Davydov
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ɝɞɟ T = t t t |
ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɱɚɫɬɨɬɵ ɩɪɢɦɟɧɟɧɢɹ ɤɚɠɞɨɝɨ |
ɬɢɩɚ ɛɨɦɛɚɪɞɢɪɨɜɳɢɤɚ£ 1 2 3 ¤ |
, t1 + t2 + t3 = 1. |
ɂɡɜɟɫɬɧɨ, ɱɬɨ ɧɚɯɨɠɞɟɧɢɟ ɨɩɬɢɦɚɥɶɧɨɣ ɫɬɪɚɬɟɝɢɢ ɞɥɹ E ɫɜɨ- |
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ɞɢɬɫɹ ɤ ɪɟɲɟɧɢɸ ɞɜɨɣɫɬɜɟɧɧɨɣ ɡɚɞɚɱɢ ɥɢɧɟɣɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚ- ɧɢɹ ɫ ɦɚɬɪɢɰɟɣ d
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ɝɞɟ |l = |
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ɢ y ɰɟɧɚ ɢɝɪɵ. Ɍɚɤ ɤɚɤ |
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ɧɚɞɨ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɧɚ ɦɚɤɫɢɦɭɦ, ɱɬɨɛɵ ɢɦɟɬɶ ɦɢɧɢɦɚɥɶɧɭɸ ɰɟɧɭ ɢɝɪɵ y (ɫɬɨɪɨɧɚ E ɢɝɪɚɟɬ ɧɚ ɦɢɧɢɦɭɦ).
ɂɬɚɤ, ɜɵɡɵɜɚɟɦ ɲɚɛɥɨɧ 7×1-ɦɚɬɪɢɰɵ ɢ ɜ ɩɟɪɜɨɣ ɫɬɪɨɤɟ ɧɚɛɢ- ɪɚɟɦ ɜɵɪɚɠɟɧɢɟ ɩɪɚɜɨɣ ɱɚɫɬɢ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ z, ɚ ɜ ɨɫɬɚɥɶɧɵɯ ɫɬɪɨɤɚɯ ɨɝɪɚɧɢɱɟɧɢɹ, ɜɤɥɸɱɚɹ ɧɟɨɬɪɢɰɚɬɟɥɶɧɨɫɬɶ ɧɟɢɡɜɟɫɬɧɵɯ.
ɉɪɢɦɟɧɹɹ ɤɨɦɚɧɞɭ Vlpsoh{ + Pd{lpl}h, ɩɨɥɭɱɚɟɦ |
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Maximum is at: ½|3 = |
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ɇɚɯɨɞɢɦ zmax = }min = z¯ = |1 + |2 + |3 |
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y¯ |
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ɉɨɥɭɱɚɟɦ, ɱɬɨ ɨɩɬɢɦɚɥɶɧɚɹ ɰɟɧɚ ɢɝɪɵ y¯ = |
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ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, |
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t¯1 = |1y¯ = |
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, s¯2 = |2y¯ = |
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ɢ s¯3 |
= |3y¯ = |
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. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, |
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ɩɨɥɭɱɟɧɵ ɨɩɬɢɦɚɥɶɧɚɹ ɫɬɪɚɬɟɝɢɹ VE ɢ ɨɩɬɢɦɚɥɶɧɚɹ ɰɟɧɚ ɢɝɪɵ y¯ |
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ɞɥɹ ɛɨɦɛɚɪɞɢɪɨɜɳɢɤɨɜ: |
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V¯E = Ã |
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ɢ y¯ = |
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Ɂ ɚ ɦ ɟ ɱ ɚ ɧ ɢ ɟ. ɐɟɧɚ ɢɝɪɵ ɞɥɹ ɞɜɭɯ ɫɬɨɪɨɧ ɜɫɟɝɞɚ ɨɞɧɚ ɢ ɬɚ ɠɟ.
