PRECISION ESTIMATOR/REPITITION TIMES=UPPER CONFIDENCE LIMIT
August Highland
hmfah3 at hotmail.com
Fri Oct 10 12:39:24 CEST 2003
PRECISION ESTIMATOR/REPITITION TIMES=UPPER CONFIDENCE LIMIT
SAMPLE #0000001:
W w, 1. c,,n~N~`G}-o,u N~,o/, oe2 +. O/21- ff 0. 2 x xy y. Figure 1: ,o/ oe2 , z $l3/4i']""-e`,
oep Case.A `G,n~'I`b u i'-E`,l_O`}&:. F $rdj5a$9$k!%%"%k%4 %j%:%`$h$jju uz, wz, vw, wx, xy $,=g!!
e(t ) $kdi2c$5$l!$:g?.a40hlz n. Ni=1(xi - u)2 -4 -2 0 2 4 0. 0 n=sample sizes, m = repetition
times, alpha = significance level.
SAMPLE #0000002:
A 1) oe21/oe22 i' 1 - ff ]""-E`N~. F (t 00)=f (t 0) - f (ujuj+1) + f (xkxi+1) <= f (t 0)$g$"$j!$ t
0 $,:g?.a40hlz$@$+$i f (t 00) = f (t 0) $g t 00 $b g $n:g?.a40hlz$h$j$k!%$h$3$m$,!$ e1, * * * , ei 2
e(t 00) $, at .$jn)$d$n$g!$t 0 $n2?dj$kl7=b$9$k!%$h$c$f!$t = t 0 $h$j$j t
$o:g?.a40hlz$g$"$k$3$h$,$o$+$k!% "":g?.a40hlz$nnc a0nc$n, 37 :G8e$K!$ 21. Re^-e`q-aw re^-e`q-aw
i']""a*ss i']""a*ss n=10 0.98 0.92 1.43071 1.15936 n=50 0.98 0.89 0.56839 0.47420 n=100 0.93 0.92
0.39684 0.33208 n=500 0.96 0.90 0.17573 0.14739 n" 10.2 A40hLZ%0%i%U. 21, oe22 n2 a'n~ ff=0.05 ff
=0.1 ff =0.05 ff =0.1. N1i=1(xi - u1)2/n1 f1-ff/2(n2, n1), 1 HHH.
SAMPLE #0000003:
(n2 - 1)s22 n $NLZ G $NBg$-$5$O |E(G)|=n - 1 $G$"$k!%$7$?$,$C$F!$ (1) ) (2), (1) ) (3)
$,$o$+$k!%!!$K!$G $OO"7k$G |E(G)| = n - 1 $H$9$k!%$b$7 !$ G $,JDO) a'N~s^..., s^...i''I`bN~ _X1 #
_X2 , / _X1 }-oN~ N (u1, oe21/n1) , _X2 }-o N~ N (u2, oe22/n2) , _X1 - _X2 i'}-oN~ N (u1 - u2,
oe21/n1 + oe22/n2), #s_}-o i''I`bI" u1 - u2 i' 1 - ff ]""-E`N~. Sp G $NA40hLZ T $r G $N :G?.A40hLZ
$H$$$&!%0J8e!$:G?.A40hLZ$r8+$D$1$kLdBj$r9M;!$9$k!% 10.4 :G?.A40hLZ9=@.%"%k%4
%j%:%`F~NO$O%3%9%H4X?t$,Dj5A$5$l$?O"7k%0%i%U 10.3 %3%9%H4X?t$H:G?.A40hLZO"7k$J%0%i%U. (n1 - 1)s21
2. c,,n~N~`G}-o N (u, oe2) , "o/ oe2 , 1. q X1 }-oN~ N (u1, oe21) ,X2 }-oN~ N (u2, oe22),
*#s}-o(R),| n1 a'D n2. 3 'e}& ;wi`u"ia,n~ s-plus _o`vdh"u""i'||}, w2"o", A sp. F (xy) oe21
w}-oN~Aa^ss *=n1 - 1 i'uj}-o.
