Вадзинский P.H. Справочник по вероятностным распределениям
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Probability calculator.
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Compute.
Ha
3KpaHe
nOHBHTCH
rpa<pHK
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t-pacnpe,lle-
neHIDI
CTbIO,lleHTa C,lleCHTbIO CTeneHHMH CB060,llhI H
rpacPHK
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t-pacnpe.n:eneHHH
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IT.2.14).
280
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t
Probability Density Function Probability Distribution Function
y=student(x;10) p=1.2*(I-istudent(abs(x);I
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0.500
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0.8
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0.6
0.250
0.4
0.125
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1.75 3.50
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none
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Inverse.
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none
t
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pe3ynbTaTa
BbNHCJleHHH nOHBHTCH qHCnO
1.812460.
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t-pacnpe,lleneHHH
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p).
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none
BBO,lla p BBeCTH qHCJlO 0.1.
(ITPH
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none
df BBeCTH qHCnO 10.
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none
t BhI,llaqH
pe3ynbTaTa
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nOHBHTCH qHCJlO
1.812460.
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6.
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BepOHTHOCTH 6HHOMHaJIbHOro pH,lla
pac-
npe.n:eJleHHH C
napaMe'TpaMH
n = 5 H P = 0.4.
B BCpOHTHOCTHOM KaJlbKYJlHTOpe
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pacnpe,lleJleHHH.
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BhlqHCneHHH, CBH3aH-
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6HHOMHaJIbHbIM
pacnpe-
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no,n:
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pacnpe,n:eJIeHIDI
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Switch to
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IT.2.15).
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STATISTICA.
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name
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napaMeTpaMH
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II.2.18.
01010
cneUH<pHKaIUlH
nepeMeHHoR
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b.
•
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KHOnKY
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Ra
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C
coo6111eHHeM
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now?
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Ta6JIHUa
rrpHMeT
BM,
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pHC.
II.2.20.
113
Ta6JIHUbi
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Po
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PI
=0.25920,
P2
=0.34560,
P3
=0.23040,
P4
= 0.07680,
Ps
=
0.01024.
(CpaBHHTe
3TH
pe3YJIbTaTbi
C
pe3YJIbTaTaMH
perneHIDI npHMe-
pa
2).
3aMe'laHue.
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perneHHH npHMepa
6BbNHCJIeHHe
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C nOMolilblO
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binom(x,p,n),
r~e
x =
0,
1, ..., 5, P =
0.4
H n =
5.
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KaqeCTBe
apryMeHTa
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=
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II.2.20.
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284
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l...
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apryMeHT
x
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1)
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T.
A.
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c.
74,
79,
81,
82,
85-87,
90]
B
KaqeCTBe
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pe3ynbTaTe
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npHMepOB
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=
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H
BepXHlOlO
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Basic Statistics
and
Tables
BbI,llenHTb
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Probability calculator.
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(Enter».
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OTKphIBIlleMCH
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Probability Distribution calculator, B
cnHCKe
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yCTaHoBHTb
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Ha
CTPOKe
Chi I
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H
II.J.enKHYTb
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cnHCKa
pacnpeAeneHHH
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(Distribution Function)
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a
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<PYHKI.J.HH
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none
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df
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cBo6o.ubI).
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BBo.ua
P
BBeCTH
qHCnO
0.01, a B none
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-
qHCnO
5.
• HaxaTb
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nOHBHTCH
HH:x<:HHH
o.uHonpOn;eHTHaH
TOqKa
x(~.O!)
= 0.554285
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C
IIHTblO
CTeneHHMH
CBOOO.ubI.
• B none
BBo.ua
P
BBeCTH
qHCnO
0.99.
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KHOIIKY
Compute.
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nOHBHTCH
BepXHHH
o.uHonpOn;eHTHaH
TOqKa
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=
15.088091
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C lliITblO
CTeneHHMH
cBo6o.uhI.
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o6pa30M,
C
TOqHOCTblO
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TPeThero
.ueCHTlfqHOrO
3HaKa
.
X(~.OI)
= 0.554,
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=
15.088.
Ha
pHC.
II.2.21
npHBe.ueHbI
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lPYHKn;HH
nnOTHOCTH
H
<pyHKn;HH
pacnpe.ueneHHH
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Ha
rpa-
<pHKe
OTMeqeHa
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=
15.088.
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nocne.uOBaTenbHOCTb
H3
12
cnyqaH-
HbIX
qHCen,
paBHOMepHO
pacnpe.ueneHHhIX
B
HHTepBaJIe
(0, 1).
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<pOpMHpoBaHHH
TPe6yeMoH
nocne.uOBaTenbHOCTH
Heo6xo-
.uHMO:
286
I....
T
:'\
,
Probability Distribution Function
Probability Density Function
p=ichi2(x;5)
.;~
y=chi(x;5)
1.0
'"
,
'LiJOI"'"
I
0.175 , , ( ,
I
0.8
0.131
0.6
0.087
0.4
0.044
0.2
0.000
r ,
,>Z,
I 0.0
1/
,
J.'