ɉɪɢ ɩɪɢɦɟɧɟɧɢɢ ɨɩɬɢɦɚɥɶɧɨɣ ɫɬɪɚɬɟɝɢɢ ¯ ɫɬɨɪɨɧɚ ɩɨɥɭɱɚɟɬ
VD D
ɜɵɢɝɪɵɲ y¯ ɞɚɠɟ ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ ɫɬɨɪɨɧɨɣ E ɨɩɬɢɦɚɥɶɧɨɣ ɫɬɪɚɬɟ-
ɝɢɢ ¯ , ɨɞɧɚɤɨ ɭ ɫɬɨɪɨɧɵ ɜɵɢɝɪɵɲ ɦɨɠɟɬ ɭɜɟɥɢɱɢɬɶɫɹ ɩɪɢ
VE D
ɩɪɢɦɟɧɟɧɢɢ ɫɬɨɪɨɧɨɣ E ɧɟɨɩɬɢɦɚɥɶɧɵɯ ɫɬɪɚɬɟɝɢɣ. Ⱥɧɚɥɨɝɢɱɧɨ, ɫɬɨɪɨɧɚ E ɦɨɠɟɬ ɢɦɟɬɶ ɛɨɥɶɲɢɣ ɜɵɢɝɪɵɲ (ɬɨɱɧɟɟ, ɦɟɧɶɲɢɣ ɩɪɨ-
ɢɝɪɵɲ) ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ ɫɬɪɚɬɟɝɢɢ ¯ , ɟɫɥɢ ɫɬɨɪɨɧɚ ɩɪɢɦɟɧɹɟɬ
VE D
ɧɟɨɩɬɢɦɚɥɶɧɵɟ ɫɬɪɚɬɟɝɢɢ.
32
15. ɉɨɩɨɥɧɟɧɢɟ ɦɟɧɸ Help
ɉɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɬɚɬɢɫɬɢɤɢ ɢɧɨɝɞɚ ɬɪɟɛɭɸɬ- ɫɹ ɬɚɛɥɢɰɵ, ɤɨɬɨɪɵɯ ɧɟɬ ɜ SWP (ɧɚɩɪɢɦɟɪ, ɜ ɞɢɫɩɟɪɫɢɨɧɧɨɦ ɚɧɚ- ɥɢɡɟ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ Ʉɨɱɪɚɧɚ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɩɨɦɟɫɬɢɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɬɚɛɥɢɰɵ ɜ Help.
ɉ ɨ ɪ ɹ ɞ ɨ ɤ ɜ ɵ ɩ ɨ ɥ ɧ ɟ ɧ ɢ ɹ
•ɋ ɩɨɦɨɳɶɸ ɬɟɤɫɬɨɜɨɝɨ ɪɟɞɚɤɬɨɪɚ DOS Navigator ɜɯɨɞɢɦ ɜ ɮɚɣɥ Swp50\Help\Reference\Mathematics\stat tables.tex ɢ ɜ ɩɨɞɪɚɡ- ɞɟɥ \subsection{Continuous Distribution} ɞɨɛɚɜɥɹɟɦ ɧɨɜɭɸ ɫɬɪɨɤɭ \hyperref{\qquad Cochran's Distribution}{}{}{stat cochran.tex}.