SAMPLE #0000004:
S21 n1 + 1 + 1/n2 i'}-oN~ 21. 7 10. :G?.A40hLZ AH9g$;M""O at 9V5A;qNA 10 0. 2. \gamma \gamma, 2
It%0%i%U$G$"$k$3$H$r!($;!%Ld!% Nc$GMQ$$$?%0%i%U 3. \omega \omega, s2p=(n1 - 1)s V (T )=V (G), E(T )
= {uz, vw, wx, wz, xy} $H$9$k$H T $O G$NA40hLZ$G$"$k!%. 1 n1 + s22 n2 <=u1 - u2 <= ( _X1 - _X2) +
Zff/2s n i=1(D- _D)n-1 , Aa^ss * =.
SAMPLE #0000005:
$,n~u: ]""-e`i'$l_o`o~dh (#n~uua^ro'toc,i`'i'i., a^~i'a'a'f!! /2002/10/7) 1 1/2ae*h -e`,lua^
r.a.fisher i'lt|i'\delta 1la^o~,l||2i`,n~|7,l3/4, y; w#,l3/4i',s^}-o#]""[b (confidence level) ,
2i`oe0-e` (probability interval), yd-2a]""-e` (confidence interval), y"-aj*),n~i'-e`,l!<\delta -e`
,luj-e`,lmvr,,n~!bo"o~mrk#-e`i'oe0*u", a"#-e`, lmc*n~]""-e`\delta yy"n~ui'1/2aebbo/< 2 u""*\delta
2.1 -e`,li'<2, 2 (*) <= F,-E`,lua^o~,l3/4i'o|j||, l2i`iG,l3/4 ^` (, y;W#, l3/4i',s^}-o #]""[b 1- ff
(o/\Upsilon 3hoe0), 2i`-aE^ ^` }-o_ss,[ y'i'oe0-E` (Probability Interval), yd-2A]""-E` (Confidence
Interval) i'$l j||. -E`,luJO'oe-E` (Random Interval) V,l,b, #O'oe-E`1]""-E`, w]""I`N~ L , U, L <=U ,
E^o/]""ss-, J#-E`V-O"""o/,b ` i'F. \gamma \gamma xyy1 * * * ytx$H=q$1$k$,!$ G $N x - y O) xyt * * *
y1y $,B8:.$9$k$3$H$K$J$j2?Dj$KH?$9$k!%$3$3$G!$| E(G00)| = n
$@$+$iA02s$NL?Bj$KL7=b$9$k!%$7$?$,$C$F!$$3$N?l9g$b G $OLZ$H$J$C$F (3) ) (1) $,!($5$l$?!% "" 2. a`<
oe1 D oe2N~"o/b, 7s^...*u"o'c,*v, /s^...uO"fl, #,H u1 -. 1. *s_}-o n (u1, oe21) d n (u2,
oe22) }a,,|"o" n1 a'd n2 a'i's o'oe, AA n $NLZ G $NBg$-$5$O |E(G)|=n - 1 $G$"$k!%$7$?$,$C$F!$ (1) )
(2), (1) ) (3) $,$o$+$k!%!!$K!$G $OO"7k$G |E(G)| = n - 1 $H$9$k!%$b$7 !$ G $,JDO). 2.
c,,n~n~`g}-o,u n~"o/, 21 3. 4 <=F1-ff/2(n1, n2)] = 1 - ff Figure 1: ,o/ oe2 , Z $l3/4i']""-E`.
SAMPLE #0000006:
Oe2 w}-on~aa^ss *=n - 1 i', uj * * * u1xkxi+1um * * * uj+1=uj * * * u1u0um+1um * * * uj+1$r;H$($P T
00 $,O"7k$G$"$k$3$H$,8@$($k!%DjM""$h$j T 00 $OLZ$H$J$k!%$^$?!$(*) $h$j 0. 2. U u v v s^..., oe21 D
oe22 N~"o/b,u1, u2 N~,o/, # oe21 /oe22 i' 1 - ff ]""-E`-aa^J-~. R`7) 4uA" Z=( _X1 - _X2) - (u1 -
u2)oeq1/n. 3 'e}& ;wi`u"ia,n~ s-plus _o`vdh"u""i'||}, w2"o" T 0 $+$i ujuj+1 $r!h$j=--$-Be$o$j$K
xkxi+1 $rIU$12C$($?%0%i%U$r T 00 $H$*$/!%T 00 $b G $NA40hLZ$G$"$k!%$J$!$J$i!$|E(T 00)| = |E(T 0)| =
n - 1 $G$"$j!$JU 3 'e}& ;Wi`U"iA,N~ S-PLUS _O`Vdh"U""i'||}, w2"O". Re^-e`q-aw re^-e`q-aw i']""a*ss
i']""a*ss n=10 0.94 0.92 2.80673 2.08482 n=30 0.97 0.93 1.20462 0.96424 ,o/ u a` o/2(n - 1) c,$l3/4,
0. 8 n. ( _x1 - _x2) - tff/2(*)sps 1n, bb r r.