,I
0.00 6.25 12.50 18.7525.00 0.00 6.25 12.50 18.75 25.00
PRC.
IT.2.2l.
rpaIPmrn
IPYHKURR
IIJIOTHOCTR
R
IPYHKURR
pacnpe~eJleHIDl
XH-KBW
aT
pacnpe~eJleHIDl
C IDlTbIO
CTeneHJIMR
cBo6o~bl.
\"~II'
•
C03.uaTb
rrycTYlO
3neKTPoHHYlO
Ta6nHIJ;y
H
npHcBoHTb
eH
HWI,
'
'i
HanpHMep
Sample1.
:,
'
•
Ha
naHenH
HHcTPyMeHToB
HaxaTb
KHonKY
Cases
(cnyqaH).
'11;'1
;1
,
',~1
• B
OTKpbIBIlleMcH
.uHaJIOrOBOM
oKHe
BbI6paTb
KOMaH.llY
Add
••.
(«)lo6aBHTb»).
OTKpOeTCH
OKHO
Add
Cases
(<<)lo6aBHTb
cnyqaH
(CTPOKH)>»
(pHC.
II.2.22).
11
i;~
PRC.
IT.2.22.
OKHO «,ll.o6aBRTb
CTPOKH
B Ta6Jlauy».
• B none Number
of
Cases
to Add
(qHCnO
,llo6aBJUleMbIX
CTPOK)
BBeCTH
qHCnO
2, a B none Insert after
Case
(<<BCTaBHTb
nocne
CTPOKH»)
-
qHCnO
10.
• HaxaTb
KHonKY
OK.
B
3neKTPoHHYlO
Ta6nHIJ;y
SAMPLE1.STA.uo6aBHTcH
.uBe
.uonon-
HHTenbHble
CTPOKH.
•
)lBa:x<:,UbI
menKHYTb
neBOH
KnaBHllIeH
MbIIlIH
no
HMeHH
nepe-
MeHHoH
VARI.
OTKpoeTcH
.uHanoroBoe
OKHO
Variable 1.
l
287
,,./
"
'
..
:,:,.:'~I(
.
,
:,'
,
._&1L;YJ:\tl>~+.,4H.qij~,Ei?,
"'"":"
il'
L.
~
i
~.l..!I1,.~JL.:I""-I!lW'
iJ:., I
..
,~._.,...
11='
•
• B
nOJIe
Name BBeCTH
HMH
nepeMeHHoH
R
(nepBasI
6YKBa
CJIO-
:;f
Ba
«random»
-
CJIyqaHHhIH).
• B
nOJIe
Column width BBeCTH 'IHCJIO 6, a B
nOJIe
Decimals -
'IHCJIO
5.
• B
nOJIe
Long name BBeCTH
HWI
=Rnd(l)
reHepaTOpa
cTaH)l;ap-
THbIX
paBHOMepHbIX
CJIyqaHHbIX
'IHCeJI
(cJIY'!aHHbIX
'IHCeJI,
pacnpe,lleJIeHHbIX
paBHOMepHO
B
HHTepBaJIe
(0,
1».
•
HaJKaTb
KRonK}'
OK.
• B
OTKphIBlIIeMCH
,llHaJIOroBOM
OKRe
STATISTICA
HaJKaTb
KRonK}'
Yes.
Ha
3KpaHe
OT06pa3HTCH
3JIeKTPOHHasI
Ta6JIHua
SAMPLEl.STA,
B
nepBOM
cToJI6ue
KOTOpOH
3anHcaHhI
12
CJIyqaHHbIX
'IHCeJI
CTaH-
,llapTHOH
paBHoMepHoH
nOCJIe,llOBaTeJIbHOCTH
(pHC.
rr.2.23).
iYil:f.
"
/,'1.:
PRC.
II.2.23.
IIocJIe,noBaTeJIbHOCTb CJIy'lail:HbIX qRCeJI, paBHOMepHO
pacnpe,neJIeH-
HbIX
B RHTepBaJIe
(0;
I), CcPOPMHPOBaHHWI
naxeTOM.
llpUMep
9.
CcP0pMHpOBaTb
nOCJIe,llOBaTeJIbHOCTb
H3
15
CTaH)l;apT-
HbIX
HOPMaJIbHbIX
CJIyqaHHhIX
'IHCeJI,
T.
~.
HOpMaJIbHhIX
CJIyqaHHbIX
'IHCeJI C
MaTeMaTH'IeCKHM
O)l(H)J;aHHeM 0 H CTaH)l;apTHhIM OTKJIOHe-
HHeM
1.
