使用积分时出错（第 85 行）：A 和 B 必须是浮点标量
Error using integral (line 85): A and B must be floating-point scalars
我有以下代码，我希望使用 MATLAB 的函数 mle() 来估计自定义分布的参数。 。
主要代码为：
x = [0 0 0 0 0.000649967501624919 0.00569971501424929 0.0251487425628719 0.0693465326733663 0.155342232888356 0.284835758212089 0.458277086145693 0.658567071646418 0.908404579771011 1.17284135793210 1.43977801109945 1.71951402429879 1.98925053747313 2.27553622318884 2.57147142642868 2.80390980450977 3.03829808509575 3.26583670816459 3.45642717864107 3.65106744662767 3.81950902454877 3.98275086245688 4.11259437028149 4.24683765811709 4.35043247837608 4.43832808359582 4.58427078646068 4.62286885655717 4.68361581920904 4.75686215689216 4.80245987700615 4.84005799710015 4.86280685965702 4.91675416229189 4.92725363731813 4.90890455477226 4.96570171491425 4.92315384230789 4.95355232238388 4.92790360481976 4.93135343232838 4.90310484475776 4.90885455727214 4.86765661716914 4.85490725463727 4.81940902954852 4.81450927453627 4.78621068946553 4.74206289685516 4.71791410429479 4.69961501924904 4.65706714664267 4.63611819409030 4.60176991150443 4.57512124393780 4.53507324633768 4.48252587370631 4.47062646867657 4.43127843607820 4.39963001849908 4.37598120093995 4.29548522573871 4.31033448327584 4.21708914554272 4.21913904304785 4.18669066546673 4.16719164041798 4.09774511274436 4.07989600519974 4.02869856507175 3.98485075746213 3.95785210739463 3.93945302734863 3.90240487975601 3.87025648717564 3.81185940702965 3.78461076946153 3.74091295435228 3.71666416679166 3.67276636168192 3.65846707664617 3.61361931903405 3.58712064396780 3.55452227388631 3.53082345882706 3.49197540122994 3.48582570871456 3.46512674366282 3.41227938603070 3.36278186090695 3.35528223588821 3.31238438078096 3.27213639318034 3.23863806809660 3.24173791310434 3.19339033048348 3.20118994050298 3.16489175541223 3.10739463026849 3.09484525773711 3.08094595270237 3.02129893505325 3.02309884505775 2.99375031248438 2.95765211739413 2.93230338483076 2.89560521973901 2.87805609719514 2.85440727963602 2.82285885705715 2.80175991200440 2.79091045447728 2.73901304934753 2.72701364931753 2.73441327933603 2.71646417679116 2.68236588170592 2.65551722413879 2.63356832158392 2.60361981900905 2.58147092645368 2.57697115144243 2.54287285635718 2.53502324883756 2.47702614869257 2.50387480625969 2.46487675616219 2.45722713864307 2.42707864606770 2.41762911854407 2.39823008849558 2.38708064596770 2.34058297085146 2.35613219339033 2.32123393830309 2.30503474826259 2.27613619319034 2.27248637568122 2.25113744312784 2.24908754562272 2.22703864806760 2.20583970801460 2.17244137793110 2.15709214539273 2.16469176541173 2.12139393030348 2.12809359532023 2.11389430528474 2.09774511274436 2.07629618519074 2.07459627018649 2.05394730263487 2.04724763761812 2.01684915754212 2.01684915754212 2.00409979501025 1.98955052247388 1.96540172991350 1.95890205489726 1.93035348232588 1.92295385230738 1.90605469726514 1.89785510724464 1.87070646467677 1.88000599970002 1.86295685215739 1.84420778961052 1.82510874456277 1.80480975951202 1.80785960701965 1.80870956452177 1.77581120943953 1.76771161441928 1.77131143442828 1.76636168191590 1.75081245937703 1.73156342182891 1.69876506174691 1.70836458177091 1.70376481175941 1.67196640167992 1.68101594920254 1.66586670666467 1.66061696915154 1.64296785160742 1.63291835408230 1.62506874656267 1.62516874156292 1.60556972151392 1.59007049647518 1.59187040647968 1.57947102644868 1.57577121143943 1.54527273636318 1.57237138143093 1.54637268136593 1.54802259887006 1.50492475376231 1.52077396130193 1.50417479126044 1.50162491875406 1.50062496875156 1.48957552122394 1.47997600119994 1.47027648617569 1.44452777361132 1.45407729613519 