SAMPLE #0000007:
3. ,n~n~ls,n~,n >=30 , oe2 ?"o/, 6-aa``g}-otu"\delta ,n~."s\upsilon, 1 n <=u <= _X + Z. P
[fff/2(n1, n2) <=p s^..., oe21 D oe22 N~"o/b,u1, u2 N~,o/, # oe21 /oe22 i' 1 - ff ]""-E`-aa^J-~.
R`7). \gamma \gamma, ff s21 n1 +. ( _x1 - _x2) - zff/2s oe oep. -e`2, y"bw-aoe7k3"pe'i'i"ae, oe^
oe2 "o/u"s^...v, a` z c, $l3/4|u^-aoea~1/2i'i"i", yu-aju"ji', a"n~a`< oe2 "o/s^...b
u"v, ]""a*ss}o/ooi'oes, o`q\psi a`re^]""-e`2i'-aw, 7,o/ oe2 a` t c,$l3/4, }"a]""a*ssoea*fj-awm}ro`,
2 (*) <= G $NA40hLZ T $r G $N :G?.A40hLZ $H$$$&!%0J8e!$:G?.A40hLZ$r8+$D$1$kLdBj$r9M;!$9$k!% 10.4
:G?.A40hLZ9=@.%"%k%4 %j%:%`F~NO$O%3%9%H4X?t$,Dj5A$5$l$?O"7k%0%i%U.
SAMPLE #0000008:
2(n - 1) ,, oe21 w}-oN~Aa^ss *=n1 - 1 i'uj}-o n >=2 $N%0%i%U G $K$D$$$F!$!!$N#3?r7o$OF1CM!% (1) G
$OLZ$G$"$k!% (2) G $OO"7k$G |E(G)| = n - 1!% (3) G $OL5JDO)E*$G |E(G)| = n -
1!%?ZL@!%A02s$NL?Bj$h$j0L?t$,. A'n~ ff=0.05 ff =0.1 ff =0.05 ff =0.1 f $rDj5A$9$k!%%"%k%4
%j%:%`$h$jJU uz, wz, vw, wx, xy $,=g!! E(T ) $KDI2C$5$l!$:G?.A40hLZ. N1 + n2 - 2
i'uj}-o, ]}-on~aa^ss *=n1 + n2 - 2 i' t }-o\delta \Omega \Omega. 1. 0 14 P [O/2ff/2(*) <=O/2 <=
O/21-ff/2(*)] = 1 - ff ] oe2 i' 1- ff ]""ssi']""-E`N~P. \omega \omega s^..., oe21 D oe22 N~"o/b,u1,
u2 N~,o/, # oe21 /oe22 i' 1 - ff ]""-E`-aa^J-~. R`7) 6.
SAMPLE #0000009:
2, 1) oe21/oe22 i' 1 - ff ]""-E`N~P n1i=1(xi - u1)2/n1 F1-ff/2(n2, n1). 2 (*) (n - 1)s2 count <-
count + 1 } } w<-leng/m cat("There are ", count, "intervals containing sd=1 W=",w,"\n")
invisible() }. Mu n i=1(D- _D)n-1 , Aa^ss * = }-o, n >=30 N~D*, ;W2U^"I`i`U"o/, _X i',s^}-oN~`G}-oC
!N`G}-o, #'I`b u i']""[bN~ 1- ff i']""-E`N~. 1 +, oe2 <=P O/2 _D=P. 37 :g8e$k!$ 2. c,,n~N~`G}-o N
(u, oe2) , "o/ oe2 , s21 n1 +.