'{.l
:i!i,
):(.mI
cPOpMHpOBaHHH
Tpe6yeMoH
nOCJIe,llOBaTeJIbHOCTH
Heo6xo-
'.~
,llHMO:
•
C03,llaTb
rryCTyIO
311eKTPOHHyro Ta611HUY H
npHCBOHTb
eH
HMH
Sample.
•
Ha
naHellH
HHCTpYMeHTOB
HaxaTb
KRonK}'
Cases
(<<clIyqaH»).
• B
oTKphIBlIIeMCH
,llHaJIOrOBOM
OKRe
BbI6paTb
KOMaH,lly
Add
•••
!if
(«,l106aBHTb») .
:·,l~.'
'I
288
• B
OTKpbIBlIIeMCH
oKRe
Add Cases, B
nOJIe
Number
of
Cases
to
Add BBeCTH 'IHCJIO 5, a B
nOlle
Insert after Case - 'IHCJIO 10.
•
HaJKaTb
KRonK}'
OK.
B
3JIeKTPoHHyro
Ta6JIHUY
SAMPLE.STA ,l106aBHTcH
IDITb
,llO-
nOJIHHTeJIbHbIX
CTpOK.
• LJ:BaJK,llbI
meJIKRyTb
lIeBOH
KJIaBHlIIeH
MbIlliH
no
HMeHH
nepe-
MeHHoH
VARI.
OTKpOeTCH
,llHaJIOrOBOe OKRO Variable
I.
• B
nOJIe
Name BBeCTH
HMH
nepeMeHHoH
Z.
• B
nOJIe
Column width BBeCTH
'IHClIO
8, a B
nOlle
Decimals -
'IHCJIO 4.
• B
nOJIe
Long name BBeCTH
HMH
=Vnormal(Rnd(I),O,I)
cPyHK-
UHH,
cPopMHpyromeH
nOCJIe,llOBaTeJIbHOCTb
cTaH,llapTHbIX
HOp-
MaJIbHbIX
CJIyqaHHbIX
'IHCeJI,
T. e.
CJIyqaHHbIX
'IHCell,
pacnpe-
,lleJIeHHbIX
no
HOpMaJIbHOMy
3aKoHy
C
napaMeTPaMH
0 H
1.
•
HaJKaTb
KRonK}'
OK.
• B
OTKpbIBlIIeMcH
,llHaJIOrOBOM
OKHe
STATISTICA
HaJKaTb
KRonK}'
Yes.
Ha
3KpaHe
oTo6pa3HTcH
3JIeKTPOHHasI
Ta6JIHua
SAMPLE.STA,
B
nepBoM
cToJI6ue
KOTOpOH
3anHcaHbI
15
CJIyqaHHbIX
'IHCeJI
CTaH-
,llapTHOH
HOpMaJIbHOH
'liDa'a
SAMPLE
STA
10.
'150
-3,0230,
2
,1601
3
-,8658'
'4
,8733
5
2147
6 -
0505
7 -
3845
1
2589
,9262
6638
-,9381
1,
0756
'
13
,5549
14
,0339
15
-,5129
'-:1
'
."
nOCJIe,llOBaTellbHOCTH
(pHC.
rr.2.24).
1!!I~13
.'
,,~
PRC.
II.2.24.
IIoCJIe,noBaTeJIbHOCTb CTaH,napTHblX HOpMaJIbHbIX
CJIy'lattHhIX
qHCeJI,
C!pOpMHpOBaHHWI
naKeTOM.
"Ii.
II
ito..
1-"
» T
nMTEPATYPA
TaCSnMl410l
1.
DaplC
JI.
C.
U
ap.
Ta6J1HUhl
pacnpeAeJIeHIDI
P3JIeg-paaca.
M.:
BQ
AH
CCCP,
1964.
2.
DOJIblUe6
JI.
H.,
CMUPH06
H.
B.
Ta6JIHUbI
MaTeMaTH'leCKOH
CTaTHCTHKH.
M.:
Hayx:a,
1983.
3.
raHuH
M
n.
Ta6JIHUbI
AJIjI
BepowrHocTHhIX
H
CTaTHCTH'IeCKHX
paC'IeToB.
n.:
BMA,1986.
4.
Ke/l/lu
T.
JI.
CTaTHCTH'leCKHe
Ta6JIHULI.
M.:
BQ
AH CCCP, 1966.
5.
Kpanu6uH
B.
B.
Ta6JIHIJ;hI
paCnpeAeJIeHIDl
BllJIh,lI;a.
M.:
Hayx:a,
1965.
6.
Oy3H
JL
D.
C60PHHK
CTaTHCTH'IeCKHX
Ta6JIHU.
M.:
BQ
AH
CCCP, 1966.
7.
IIazypo6a
B.
H.
Ta6JIHULI
HenOJIHolt
raMMa-<p)'HKI..IHH.
M.:
BQ
AH
CCCP,
1963.
8.
IIUpCOH
K
Ta6JIHIJ;hI
HenOJIHOH
6eTa-<PYHKUHH.