1.44272786360682 1.43247837608120 1.41657917104145 1.40787960601970 1.39323033848308 1.40282985850707 1.39403029848508 1.38233088345583 1.37888105594720 1.37943102844858 1.36183190840458 1.34808259587021 1.34503274836258 1.33703314834258 1.33308334583271 1.32253387330633 1.32698365081746 1.29963501824909 1.30758462076896 1.29103544822759 1.29473526323684 1.27413629318534 1.26858657067147 1.27888605569722 1.26063696815159 1.27863606819659 1.25168741562922 1.23913804309785 1.24788760561972 1.22308884555772 1.24198790060497 1.22133893305335 1.20678966051697 1.20098995050247 1.20343982800860 1.18779061046948 1.19024048797560 1.17194140292985 1.17369131543423 1.16869156542173 1.15814209289536 1.15429228538573 1.15904204789761 1.12774361281936 1.15344232788361 1.13744312784361 1.12909354532273 1.12479376031198 1.11099445027749 1.11469426528674 1.11064446777661 1.10464476776161 1.10309484525774 1.10689465526724 1.07654617269137 1.07884605769712 1.07359632018399 1.06864656767162 1.07544622768862 1.06689665516724 1.04884755762212 1.06164691765412 1.04979751012449 1.04529773511324 1.02839858007100 1.03634818259087 1.01709914504275 1.02089895505225 1.01024948752562 1.01549922503875 1.01319934003300 1.01404929753512 1.00839958002100 0.995400229988501 0.989850507474626 0.978801059947003 0.977551122443878 0.980450977451127 0.975451227438628 0.969201539923004 0.964151792410380 0.964601769911504 0.958802059897005 0.955702214889256 0.948602569871506 0.960751962401880 0.941352932353382 0.928653567321634 0.949002549872506 0.937053147342633 0.913854307284636 0.916204189790510 0.915454227288636 0.902604869756512 0.909454527273636 0.895505224738763 0.898355082245888 0.894455277236138 0.902454877256137 0.883705814709265 0.888405579721014 0.876356182190891 0.881555922203890 0.878156092195390 0.868456577171141 0.870406479676016 0.863906804659767 0.862456877156142 0.858757062146893 0.851307434628269 0.851107444627769 0.833908304584771 0.843507824608770 0.831708414579271 0.836858157092145 0.829058547072646 0.828508574571272 0.822908854557272 0.820508974551273 0.815559222038898 0.819709014549273 0.809609519524024 0.813409329533523 0.800759962001900 0.806609669516524 0.806959652017399 0.792260386980651 0.787660616969152 0.783810809459527 0.794960251987401 0.771061446927654 0.788910554472276 0.789510524473776 0.763061846907655 0.776761161941903 0.767561621918904 0.773611319434028 0.750262486875656 0.765811709414529 0.765911704414779 0.748012599370032 0.741612919354032 0.757312134393280 0.752612369381531 0.741362931853407 0.742212889355532 0.741912904354782 0.743162841857907 0.732963351832408 0.732813359332033 0.733363331833408 0.721913904304785 0.716664166791661 0.726713664316784 0.709764511774411 0.700064996750163 0.710764461776911 0.717664116794160 0.707314634268287 0.707114644267787 0.705614719264037 0.709164541772911 0.696665166741663 0.680765961701915 0.686715664216789 0.694465276736163 0.683015849207540 0.681715914204290 0.694465276736163 0.688615569221539 0.680665966701665 0.672316384180791 0.672866356682166 0.656517174141293 0.665316734163292 0.671566421678916 0.666266686665667 0.652917354132293 0.663366831658417 0.651917404129794 0.663816809159542 0.661366931653417 0.647017649117544 0.655167241637918 0.647867606619669 0.636918154092295 0.645467726613669 0.633118344082796 0.640217989100545 0.634668266586671 0.618669066546673 0.635068246587671 0.632568371581421 0.623118844057797 0.623868806559672 0.623718814059297 0.621368931553422 0.623768811559422 0.608419579021049 0.616019199040048 0.609869506524674 0.606569671516424 0.614019299035048 0.610269486525674 0.596520173991300 0.595570221488926 0.593270336483176 0.596670166491675 0.598470076496175 