•ɋ ɩɨɦɨɳɶɸ ɬɟɤɫɬɨɜɨɝɨ ɪɟɞɚɤɬɨɪɚ DOS Navigator ɜɯɨɞɢɦ ɜ ɮɚɣɥ Swp50\Help\Reference\Mathematics\st02 04.tex, ɜɵɞɟɥɹɟɦ ɢ ɤɨɩɢɪɭɟɦ ɜɟɫɶ ɩɨɞɪɚɡɞɟɥ \subsection{Normal Distribution\label{normal distribution}}, ɜɫɬɚɜɥɹɟɦ ɟɝɨ ɤɨɩɢɸ ɩɨɫɥɟ ɷɬɨɝɨ ɪɚɡɞɟɥɚ ɢ ɪɟɞɚɤ-
ɬɢɪɭɟɦ, ɡɚɦɟɧɹɹ Normal Distribution ɧɚ Cochran's Distribution ɢ stat normal.tex ɧɚ stat cochran.tex, ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɫɥɟɞɭɸɳɢɣ ɮɪɚɝ-
ɦɟɧɬ ɜ ɜɢɞɟ ɧɨɜɨɝɨ ɩɨɞɪɚɡɞɟɥɚ:
\subsection{Cochran's Distribution\label{cochran's distribution}} \begin{center}\begin{tabular}{||l||}\hline\hline \hyperref{\FRAME{itbpF}{0.3632in}{0.3693in}{0.1219in}{}{} {13.gif}{\special {language "Scientific Word"; type"GRAPHIC"; maintain-aspect-ratio TRUE; display "PICT"; valid file "F"; width 0.3632in;height 0.3693in; depth 0.1219in;
original-width 0.6356in; original-height 0.646in; cropleft "0"; croptop "1"; cropright "1"; cropbottom "0"; filename '13.gif'; file-properties "XNPEU";}} Click here for cochran's distribution tables.}{}{}{stat cochran.tex} \\ \hline\hline \end{tabular}\bigskip\end{center}.
• ɋ ɩɨɦɨɳɶɸ SWP ɫɨɡɞɚɟɦ ɧɨɜɵɣ ɮɚɣɥ stat cochran.tex. Ⱦɥɹ ɷɬɨɝɨ ɨɬɤɪɵɜɚɟɦ ɮɚɣɥ Swp50\Help\Reference\Mathematics\stat f.tex,
ɫ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Iloh + Vdyh Dv ɫɨɯɪɚɧɹɟɦ ɟɝɨ ɩɨɞ ɧɨɜɵɦ
33
ɢɦɟɧɟɦ stat cochran.tex ɢ ɪɟɞɚɤɬɢɪɭɟɦ ɟɝɨ, ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɫɥɟɞɭ- ɸɳɢɣ ɞɨɤɭɦɟɧɬ.
Ʉɪɢɬɢɱɟɫɤɢɟ ɬɨɱɤɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ʉɨɱɪɚɧɚ
Ɍɚɛɥɢɰɵ Ʉɨɱɪɚɧɚ ɞɚɸɬ ɡɧɚɱɟɧɢɹ ɤɪɢɬɢɱɟɫɤɨɣ ɬɨɱɤɢ x, ɫɨɨɬɜɟɬ- ɫɬɜɭɸɳɢɟ ɫɬɟɩɟɧɹɦ ɫɜɨɛɨɞɵ 1 ɢ 2 ɢ ɭɪɨɜɧɸ ɡɧɚɱɢɦɨɫɬɢ , ɬɚɤɢɟ, ɱɬɨ Pr ([ x) = .
1 = q 1 ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ.
2 = p ɤɨɥɢɱɟɫɬɜɨ ɜɵɛɨɪɨɤ.