M.: BQ AH CCCP,
1974.
9.
CIlY14lCuu
E. E.
Ta6JIHUbI
AJIjI
BhI'IHCJIeHHR
HenOJIHOH
raMMa-<PYHKUHH
H
<PYHKUHH
BepoRTHocTeii
X.
2
•
n.:
H3A-BO
AH
CCCP,
1950.
10.
Ta6/1u14bl
HOpMllJILHOrO
HHTerpaJIa,
HOpMaJIbHolt
IUIOTHOCTH
H ee
HOpMHpO-
BaHHhIX
npOH3BOAHLIX
/
IlOA
peA.
H.
B.
CMHpHoBa.
M.:
H3A-BO
AH CCCP,
1960.
11.
Ta6/1u14bl
<PYHKUHIt
pacnpeAeJIeHHR
H
IUIoTHocreii
paCnpeAeJIeHIDl
CTbIO-
AeHTa
/ IloA
peA.
H.
B.
CMHpHoBa.
M.:
H3A-BO
AH CCCP,
1960.
12.
Ta6/1u14bl
BepORTHOCTHhIX
<PYHKUHIt.
T.
2.
M.: BQ AH CCCP,
1959.
CnpaBO'lHMKM
13.
A6e3zaY3
r. r.
U
ap.
CnpaBO'lHHK
no
BepOgTHOCTHhIM
paC'IeTaM.
M.:
BoeHH3-
AaT,
1970.
14.
A6paM08um14
M.,
CmuzaH
H.
CnpaBO'lHHK
no
CneIJ;HllJILHhlM
<PYHKUHRM
C
<popMYJIaMH,
rpa<pHKaMH
H
MaTeMaTH'IeCKHMH
Ta6JIHIJ;aMH.
M.:
Hayx:a,
1979.
15.
Aii8a3RH
C.
A. U
ap.
IlpHKJIaAHag
CTaTHCTHKa:
OCHOBhI
MOAeJIHpOBaHHR
H
nepBH'lHag
06pa6OTKa
AaHHLIX.
M.:
<l>HHaHchI
H
CTaTHCTHKa,
1983.
16.
DpoHlumeuH
H.
H.,
CeMeHaRe6
K
A.
CnpaBO'IHHK
no
MaTeMaTHKe
AJIjI
HIDKe-
HepoB
H
Y'lamHXCg
B1)'30B.
M.:
Hayx:a,
1980.
17.
Baa3UHCICUU
P.
H.
faMMa-
H
6eTa-paCnpeAeJIeHHR.
n.:
BMA,
1989.
18.
KOPO/llOlC
B.
C.
U
ap.
CnpaBO'IHHK
no
TeOpHH
BepowrHocTeH
H
MaTeMaTH'le-
CKoA
CTaTHCTHKe.
KHeB:
Hayx:oBa
A)'MKa,
1978.
19.
IIO/IJlapa
,ax.
CnpaBO'lHHK
no
BhI'IHCJIHTeJlbHhlM
MeTOJJ;aM
CTaTHCTHKH
M.:
<l>HHaHchI
H
CTaTHCTHKa,
1982.
20.
XacmuHzc
H.,
IIulColC
,ax.
CnpaBO'lHHK
no
CTaTHCTH'IeCKHM
pacnpeAeJIeHH-
gM.
M.:
CTaTHCTHKa,
1980.
21.
MameMamU'IeCICOR
3HQHKJIOne,lJ;Hjl.
M.:
COB.
3HQHKJIOne,lJ;Hjl,
1977.
22.
Johnson
N. L., Kotz
S.
Distributions
in
Statistics.
Vol.
1.
Discrete Distributi-
ons. Boston: Houghton Muffiin,
1969.
290
...
l'l~,
Ii
~'.i
'~~:
I,lj
;~'~
11
L
23.
Johnson
N. L., Kotz
S.
Distributions in Statistics. Vol.
2.
Continuous Univari-
ate Distributions. Boston: Houghton Muffiin,
1970.
24.
Johnson
N. L., Kotz
S.
Distributions in Statistics.
Vol.
3.
Continuous Univari-
ate Distributions. Boston: Houghton Muffiin,
1970.
rOCYAapCTBeHHwe CTaHAapTW
25.
faCT
11.001-73.
IlpHKJIaAHag
CTaTHCTHKa:
PMhI
npeAnO'lTHTeJIbHLIX
'1HC-
JIeHHbIX
3Ha'leHHIt
CTaTHCTH'IeCKHX
xapaKTepHcTHK.
M.:
H3JJ;-BO
CTaHAap-
TOB,
1973.
26.
faCT
11.002-73 (CT
C3B
545-77).
IlpHKJIaAHag
CTaTHCTHKa:
IlpaBHJIa
oueHKH
aHOpMaJIbHOCTH
pe3YJIbTaTOB
Ha6JIIOAeHHH.