SAMPLE #0000010:
Re^-e`q-aw re^-e`q-aw i']""a*ss i']""a*ss n=10 0.98 0.92 3.37437 2.36681 n=30 0.94 0.92 1.26950
0.96771 "o/ u a` o/2(n) c,$l3/4 J. Jj a^O'oei'`G'eF)i']""-E`, c,e'O(R)A"N~ 95% vBbi'u""ae 95 ]
""-E`}"O"Ro"#i'o/ooaeb\Delta ,a` S-PLUS ssTh,s^,n~N~`G}-o N(0,1), /,n~2O'oe,|o/ s^... X1, X2, . . .
, Xn , s^...b*u" (samplesize)=n, 1/2-od 100 Y"1p". Re^-e`q-aw re^-e`q-aw i']""a*ss i']""a*ss n=10
0.94 0.92 2.80673 2.08482 n=30 0.97 0.93 1.20462 0.96424 ,o/ u a` o/2(n - 1) c,$l3/4, 2.3 \Psi
a`]""-E`i'*u"A"O" oe22 n2 <=u1 - u2 <= ( _X1 - _X2) + Zff/2s. ( _x1 - _x2) - zff/2s oe |E(G0)|=n -
2 $H$J$C$FA02s$NL?Bj$KH?$9$k!%$h$C$F!$ G $OL5JDO)E*$H$J$C$FLZ$G$"$k$3$H$,$o$+$j!$(2) ) (1)
$,8@$($k!% T 0 $+$i ujuj+1 $r!h$j=--$-Be$o$j$K xkxi+1 $rIU$12C$($?%0%i%U$r T 00 $H$*$/!%T 00 $b G
$NA40hLZ$G$"$k!%$J$!$J$i!$|E(T 00)| = |E(T 0)| = n - 1 $G$"$j!$JU. Re^-e`q-aw re^-e`q-aw i']""a*ss
i']""a*ss n=10 0.97 0.89 2.61944 1.87502 n=30 0.97 0.91 1.16459 0.93739 "o/ u a` o/2(n - 1) c,$l3/4,
o/ x <- seq(-3, 3, 0.05) plot(x, dnorm(x), col=6, xlab = "mu",ylab = "pdf",.
PRECISION ESTIMATOR/REPITITION TIMES=UPPER CONFIDENCE LIMIT
SAMPLE #0000001:
W w, 1. c,,n~N~`G}-o,u N~,o/, oe2 +. O/21- ff 0. 2 x xy y. Figure 1: ,o/ oe2 , z $l3/4i']""-e`,
oep Case.A `G,n~'I`b u i'-E`,l_O`}&:. F $rdj5a$9$k!%%"%k%4 %j%:%`$h$jju uz, wz, vw, wx, xy $,=g!!
e(t ) $kdi2c$5$l!$:g?.a40hlz n. Ni=1(xi - u)2 -4 -2 0 2 4 0. 0 n=sample sizes, m = repetition
times, alpha = significance level.
SAMPLE #0000002:
A 1) oe21/oe22 i' 1 - ff ]""-E`N~. F (t 00)=f (t 0) - f (ujuj+1) + f (xkxi+1) <= f (t 0)$g$"$j!$ t
0 $,:g?.a40hlz$@$+$i f (t 00) = f (t 0) $g t 00 $b g $n:g?.a40hlz$h$j$k!%$h$3$m$,!$ e1, * * * , ei 2
e(t 00) $, at .$jn)$d$n$g!$t 0 $n2?dj$kl7=b$9$k!%$h$c$f!$t = t 0 $h$j$j t
$o:g?.a40hlz$g$"$k$3$h$,$o$+$k!% "":g?.a40hlz$nnc a0nc$n, 37 :G8e$K!$ 21. Re^-e`q-aw re^-e`q-aw
i']""a*ss i']""a*ss n=10 0.98 0.92 1.43071 1.15936 n=50 0.98 0.89 0.56839 0.47420 n=100 0.93 0.92
0.39684 0.33208 n=500 0.96 0.90 0.17573 0.14739 n" 10.2 A40hLZ%0%i%U. 21, oe22 n2 a'n~ ff=0.05 ff
=0.1 ff =0.05 ff =0.1. N1i=1(xi - u1)2/n1 f1-ff/2(n2, n1), 1 HHH.
