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Ronny_chou

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P=[0.5070 1.318 2.772 4.338 6.241 7.839 9.849 14.66 19.35 24.56 29.93  34.13 39.04  46.20] ;
n=[0.4429 1.085 1.901 2.533 3.162 3.697 4.209 5.052 6.043 6.754 7.489 8.279 9.184 10.16];
ÏëÒªÄâºÏ³ÉÇúÏßf(x) = nmax*(b*x)^(1/k)/(1+(b*x)^(1/k)) Óëf(x) = nmax*x/(1+(a*x)^k)^(1/k) µÄÐÎʽ£¬È»ºóÎÒ
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1.1. General model:
     f(x) = nmax*(b*x)^(1/k)/(1+(b*x)^(1/k))
Coefficients (with 95% confidence bounds):
       b =   0.0001122  (-0.001508, 0.001732)
       k =       1.658  (1.348, 1.968)
       nmax =       248.9  (-1699, 2197)

Goodness of fit:
  SSE: 0.3045
  R-square: 0.9975
  Adjusted R-square: 0.9971
  RMSE: 0.1664

1.2 General model:
    General model:
     f(x) = nmax*a*x/(1+(a*x)^k)^(1/k)
Coefficients (with 95% confidence bounds):
       a =    0.001947  (-0.01345, 0.01735)
       k =      0.1019  (-0.1258, 0.3297)
       nmax =   3.203e+04  (-5.908e+05, 6.549e+05)

Goodness of fit:
  SSE: 0.3006
  R-square: 0.9976
  Adjusted R-square: 0.9971
  RMSE: 0.1653

µ«ÊÇÓÃoriginÄ£Äâ½á¹ûÈçÏ£º
£¨1£©     f(x) = nmax*(b*x)^(1/k)/(1+(b*x)^(1/k)) Ä£Äâ½á¹û

Origin×Ô¶¨ÒåÄ£ÄâÓëmatlabÖÐcftool¹¤¾ßÏäÄâºÏ½á¹û±È½Ï

£¨2£© f(x) = nmax*x/(1+(a*x)^k)^(1/k) Ä£Äâ½á¹û

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  • ¸½¼þ 1 : simulation2.jpg
  • 2015-09-23 11:32:52, 666.02 K
  • ¸½¼þ 2 : simulation2.jpg
  • 2015-09-23 11:34:19, 666.02 K

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1£º
µÚÒ»¸ö¹«Ê½£ºy = nmax*(b*x)^(1/k)/(1+(b*x)^(1/k))£¬²»Äܼò»¯ÏÂÂð£¬ÍêÈ«µÈͬÓÚ£º

y = nmax/(1+(b*x)^k);£¬¿´×Ŷ¼ÇåˬЩ¡£Ö±½ÓÄâºÏÕâ¸ö¹«Ê½µÄ»°£¬Ä¿±êº¯Êý£¨SSE£©»ù±¾Ò»Ñùµ«nmaxºÍb²»Îȶ¨£º
1£©
¾ù·½²î(RMSE):0.146688964176323
²Ð²îƽ·½ºÍ(SSE):0.301247130955714
Ïà¹ØÏµÊý(R): 0.998801066757962
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.997603570956843
È·¶¨ÏµÊý(DC): 0.997545478102313
¿¨·½ÏµÊý(Chi-Square): 0.085846619465631
Fͳ¼Æ(F-Statistic): 2240.76224587093

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
b        6.38790682352766E-17
nmax        3715236827.67985
k        -0.589760207223845

2£©
¾ù·½²î(RMSE):0.146688964157574
²Ð²îƽ·½ºÍ(SSE):0.301247130878707
Ïà¹ØÏµÊý(R): 0.998801066740756
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.997603570922471
È·¶¨ÏµÊý(DC): 0.997545478102941
¿¨·½ÏµÊý(Chi-Square): 0.0858466176890851
Fͳ¼Æ(F-Statistic): 2240.76224644373

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
b        2.37230022879993E-20
nmax        391719737466.736
k        -0.589760208502794

Ó¦¸ÃÊÇ·½³ÌµÄÐÎʽÔì³ÉÕâÖÖ½á¾Ö£¬Èç¹û²»¿¼ÂDzÎÊýÎïÀíÒâÒ壬Æäʵ¹«Ê½£ºy = nmax/(1+(b*x)^k); --¡·y = nmax/(1+b^k*x^k); -->y = nmax/(1+b1*x^k);

´ËʱÎȶ¨Î¨Ò»£º
¾ù·½²î(RMSE):0.146648461643796
²Ð²îƽ·½ºÍ(SSE):0.301080798234885
Ïà¹ØÏµÊý(R): 0.998804382533961
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.997610194569047
È·¶¨ÏµÊý(DC): 0.997546833359388
¿¨·½ÏµÊý(Chi-Square): 0.0881571807051252
Fͳ¼Æ(F-Statistic): 2242.00015969098

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
nmax        -863.166782962704
b        -823.26708610708
k        -0.586003926097037

2£ºµÚ¶þ¸öʽ×Ó£º y = nmax*a*x/(1+(a*x)^k)^(1/k)

1stOptÇó½âÎȶ¨Î¨Ò»£¬MatlabÎó²îÌ«´ó£¬OriginÒ²Óвî¾à£º

¾ù·½²î(RMSE):0.144604300178649
²Ð²îƽ·½ºÍ(SSE):0.292745650822194
Ïà¹ØÏµÊý(R): 0.998819337279252
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.997640068522964
È·¶¨ÏµÊý(DC): 0.997614747041354
¿¨·½ÏµÊý(Chi-Square): 0.06651177594336
Fͳ¼Æ(F-Statistic): 2305.83510233767

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
nmax        185924116.646796
a        5.71405015369486E-5
k        0.0511661433683439
2Â¥2015-09-23 22:21:18
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Ronny_chou

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ÒýÓûØÌû:
2Â¥: Originally posted by dingd at 2015-09-23 22:21:18
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dingd

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ÒýÓûØÌû:
3Â¥: Originally posted by Ronny_chou at 2015-09-24 10:32:53
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Ronny_chou

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ÒýÓûØÌû:
4Â¥: Originally posted by dingd at 2015-09-24 14:02:21
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