M.:
H3A-BO
CTaHAap-
TOB,
1982.
27.
faCT
11.003-73.
IlpHKJIaAHag
CTaTHCTHKa:
PaBHoMepHo
pacnpeAeJIeHHhle
CJIY'!aHHhle
'1HCJIa.
M.:
H3JJ;-BO
CTaHAapTOB,
1973.
28.
fOCT
11.004-74 (CT
C3B
876-78).
IlpHKJIaAHag
CTaTHCTHKa:
IlpaBHJIa
onpeAeJIeHHR
OIJ;eHOK
H
AOBepHTeJIbHbIX
rpaHHIJ;
AJIjI
rrapaMeTPoB
HOpMaJIb-
HOro
paCnpeAeJIeHHR.
M.:
H3A-BO
CTaHAapTOB,
1981.
29.
faCT
11.005-74.
IlpHKJIaAHag
CTaTHCTHKa:
IlpaBHJIa
onpeJJ;eJIeHHR
OIJ;e-
HOK
H
AOBepHTeJIbHLIX
rpaHHIJ;
AJIjI
napaMeTPoB
3KcrrOHeHUHaJIbHOrO
pac-
npeAeJIeHHR
H
pacnpeAeJIeHHR
IlyaccoHa. M.:
H3A-BO
craHAaprOB,
1974.
30.
faCT
11.006-74 (CT
C3B
1190-78).
IlpHKJIaAHag
CTaTHCTHKa:
IlpaBHJIa
rrpoBepKH
comaCHR
onhlTHoro
pacnpeAeJIeHHJI
C
TeOpeTH'IeCKHM.
M.:
H3A-BO
CTaHAapTOB,
1981.
31.
faCT
11.007-74.
IlpHKJIaAHag
CTaTHCTHKa:
IlpaBHJIa
onpeAeJIeHHR
oueHOK
H
AOBepHTeJIbHbIX
rpaHHU
AJIjI
napaMeTPoB
pacrrpeJJ;eJIeHHR
BeH6YJIJla.
M.:
H3A-BO
CTaHAaprOB,
1980.
32.
faCT
11.008-75.
IlpHKJIaAHag
CTaTHCTHKa:
IlpaBHJIa
rrocTPoeHHR
H
rrpH-
MeHeHHR
BepOwrHOCTHbIX
cerOK.
M.:
H3A-BO
CTaHAapTOB,
1976.
33.
faCT
11.009-73.
IlpHKJIaAHag
CTaTHCTHKa:
IlpaBHJIa
onpeAeJIeHHR
oue-
HOK
H
AOBepHTeJIbHLIX
rpaHHU
AJIjI
rrapaMeTPOB
JIOrapH<pMH'IeCKH
HOpMaJIb-
HOro
pacrrpeAeJIeHHR.
M.:
H3A-BO
CTaHAapTOB,
1980.
34.
faCT
11.010-81.
IlpHKJIaAHag
CTaTHCTHKa:
IlpaBHJIa
onpeAeJIeHHR
oue-
HOK
napaMeTpoB
H
AOBepHTeJIbHLIX
HHTepBaJIOB
AJIjI
6HHOMHaJIbHOrO
H
OT-
PHUaTeJIbHOrO
6HHOMHaJIbHOro
pacnpeAeJIeHHR.
M.:
H3A-BO
CTaHAapTOB,
1981.
PYKOBOACTBa
oCSl.L.l.ero
xapaKTepa
35.
DOP08UIC06
B.
n.
IlorryJIJIPHoe
BBeJJ;eHHe
B
nporpaMMY
STATISTICA. M.:
KOMnbIOTep
npecc,
1998.
36.
DOP06UIC06
B.
II.,
DOP06UIC06
H.
II.
STATISTICA.
CTaTHCTH'leCKHH
aHaJIH3
H
06pa60TKa
JJ;aHHLIX
B
cpeJJ;e
Windows. M.: <l>HnHH'b,
1997.
37.
DYC/leHICO
H.
n.
U
ap.
MeToA
CTaTHCTH'IeCKHX
HCrrhITaHHH
(MeToA
MOHTe-
KaPJIo). M.: fH<I>Mn,
1962.
38.
raHUH
M.
n.,
C6elUHuICo6
A. A.
TeopHR
BepOgTHOCreH
H
ee
npHMeHeHHe
AJIjI
pemeHHR
3aAa'l
BM<I>.
n.: BMOnA,
1968.
39.
raHUH
M.
n.
PemeHHe
npHKJIaAHLIX
3aAa'l
TeopHH
BepowrHocTeH.
BhID.
2.
CJIY'!aHHhle
BeJIH'fHHhI.
n.: BMOnYA,
1973.
40.
rOJleHlCo,a.
H.
MoAeJIHpOBaHHe
H
CTaTHCTH'IeCKHH
aHaJIH3
nceBAOCJIY'!aHHLIX
'!HceJI
Ha
3JIeKTPOHHLIX
Bhl'lHCJIHTeJIbHbIX
MaIlIHHax.