SAMPLE #0000003:
(n2 - 1)s22 n $NLZ G $NBg$-$5$O |E(G)|=n - 1 $G$"$k!%$7$?$,$C$F!$ (1) ) (2), (1) ) (3)
$,$o$+$k!%!!$K!$G $OO"7k$G |E(G)| = n - 1 $H$9$k!%$b$7 !$ G $,JDO) a'N~s^..., s^...i''I`bN~ _X1 #
_X2 , / _X1 }-oN~ N (u1, oe21/n1) , _X2 }-o N~ N (u2, oe22/n2) , _X1 - _X2 i'}-oN~ N (u1 - u2,
oe21/n1 + oe22/n2), #s_}-o i''I`bI" u1 - u2 i' 1 - ff ]""-E`N~. Sp G $NA40hLZ T $r G $N :G?.A40hLZ
$H$$$&!%0J8e!$:G?.A40hLZ$r8+$D$1$kLdBj$r9M;!$9$k!% 10.4 :G?.A40hLZ9=@.%"%k%4
%j%:%`F~NO$O%3%9%H4X?t$,Dj5A$5$l$?O"7k%0%i%U 10.3 %3%9%H4X?t$H:G?.A40hLZO"7k$J%0%i%U. (n1 - 1)s21
2. c,,n~N~`G}-o N (u, oe2) , "o/ oe2 , 1. q X1 }-oN~ N (u1, oe21) ,X2 }-oN~ N (u2, oe22),
*#s}-o(R),| n1 a'D n2. 3 'e}& ;wi`u"ia,n~ s-plus _o`vdh"u""i'||}, w2"o", A sp. F (xy) oe21
w}-oN~Aa^ss *=n1 - 1 i'uj}-o.
SAMPLE #0000004:
S21 n1 + 1 + 1/n2 i'}-oN~ 21. 7 10. :G?.A40hLZ AH9g$;M""O at 9V5A;qNA 10 0. 2. \gamma \gamma, 2
It%0%i%U$G$"$k$3$H$r!($;!%Ld!% Nc$GMQ$$$?%0%i%U 3. \omega \omega, s2p=(n1 - 1)s V (T )=V (G), E(T )
= {uz, vw, wx, wz, xy} $H$9$k$H T $O G$NA40hLZ$G$"$k!%. 1 n1 + s22 n2 <=u1 - u2 <= ( _X1 - _X2) +
Zff/2s n i=1(D- _D)n-1 , Aa^ss * =.
SAMPLE #0000005:
$,n~u: ]""-e`i'$l_o`o~dh (#n~uua^ro'toc,i`'i'i., a^~i'a'a'f!! /2002/10/7) 1 1/2ae*h -e`,lua^
r.a.fisher i'lt|i'\delta 1la^o~,l||2i`,n~|7,l3/4, y; w#,l3/4i',s^}-o#]""[b (confidence level) ,
2i`oe0-e` (probability interval), yd-2a]""-e` (confidence interval), y"-aj*),n~i'-e`,l!<\delta -e`
,luj-e`,lmvr,,n~!bo"o~mrk#-e`i'oe0*u", a"#-e`, lmc*n~]""-e`\delta yy"n~ui'1/2aebbo/< 2 u""*\delta
2.1 -e`,li'<2, 2 (*) <= F,-E`,lua^o~,l3/4i'o|j||, l2i`iG,l3/4 ^` (, y;W#, l3/4i',s^}-o #]""[b 1- ff
(o/\Upsilon 3hoe0), 2i`-aE^ ^` }-o_ss,[ y'i'oe0-E` (Probability Interval), yd-2A]""-E` (Confidence
Interval) i'$l j||. -E`,luJO'oe-E` (Random Interval) V,l,b, #O'oe-E`1]""-E`, w]""I`N~ L , U, L <=U ,
E^o/]""ss-, J#-E`V-O"""o/,b ` i'F. \gamma \gamma xyy1 * * * ytx$H=q$1$k$,!$ G $N x - y O) xyt * * *
y1y $,B8:.$9$k$3$H$K$J$j2?Dj$KH?$9$k!%$3$3$G!$| E(G00)| = n
$@$+$iA02s$NL?Bj$KL7=b$9$k!%$7$?$,$C$F!$$3$N?l9g$b G $OLZ$H$J$C$F (3) ) (1) $,!($5$l$?!% "" 2. a`<
oe1 D oe2N~"o/b, 7s^...*u"o'c,*v, /s^...uO"fl, #,H u1 -. 1. *s_}-o n (u1, oe21) d n (u2,
oe22) }a,,|"o" n1 a'd n2 a'i's o'oe, AA n $NLZ G $NBg$-$5$O |E(G)|=n - 1 $G$"$k!%$7$?$,$C$F!$ (1) )
(2), (1) ) (3) $,$o$+$k!%!!$K!$G $OO"7k$G |E(G)| = n - 1 $H$9$k!%$b$7 !$ G $,JDO). 2.
