapter |14 pages

n the Posterior ments for. and

chapter |3 pages

tions of

chapter |8 pages

nnI2/r( F

((1,+

chapter 1|5 pages

-cvhe~~

chapter |3 pages

= l,. . ,

> > 0, 1, , . , P,.

chapter |4 pages

If. Jlathai

0731, , E(O$,,a)b ove. Also ob-

chapter x|1 pages

("-")V,,, is of the form

= 2, = 1,

chapter |2 pages

SERIES, An,

NON-

chapter |7 pages

Coin tegration of Econon~ic

CT Rcgrcssiorr rnotlels and sim~dta.neouse quations nrodcls

chapter |1 pages

Yo.Y1,. .YT. B

Yt-l. 20.6 Nonstationary Models 1. This is the case when B Yt=Yt-l+Z,. Yo = &YtYi= =

chapter |1 pages

AYLh as no trend, the tiifk~.criciui?o; p

1, i l, . . , p. LT7e ca.

chapter l|10 pages

/ L

, are the solutions to
ByYtPl

chapter |8 pages

T. Since the process {XT,,

clr and are real valued ant1 positive scql~criccsa pproitchi~~zegr o

chapter |9 pages

j(.)

> C; = 1/(1 = Ho =

chapter |8 pages

Note

= 0. = 0 C(L1) M f~ M = 0.
ByNote 3

chapter |14 pages

[S :

P) is continiloi~sm d P P+ )-(2'/ap3 ~ = l,
By(P)is a positive dcfiriite rrlatiix.

part |2 pages

PART V INFERENCE APPLICATIONS

chapter 24|2 pages

Extensions of

Isoperirn e tric

chapter |2 pages

Error

chapter |8 pages

Allocation of

chapter |9 pages

ePositive

phrases Croup testing. IIH procedure, efficiency, ro-

chapter |14 pages

+ [j)

= .80, E{Y;) a

chapter |2 pages

P.G .

l)(f + .. , = 4.

chapter |2 pages

M.M athai P.

chapter |1 pages

P.G . -2loschopoulos

= (sI1 l~l+Y.

chapter |3 pages

on~in;~tloRne sults

(Irl',
Byl,(.) > a

chapter |5 pages

d;(r)

chapter I|11 pages

). imtl tlwa.ng, T. (1989). Universal domiriatiori a.nd

chapter |28 pages

if

1Cb =
By(0>

chapter 8|3 pages

De Vcstnx, R. D. mtl Kriegcr,

15. Marl&ou, M., Rasu,

chapter |7 pages

@TT hc problem of nonparametric estimation of a srnootli,

f except

chapter |9 pages

.3.1 Case of Smooth ensiky over a Finite

chapter 31|7 pages

Multipolishing Large Two-

W. Tukey

chapter |2 pages

u v.

= 0.
By1c;vTv rr/vTw Yvw"'/w"v-l Gvr,w here we made us of the fact that l

chapter |2 pages

W. Tukey

chapter |7 pages

References

chapter |14 pages

n Distances an easures of

chapter |4 pages

ulae for Pro

chapter |9 pages

= -+

chapter |7 pages

(C,"Cl

chapter 34|2 pages

Estimation of Cycling Eflect on Reliability

R and let TTc be the z(.). = P{T,(

chapter |19 pages

meet on Rc1iel)ilit.y

chapter |1 pages

B.S ackrowitz

B,z ). < B1 B; > B2

chapter |6 pages

THCORE~I

A B,iyei tcst is = Xll+
By2 for every

chapter |8 pages

F. Neuts

chapter |35 pages

on Functional

chapter l|17 pages

,., 419, 427. 430.

M, 10-12, 121, 145
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