M.:
Hayx:a,
fP<I>Mn,
1969.
41.
,abRICOH06
B.
n.
CnpaBO'IHHK
no
CHCTeMe
CHMBOJIbHolt
MaTeMaTHKH
DERIVE.
M.: CK IlPECC,
1998.
291
~~
,,~,
\10
A'l"
1.1
, I
'~
.i
1
42.
H6aHo6
B.
P.
MeTO)l;hI
BbItIHCJIeHHR
Ha
3BM.
KHeB:
HaYKOBa
)l;YMKa,
1986.
43. KHym
p.
HCKYCCTBO
npOrpaMMHpOBaHKH
MR
3BM.
T.2.
IIOJIY'!HCJIeHHbIe
aJIropHTMbI.
M.:
MHp, 1977.
44. JIIOK 10.
CneUHaJIbHhIe
MaTeMaTHtIeCKHe
epYHKJ.J;HH
H
HX
anrrpoKcHMaUIDI.
M.:
MHP,
1980.
45. llono6
E.
A.,
TeCAep
r.
C.
BbItIHCJIeHHe
epYHKJ.J;HR
Ha
3BM.
KHeB:
HaYKoBa
,D;}'MKa,
1984.
.
46.
C60pHUK
Ha)"IHhIX rrporpaMM
Ha
<1>opTpaHe.
BbIIl.
1.
CTaTHcTHKa.
M.:
CTa-
rnCTHKa,
1974.
47.
C060Ab
H.
M.
lJHCJIeHHhIe
MeTO,D;hI
MOHTe-KapJIo.
M.:
Hayx:a,
fP<1>MJI,
1973.
48.
TIOpUH
10. H., MaKapo6 A.
A.
CTaTRCTHtIeCKHH
aHaJIH3
,D;aHHbIX
Ha
KOMrrbIO-
Tepe.
M.:
HH<1>PA·
M,
1998.
49.
f1JeMep
B.
BBe)l;eHRe
B
TeopRIO
BepOHTHOCTeR
R
ee
rrpHJIOXeHIDI.
T.
1.
M.:
MRp,1984.
•
SO.
XaH
r.,
llIanupo
C.
CTarnCTHtIeCKHe
MO)l;eJIR
B
HH)J(eHepHhIX
3a)J;atIax.
M.:
MRp,
1969.
"..
~~
II
I\·f
IV:
ornABnEHHE
r
naaa
1
CnPABOYHblE
JJ,AHHbIE
06UJ,Ero
XAPAKTEPA
1.1.
OCHoBHbIe
nOlUlTIDl R
orrpe)l;eJIeHKH
. . . . . . . . . . .
3
1.2.
COOTHOmeHIDI
Me)J()J;y
pacrrpe.n:eJIeHHHMR
. . . . . . . . .
19
1.3.
CRMMeTpHtIHble,
CMemeHHbIe
R
ycetIeHHbIe
pacrrpe,D;eJIeHIDI.
CMe-
Iii"
CR
pacnpe)l;eJIeHRR
. . . . . . .
22
1.4.
OueHHBaHRe
rrapaMeTpoB
....
29
1.5.
feHepHpoBaHHe
cJIY'!aHHbIX
tIRCeJI
32
1.6.
Ta6JIHUbI,
TeXHHKa
BbltIRCJIeHRR
33
1.7.
YKaJaTeJIb
0603HatIeHRH
..
34
rnaaa
2
AIt1CKPETHblE (I...\EJlOYIt1CIlEHHbIE)
PACnpE,!J,EJlEHIt1~
2.1.
,LJ;HcKpeTHoe
paBHOMepHoe
pacrrpe,D;eJIeHHe
40
2.2.
Pacrrpe,D;eJIeHHe
IIyaccoHa . . .
42
'_of
2.3.
Pacnpe.n:eJIeHHe
oepHYJIJlR
. . . . . . .
46
2.4.
ORHOMHaJIbHOe
pacnpe,D;eJIeHRe.
. . . .
48
2.5.
[eoMeTpH'JeCKOe
pacrrpe)l;eJIeHRe
. . . .
53
2.5.1.
feoMeTpH'leCKOe
pacrrpe,D;eJIeHRe
1 .
53
2.5.2.
feOMeTpHtIeCKOe
pacrrpe)l;eJIeHRe
2
(pacrrpe,D;eJIeHRe
<1>appR)
56
2.6.
OTpRu;aTeJIbHOe
6RHOMHaJIbHOe
pacnpe)l;eJIeHHe
. . . . . . . . .
58
2.6.1.
OTpRu;aTeJIbHOe
6RHOMHaJIbHOe
pacnpe)l;eJIeHHe
1
.....
58
2.6.2.