c,,n~n~`g}-o,u n~"o/, 21 3. 4 <=F1-ff/2(n1, n2)] = 1 - ff Figure 1: ,o/ oe2 , Z $l3/4i']""-E`.
SAMPLE #0000006:
Oe2 w}-on~aa^ss *=n - 1 i', uj * * * u1xkxi+1um * * * uj+1=uj * * * u1u0um+1um * * * uj+1$r;H$($P T
00 $,O"7k$G$"$k$3$H$,8@$($k!%DjM""$h$j T 00 $OLZ$H$J$k!%$^$?!$(*) $h$j 0. 2. U u v v s^..., oe21 D
oe22 N~"o/b,u1, u2 N~,o/, # oe21 /oe22 i' 1 - ff ]""-E`-aa^J-~. R`7) 4uA" Z=( _X1 - _X2) - (u1 -
u2)oeq1/n. 3 'e}& ;wi`u"ia,n~ s-plus _o`vdh"u""i'||}, w2"o" T 0 $+$i ujuj+1 $r!h$j=--$-Be$o$j$K
xkxi+1 $rIU$12C$($?%0%i%U$r T 00 $H$*$/!%T 00 $b G $NA40hLZ$G$"$k!%$J$!$J$i!$|E(T 00)| = |E(T 0)| =
n - 1 $G$"$j!$JU 3 'e}& ;Wi`U"iA,N~ S-PLUS _O`Vdh"U""i'||}, w2"O". Re^-e`q-aw re^-e`q-aw i']""a*ss
i']""a*ss n=10 0.94 0.92 2.80673 2.08482 n=30 0.97 0.93 1.20462 0.96424 ,o/ u a` o/2(n - 1) c,$l3/4,
0. 8 n. ( _x1 - _x2) - tff/2(*)sps 1n, bb r r.
SAMPLE #0000007:
3. ,n~n~ls,n~,n >=30 , oe2 ?"o/, 6-aa``g}-otu"\delta ,n~."s\upsilon, 1 n <=u <= _X + Z. P
[fff/2(n1, n2) <=p s^..., oe21 D oe22 N~"o/b,u1, u2 N~,o/, # oe21 /oe22 i' 1 - ff ]""-E`-aa^J-~.
R`7). \gamma \gamma, ff s21 n1 +. ( _x1 - _x2) - zff/2s oe oep. -e`2, y"bw-aoe7k3"pe'i'i"ae, oe^
oe2 "o/u"s^...v, a` z c, $l3/4|u^-aoea~1/2i'i"i", yu-aju"ji', a"n~a`< oe2 "o/s^...b
u"v, ]""a*ss}o/ooi'oes, o`q\psi a`re^]""-e`2i'-aw, 7,o/ oe2 a` t c,$l3/4, }"a]""a*ssoea*fj-awm}ro`,
2 (*) <= G $NA40hLZ T $r G $N :G?.A40hLZ $H$$$&!%0J8e!$:G?.A40hLZ$r8+$D$1$kLdBj$r9M;!$9$k!% 10.4
:G?.A40hLZ9=@.%"%k%4 %j%:%`F~NO$O%3%9%H4X?t$,Dj5A$5$l$?O"7k%0%i%U.