Pr ([ x) =
ɍɪɨɜɟɧɶ ɡɧɚɱɢɦɨɫɬɢ = 0=05
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0.9985 |
0.9750 |
0.9392 |
0.9057 |
0.8772 |
0.8534 |
0.8332 |
3 |
0.9669 |
0.8709 |
0.7977 |
0.7457 |
0.7071 |
0.6771 |
0.6530 |
4 |
0.9065 |
0.7679 |
0.6841 |
0.6287 |
0.5895 |
0.5598 |
0.5365 |
5 |
0.8412 |
0.6338 |
0.5981 |
0.5440 |
0.5063 |
0.4783 |
0.4564 |
6 |
0.7808 |
0.6161 |
0.5321 |
0.4803 |
0.4447 |
0.4184 |
0.3980 |
7 |
0.7271 |
0.5612 |
0.4800 |
0.4307 |
0.3974 |
0.3726 |
0.3535 |
8 |
0.6798 |
0.5157 |
0.4377 |
0.3910 |
0.3595 |
0.3362 |
0.3185 |
9 |
0.6385 |
0.4775 |
0.4027 |
0.3584 |
0.3286 |
0.3067 |
0.2901 |
10 |
0.6020 |
0.4450 |
0.3733 |
0.3311 |
0.3029 |
0.2823 |
0.2666 |
12 |
0.5410 |
0.3924 |
0.3624 |
0.2880 |
0.2624 |
0.2439 |
0.2299 |
15 |
0.4709 |
0.3346 |
0.2758 |
0.2419 |
0.2195 |
0.2034 |
0.1911 |
20 |
0.3894 |
0.2705 |
0.2205 |
0.1921 |
0.1735 |
0.1602 |
0.1501 |
24 |
0.3434 |
0.2354 |
0.1907 |
0.1656 |
0.1493 |
0.1374 |
0.1286 |
30 |
0.2929 |
0.1980 |
0.1593 |
0.1377 |
0.1237 |
0.1137 |
0.1061 |
40 |
0.2370 |
0.1576 |
0.1259 |
0.1082 |
0.0968 |
0.0887 |
0.0827 |
60 |
0.1737 |
0.1131 |
0.0895 |
0.0765 |
0.0682 |
0.0623 |
0.0583 |
120 |
0.0998 |
0.0632 |
0.0495 |
0.0419 |
0.0371 |
0.0337 |
0.0312 |
4 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
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ɍɪɨɜɟɧɶ ɡɧɚɱɢɦɨɫɬɢ = 0=05
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2 |
0.8159 |
0.8010 |
0.7880 |
0.7341 |
0.6602 |
0.5813 |
0.5000 |
3 |
0.6333 |
0.6167 |
0.6025 |
0.5466 |
0.4748 |
0.4031 |
0.3333 |
4 |
0.5175 |
0.5017 |
0.4884 |
0.4366 |
0.3720 |
0.3093 |
0.2500 |
5 |
0.4387 |
0.4241 |
0.4118 |
0.3645 |
0.3066 |
0.2013 |
0.2000 |
6 |
0.3817 |
0.3682 |
0.3568 |
0.3135 |
0.2612 |
0.2119 |
0.1667 |
7 |
0.3384 |
0.3259 |
0.3154 |
0.2756 |
0.2278 |
0.1833 |
0.1429 |
8 |
0.3043 |
0.2926 |
0.2829 |
0.2462 |
0.2022 |
0.1616 |
0.1250 |
9 |
0.2768 |
0.2659 |
0.2568 |
0.2226 |
0.1820 |
0.1446 |
0.1111 |
10 |
0.2541 |
0.2439 |
0.2353 |
0.2032 |
0.1655 |
0.1308 |
0.1000 |