OTpHll;aTeJIbHOe
6RHOMRaJIbHOe
pacnpe,D;eJIeHlfe
2
(pacnpe,D;e-
JIeHHe
IIaCKaJIH)
. . . . . . . . . . . . . . . . . . .
64
2.7. fHIlepreoMeTpHtIeCKOe
pacrrpe)l;eJIeHRe
. . . . . . . . . . . .
67
2.8.
OTpRu;aTeJIbHOe
mnepreoMeTpH'JeCKOe
pacrrpe)l;eJIeHRe
.....
73
2.8.1.
OTpRuaTeJIbHOe
rHIlepreoMeTpHtIeCKOe
pacrrpe,D;eJIeHRe
1 .
73
2.8.2.
OTpRuaTeJIbHOe
rHrrepreoMeTpHtIeCKOe
pacrrpe)l;eJIeHRe
2 .
77
2.9.
JIorapRepMHtIeCKOe
pacnpe,D;eJIeHHe
. . . .
81
2.9.1.
JIorapRepMRtIeCKOe
pacnpe,D;eJIeHHe
1
81
2.9.2.
JIorapRepMH'JeCKOe
pacnpe,D;eJIeHKe
2
84
2.10.
Pacrrpe,D;eJIeHRe
IIoRa
.
86
2.10.1.
Pacrrpe.n:eJIeHRe
nORa
1.
. . . . .
86
2.10.2.
Pacrrpe)l;eJIeHHe
IIoRa
2
(rrpe,D;eJIbHaH
epopMa)
90
2.11.
,LJ;3eTa-pacrrpe.n:eJIeHRe
(3aKoH
IJ.Rnepa-3cToyrra) .
93
2.12.
Pacrrpe,D;eJIeHRe
oopeJIH-
TaHHepa
.
97
~
293
~
'1.1
".
':'\:~"
,0
J..
,~
rllaBa
3
B.
P8cnpeAeneHHfI
C
B03MO)/(HbIMH
3H8'1eHHflMH
HEnPEPblBHblE
PACnpE,QEJlEHlJIfl
H8
orp8HWleHHOM
HHTepBane
A.
P8cnpeAeneHHfI
C
B03MO)/(HbIMH
3H8'1eHHflMH
H8
BCel1
'1HCnOBOI1 OCH
/Yl~,
• 3.25. PaBHoMepHoe (npJlMOyrOJIbHoe)
pacnpe~eJIeHHe
209
3.26.
DeTa-paCnpe~eJIeHHe
nepBoro
po~a
. . . . 212
3.1.
HOpMaJIbHOe
pacnpe~eJIeHHe
(pacnpe.L\eJIeHHe
faycca-JIanJIaca)
. .
102
3.26.1.
KJIaccHllecKoe
6eTa-pacnpe~eJIeHHe
212
3.2.
ABYCTopoHHee
nOKa3aTeJIbHOe
pacnpe~eJIeHHe
(pacnpe~eJIeHHe
3.26.2.
0606meHHoe
6eTa-paCnpe~eJIeHHe.
221
JIanJIaca) . . . . . . . . . . . . . . .
109
.3.27.
IIapa6oJIHlIecKoe
pacnpe.L\eJIeHHe
225
3.3.
Pacnpe~eJIeHHe
KOlliH .
112
3.28.
Pacnpe~eJIeHHe
apKCHHYca
. . . . . . . . 228
3.4.
Pacnpe~eJIeHHe
3KcTpeMaJIbHOrO
3HallemUl . . .
115
.',
'.,
3.29.
Pacnpe~eJIeHHe
CHMllCOHa . . . . . . . . 230
3.4.1.
Pacnpe~eJIeHHe
MHHHMaJIbHOrO
3HallemUl
115
II
3.30.
YcelleHHoe
HOpMaJIbHOe
pacnpe~eJIeHHe
(~BYXCTopoHHee
ycelle-
3.4.2.
Pacnpe~eJIeHHe
MaKCHMaJIbHOrO
3HallemUl
118
HHe)
233
3.5. ABoifHoe
nOKaJaTeJIbHOe
pacnpe~eJIeHHe
....
120
3.6.
JIorHcTHlIecKoe
pacnpe~eJIeHHe
. . . . . . . .
124
t
3.7.
Pacnpe~eJIeHHe
qaMnepHaYHa .
127
ii
r.
P8cnpeAeneHHfI,
Hcnonb3yeMbie
B
M8TeM8TWIeCK0l1
CT8THCTHKe
3.8.
Pacnpe~eJIeHHe
lIIapJIbe
(PM
fpaMa-lIIapJIbe
THna A) 130
'~'
)
3.31.
x2-Pacnpe~eJIeHHe
IIHpcoHa
.
237
,
5.
P8cnpeAeneHHfI
C
B03MO)/(HblMH
3H8'1eHHflMH
3.32.
x-Pacnpe~eJIeHHe
IIHpcoHa
.