0.597770111494425 0.593720313984301 0.592770361481926 0.585420728963552 0.580870956452177 0.584120793960302 0.580270986450677 0.577971101444928 0.579021048947553 0.572821358932053 0.585970701464927 0.572921353932303 0.567071646417679 0.569971501424929 0.571271436428179 0.568421578921054 0.567421628918554 0.569521523923804 0.563721813909305 0.558772061396930 0.562171891405430 0.557872106394680 0.549072546372681 0.558722063896805 0.536973151342433 0.561021948902555 0.544172791360432 0.552122393880306 0.553072346382681 0.546222688865557 0.551472426378681 0.540772961351932 0.541122943852807 0.542772861356932 0.530323483825809 0.526023698815059 0.529273536323184 0.524573771311435 0.525923703814809 0.524923753812309 0.516474176291185 0.527273636318184 0.527723613819309 0.518424078796060 0.517874106294685 0.516074196290186 0.517924103794810 0.523173841307935 0.514474276286186 0.513174341282936 0.498875056247188 0.518024098795060 0.507924603769812 0.505524723763812 0.507174641267937 0.502874856257187 0.502624868756562 0.500624968751562 0.510824458777061 0.490925453727314 0.492675366231688 0.489925503724814 0.478126093695315 0.485775711214439 0.491775411229439 0.489925503724814 0.491325433728314 0.487225638718064 0.485725713714314 0.485675716214189 0.477676116194190 0.483875806209690 0.478026098695065 0.470176491175441 0.471926403679816 0.483625818709065 0.469376531173441 0.474026298685066 0.467826608669567 0.462426878656067];
Censored = ones(1,size(x,2));%
custpdf = @eval_custpdf;
custcdf = @eval_custcdf;
phat = mle(x,'pdf', custpdf,'cdf', custcdf,'start',[1 0.1 0.3 0.1 0.01 -0.3],...
'lowerbound',[0 0 0 0 0 -inf],'upperbound',[inf inf inf inf inf inf],'Censoring',Censored);
% Cheking how close the estimated PDF and CDF match with those from the data x
t = 0.001:0.001:0.5;
figure();
plot(t,x);hold on
plot(t,custpdf(t, phat(1), phat(2), phat(3), phat(4), phat(5), phat(6)))
figure();
plot(t,cumsum(x)./sum(x));hold on
plot(t,custcdf(t, phat(1), phat(2), phat(3), phat(4), phat(5), phat(6)))
函数是：
function out = eval_custpdf(x,myalpha,mybeta,mytheta,a,b,c)
first_integral = integral(@(x) eval_K(x,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x);
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
exponent_term = exp(-theta_t_ratio.^mybeta-(c.*(incomplete_gamma./n_gamma)));
numerator = first_integral.* mybeta.*incomplete_gamma.^(a-1).*...
theta_t_ratio.^(myalpha*mybeta+1).*exponent_term;
denominator = mytheta.* n_gamma.^(a+b-1).* (n_gamma-incomplete_gamma.^mybeta).^(1-b);
out = numerator./denominator;
end
function out = eval_custcdf(x,myalpha,mybeta,mytheta,a,b,c)
first_integral = integral(@(x) eval_K(x,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x);
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
second_integral = integral(@(x) eval_K(x,a,b,c),0, incomplete_gamma.^mybeta./n_gamma);
% |<----- PROBLEMATIC LINE ----->|
out = first_integral*second_integral;
end
function out = eval_K(x,a,b,c)
out = x.^(a-1).*(1-x).^(b-1).*exp(-c.*x);
end
导致问题的积分是函数 eval_custcdf() 中的第二个积分，因为它的上限是一个数组（由 PROBLEMATIC LINE 表示）。
有没有办法从数组 x 中获取单个值，使上限保持为标量？然后计算cdf使得cdf的输出是一个数组？使用 forloop，也许吧？但我似乎无法弄清楚如何实现它？
我该如何解决这个问题？
如有任何帮助，我们将不胜感激。
提前致谢。
eval_custcdf 是预期 return 1D array of length n 的函数
给定的 n 数据输入。- 我使用
for loop 计算给定输入的输出，然后
return 整个数组作为 eval_custcdf 的输出
我一次传递一个输入数组元素
这就是 eval_custcdf 的样子
function out = eval_custcdf(x,myalpha,mybeta,mytheta,a,b,c)
out = zeros(size(x));
for i = 1: length(x)
first_integral = integral(@(w) eval_K(w,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x(i));
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
second_integral = integral(@(w) eval_K(w,a,b,c),0, incomplete_gamma.^mybeta./n_gamma);
out(i) = first_integral*second_integral;