SAMPLE #0000008:
2(n - 1) ,, oe21 w}-oN~Aa^ss *=n1 - 1 i'uj}-o n >=2 $N%0%i%U G $K$D$$$F!$!!$N#3?r7o$OF1CM!% (1) G
$OLZ$G$"$k!% (2) G $OO"7k$G |E(G)| = n - 1!% (3) G $OL5JDO)E*$G |E(G)| = n -
1!%?ZL@!%A02s$NL?Bj$h$j0L?t$,. A'n~ ff=0.05 ff =0.1 ff =0.05 ff =0.1 f $rDj5A$9$k!%%"%k%4
%j%:%`$h$jJU uz, wz, vw, wx, xy $,=g!! E(T ) $KDI2C$5$l!$:G?.A40hLZ. N1 + n2 - 2
i'uj}-o, ]}-on~aa^ss *=n1 + n2 - 2 i' t }-o\delta \Omega \Omega. 1. 0 14 P [O/2ff/2(*) <=O/2 <=
O/21-ff/2(*)] = 1 - ff ] oe2 i' 1- ff ]""ssi']""-E`N~P. \omega \omega s^..., oe21 D oe22 N~"o/b,u1,
u2 N~,o/, # oe21 /oe22 i' 1 - ff ]""-E`-aa^J-~. R`7) 6.
SAMPLE #0000009:
2, 1) oe21/oe22 i' 1 - ff ]""-E`N~P n1i=1(xi - u1)2/n1 F1-ff/2(n2, n1). 2 (*) (n - 1)s2 count <-
count + 1 } } w<-leng/m cat("There are ", count, "intervals containing sd=1 W=",w,"\n")
invisible() }. Mu n i=1(D- _D)n-1 , Aa^ss * = }-o, n >=30 N~D*, ;W2U^"I`i`U"o/, _X i',s^}-oN~`G}-oC
!N`G}-o, #'I`b u i']""[bN~ 1- ff i']""-E`N~. 1 +, oe2 <=P O/2 _D=P. 37 :g8e$k!$ 2. c,,n~N~`G}-o N
(u, oe2) , "o/ oe2 , s21 n1 +.
SAMPLE #0000010:
Re^-e`q-aw re^-e`q-aw i']""a*ss i']""a*ss n=10 0.98 0.92 3.37437 2.36681 n=30 0.94 0.92 1.26950
0.96771 "o/ u a` o/2(n) c,$l3/4 J. Jj a^O'oei'`G'eF)i']""-E`, c,e'O(R)A"N~ 95% vBbi'u""ae 95 ]
""-E`}"O"Ro"#i'o/ooaeb\Delta ,a` S-PLUS ssTh,s^,n~N~`G}-o N(0,1), /,n~2O'oe,|o/ s^... X1, X2, . . .
, Xn , s^...b*u" (samplesize)=n, 1/2-od 100 Y"1p". Re^-e`q-aw re^-e`q-aw i']""a*ss i']""a*ss n=10
0.94 0.92 2.80673 2.08482 n=30 0.97 0.93 1.20462 0.96424 ,o/ u a` o/2(n - 1) c,$l3/4, 2.3 \Psi
a`]""-E`i'*u"A"O" oe22 n2 <=u1 - u2 <= ( _X1 - _X2) + Zff/2s. ( _x1 - _x2) - zff/2s oe |E(G0)|=n -
2 $H$J$C$FA02s$NL?Bj$KH?$9$k!%$h$C$F!$ G $OL5JDO)E*$H$J$C$FLZ$G$"$k$3$H$,$o$+$j!$(2) ) (1)
$,8@$($k!% T 0 $+$i ujuj+1 $r!h$j=--$-Be$o$j$K xkxi+1 $rIU$12C$($?%0%i%U$r T 00 $H$*$/!%T 00 $b G
$NA40hLZ$G$"$k!%$J$!$J$i!$|E(T 00)| = |E(T 0)| = n - 1 $G$"$j!$JU. Re^-e`q-aw re^-e`q-aw i']""a*ss
i']""a*ss n=10 0.97 0.89 2.61944 1.87502 n=30 0.97 0.91 1.16459 0.93739 "o/ u a` o/2(n - 1) c,$l3/4,
o/ x <- seq(-3, 3, 0.05) plot(x, dnorm(x), col=6, xlab = "mu",ylab = "pdf",.
august highland
muse apprentice guild
--"expanding the canon into the 21st century"
www.muse-apprentice-guild.com
culture animal
--"following in the footsteps of tradition"
www.cultureanimal.com
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