242
H8
nOnO)/(HTenbHOI1
nonyocH
3.33.
t-Pacnpe~eJIeHHe
CTbIO.L\ema
. . . . . . . . . . . . . . . .
..
245
.'
3.34.
F-pacnpe~eJIeHHe
cIlHIIIepa-CHe~eKopa
(pacnpe~eJIeHHe
~Hcnep-
j
CHOHHOro
oTHollieHIDI) . . . . . . . . . . . . . . . . . . . . .
249
3.9.
IIoKaJaTeJIbHoe (3KcnOHeHIJ;HaJIbHoe)
pacnpe~eJIeHHe
133
3.35.
Z-pacnpe~eJIeHHe
cIlHIIIepa . . . . . . . . . . . . . . . . . . .
256
3.10.
faMMa-paCnpe.L\eJIeHHe . 136
3.10.1.
KJIaccHllecKoe
(~ByxnapaMeTpHllecKoe)
raMMa
-pacnpe-
I
I"
IIpHJIo)KeHHe
1.
fpa<pHKH,lI)Ul
BI>I6opa
THlla
CrJIa)KHBaIOmerO
pacnpe-
.L\eJIeHHe
.
136
~eJIemrn
·BepOJITHOCTeH.
. . . . . . . . . . . . . . . . . . . .
259
3.10.2.
CMemeHHoe (TpeXnapaMeTpHllecKoe)
raMMa-paCnpe~eJIe-
HHe
. 142
'
,I
IIpHJIo)KeHHe 2.
BepOJITHOCTHI>Ie
pacnpe~eJIeHIDI
B
CTaTHCTHlIecKHX
3.11.
Pacnpe~eJIeHHe
3pJIaHfa . . . . . . . . . . . . . . . . . . .
145
naKeTax
npHKJIa.AHI>IX
nporpaMM,lI)Ul
II3BM
.
263
3.11.1.
Pacnpe~eJIeHHe
3pJIaHra
m-ro
nOPMKa .
145
JIHTeparypa . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
290
3.11.2.
HOpMHpoBaHHoe
pacnpe~eJIeHHe
3pJIaHra
m-ro
nOPMKa
147
3.11.3.
0606meHHoe
pacnpe~eJIeHHe
3pJIaHra BToporo
nopMKa
150
3.12.
Pacnpe~eJIeHHe
BeH6YJIJIa-fHe~eHKo
.
153
3.12.1. KJIaccHllecKoe
(~ByxnapaMeTpHlleCKoe)
pacnpe~eJIeHHe
Beif6YJIJIa-
fHe~eHKo
(pacnpe~eJIeHHe
MHHHMaJIbHOrO
3HalleHIDI THna III) . . . . . . . . . . . . . . . . .
153
3.12.2.
CMemeHHoe (TpexnapaMeTpHlleCKoe)
pacnpe~eJIeHHe
Beif-
6YJIJIa-rHe~eHKo
.
159
i~
,
3.13. fHnep3KCnOHeHIJ;HaJIbHOe
pacnpe~eJIeHHe
BToporo nOPMKa .
162
'.!i"
x,j
3.14.
Pacnpe~eJIeHHe
MO~m1
n-MepHoro cJIYllaHHoro
BeKTOpa
.
165
3.15.
Pacnpe~eJIeHHe
P3JIeJl
. . . . . . . . . . . . . . . . . . . . .
168
"jl
..
3.16.
0606meHHoe
pacnpe~eJIeHHe
P3JIeJl
(pacnpe~eJIeHHe
P3JIeJl-
I .
1,\'
Palica) .
171
:~~:
(
3.17.
Pacnpe~eJIeHHe
MaKCBeJIJIa
. . . .
175
t;
3.18.
Pacnpe~eJIeHHe
HaKaraMH
....
179
3.19.
DeTa-paCnpe~eJIeHHe
BToporo
po~a
.
182
•
3.20. JIorapH<pMHlIeCKH
HOpMaJIbHOe
(JIOrHOpMaJIbHoe)
pacnpe~eJIeHHe
.
186
3.21.
Pacnpe~eJIeHHe
IIapeTo
.
190
3.22.
Pacnpe~eJIeHHe
MO~m1
HOpMaJIbHOH
CJIYllaifHOif
BeJIH'lHHI>I
(OT-
paJKeHHOe
HOpMaJIbHOe
pacnpe~eJIeHHe).
. . . . . . . . . . .
194
3.23.
YcelleHHoe
HOpMaJIbHOe
pacnpe~eJIeHHe
(OMOCTopoHHee
ycelle-
HHe) .
200
3.23.1. YcelleHHe
CJIeBa
.
200
3.23.2.
YcelleHHe cnpaBa . . . . . . . . . . . . . . . . . . .
203
3.24.
06paTHoe rayccoBcKoe
pacnpe.L\eJIeHHe
(pacnpe~eJIeHHe
BaJIb~a).
206
j
294
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