12 |
0.2187 |
0.2098 |
0.2020 |
0.1737 |
0.1403 |
0.1100 |
0.0833 |
15 |
0.1815 |
0.1736 |
0.1671 |
0.1429 |
0.1144 |
0.0889 |
0.0667 |
20 |
0.1422 |
0.1357 |
0.1303 |
0.1108 |
0.0879 |
0.0675 |
0.0500 |
24 |
0.1216 |
0.1160 |
0.1113 |
0.0942 |
0.0743 |
0.0567 |
0.0417 |
30 |
0.1002 |
0.0958 |
0.0921 |
0.0771 |
0.0604 |
0.0457 |
0.0333 |
40 |
0.0780 |
0.0745 |
0.0713 |
0.0595 |
0.0462 |
0.0347 |
0.0250 |
60 |
0.0552 |
0.0520 |
0.0497 |
0.0411 |
0.0316 |
0.0234 |
0.0167 |
120 |
0.0292 |
0.0279 |
0.0266 |
0.0218 |
0.0165 |
0.0120 |
0.0083 |
4 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
|
|
|
|
|
|
|
|
• ɑɬɨɛɵ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɷɬɨɣ ɬɚɛɥɢɰɟɣ, ɩɪɢɦɟɧɹɸɬ ɤɨɦɚɧɞɭ
Khos + Vhdufk + Glvwulexwlrq wdeohv (ɢɥɢ Vwdwlvwlfdo wdeohv) + Frqwlqxrxv Glvwulexwlrqv + Frfkudq'v Glvwulexwlrq. Ɇɨɠɧɨ ɢɫ-
ɩɨɥɶɡɨɜɚɬɶ ɢ ɞɪɭɝɢɟ ɩɭɬɢ ɜɵɡɨɜɚ ɬɚɛɥɢɰɵ. ɇɚɩɪɢɦɟɪ, Khos
+ Frqwhqwv + Uhihuhqfh Oleudu| + Pdwkhpdwlfv + Wdeohv + Vwdwlvwlfdo Glvwulexwlrq Wdeohv + Frqwlqxrxv Glvwulexwlrqv +
Frfkudq'v Glvwulexwlrq. Ɇɨɠɧɨ ɢɫɤɚɬɶ ɷɬɭ ɬɚɛɥɢɰɭ ɩɨ ɤɥɸɱɟɜɨɦɭ ɫɥɨɜɭ Wdeohv>uhihuhqfh ɢɥɢ Vwdwlvwlfv ɢ ɬ.ɞ.
35
Ʌɢɬɟɪɚɬɭɪɚ
1.Ȼɭɫɥɚɟɜ Ⱥ.ɉ., Ⱦɚɜɵɞɨɜ ȿ.Ƚ., əɲɢɧɚ Ɇ.ȼ. Ʉɨɦɩɶɸɬɟɪɧɚɹ ɦɚɬɟ- ɦɚɬɢɤɚ: Ɇɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ ɩɨ ɩɪɢɦɟɧɟɧɢɸ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɚɤɟɬɨɜ ɜ ɤɭɪɫɟ ɜɵɫɲɟɣ ɦɚɬɟɦɚɬɢɤɢ/ ɆȺȾɂ(Ɍɍ). Ɇ., 1996.
50 c.: ɢɥ.
2.Ƚɦɭɪɦɚɧ ȼ.ȿ. Ɍɟɨɪɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɫɬɚɬɢɫ- ɬɢɤɚ. ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. ɂɡɞ. 7-ɟ, ɫɬɟɪɟɨɬɢɩɧɨɟ. Ɇ.: ȼɵɫɲɚɹ ɲɤɨɥɚ, 1999. 479 ɫ.: ɢɥ.
3.Ⱦɚɜɵɞɨɜ ȿ.Ƚ. Ɇɚɬɟɦɚɬɢɱɟɫɤɢɣ ɩɚɤɟɬ Scientific WorkPlace 3.0
ɜɤɭɪɫɟ ɜɵɫɲɟɣ ɦɚɬɟɦɚɬɢɤɢ. Ɍɟɯɧɨɥɨɝɢɹ ɪɚɛɨɬɵ ɢ ɩɪɚɤɬɢɤɚ ɪɟɲɟ- ɧɢɹ ɡɚɞɚɱ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ/ ɆȺȾɂ(ȽɌɍ). Ɇ., 2002. 105 ɫ.: ɢɥ.
4.Ⱦɚɜɵɞɨɜ ȿ.Ƚ. ɂɧɬɟɝɪɢɪɨɜɚɧɧɚɹ ɫɢɫɬɟɦɚ Scientific WorkPlace 4.0: Ɍɟɯɧɨɥɨɝɢɹ ɪɚɛɨɬɵ ɢ ɩɪɚɤɬɢɤɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ. Ɇ.: Ɏɢɧɚɧɫɵ ɢ ɫɬɚɬɢɫɬɢɤɚ. 2003. 208 ɫ.: ɢɥ. (Ⱦɢɚɥɨɝ ɫ ɤɨɦɩɶɸɬɟɪɨɦ).
36