end
end
我有以下代码，我希望使用 MATLAB 的函数 mle() 来估计自定义分布的参数。
主要代码为：
x = [0 0 0 0 0.000649967501624919 0.00569971501424929 0.0251487425628719 0.0693465326733663 0.155342232888356 0.284835758212089 0.458277086145693 0.658567071646418 0.908404579771011 1.17284135793210 1.43977801109945 1.71951402429879 1.98925053747313 2.27553622318884 2.57147142642868 2.80390980450977 3.03829808509575 3.26583670816459 3.45642717864107 3.65106744662767 3.81950902454877 3.98275086245688 4.11259437028149 4.24683765811709 4.35043247837608 4.43832808359582 4.58427078646068 4.62286885655717 4.68361581920904 4.75686215689216 4.80245987700615 4.84005799710015 4.86280685965702 4.91675416229189 4.92725363731813 4.90890455477226 4.96570171491425 4.92315384230789 4.95355232238388 4.92790360481976 4.93135343232838 4.90310484475776 4.90885455727214 4.86765661716914 4.85490725463727 4.81940902954852 4.81450927453627 4.78621068946553 4.74206289685516 4.71791410429479 4.69961501924904 4.65706714664267 4.63611819409030 4.60176991150443 4.57512124393780 4.53507324633768 4.48252587370631 4.47062646867657 4.43127843607820 4.39963001849908 4.37598120093995 4.29548522573871 4.31033448327584 4.21708914554272 4.21913904304785 4.18669066546673 4.16719164041798 4.09774511274436 4.07989600519974 4.02869856507175 3.98485075746213 3.95785210739463 3.93945302734863 3.90240487975601 3.87025648717564 3.81185940702965 3.78461076946153 3.74091295435228 3.71666416679166 3.67276636168192 3.65846707664617 3.61361931903405 3.58712064396780 3.55452227388631 3.53082345882706 3.49197540122994 3.48582570871456 3.46512674366282 3.41227938603070 3.36278186090695 3.35528223588821 3.31238438078096 3.27213639318034 3.23863806809660 3.24173791310434 3.19339033048348 3.20118994050298 3.16489175541223 3.10739463026849 3.09484525773711 3.08094595270237 3.02129893505325 3.02309884505775 2.99375031248438 2.95765211739413 2.93230338483076 2.89560521973901 2.87805609719514 2.85440727963602 2.82285885705715 2.80175991200440 2.79091045447728 2.73901304934753 2.72701364931753 2.73441327933603 2.71646417679116 2.68236588170592 2.65551722413879 2.63356832158392 2.60361981900905 2.58147092645368 2.57697115144243 2.54287285635718 2.53502324883756 2.47702614869257 2.50387480625969 2.46487675616219 2.45722713864307 2.42707864606770 2.41762911854407 2.39823008849558 2.38708064596770 2.34058297085146 2.35613219339033 2.32123393830309 2.30503474826259 2.27613619319034 2.27248637568122 2.25113744312784 2.24908754562272 2.22703864806760 2.20583970801460 2.17244137793110 2.15709214539273 2.16469176541173 2.12139393030348 2.12809359532023 2.11389430528474 2.09774511274436 2.07629618519074 2.07459627018649 2.05394730263487 2.04724763761812 2.01684915754212 2.01684915754212 2.00409979501025 1.98955052247388 1.96540172991350 1.95890205489726 1.93035348232588 1.92295385230738 1.90605469726514 1.89785510724464 1.87070646467677 1.88000599970002 1.86295685215739 1.84420778961052 1.82510874456277 1.80480975951202 1.80785960701965 1.80870956452177 1.77581120943953 1.76771161441928 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Censored = ones(1,size(x,2));%
custpdf = @eval_custpdf;
custcdf = @eval_custcdf;
phat = mle(x,'pdf', custpdf,'cdf', custcdf,'start',[1 0.1 0.3 0.1 0.01 -0.3],...
'lowerbound',[0 0 0 0 0 -inf],'upperbound',[inf inf inf inf inf inf],'Censoring',Censored);
% Cheking how close the estimated PDF and CDF match with those from the data x
t = 0.001:0.001:0.5;
figure();
plot(t,x);hold on
plot(t,custpdf(t, phat(1), phat(2), phat(3), phat(4), phat(5), phat(6)))
figure();
plot(t,cumsum(x)./sum(x));hold on
plot(t,custcdf(t, phat(1), phat(2), phat(3), phat(4), phat(5), phat(6)))
函数是：
function out = eval_custpdf(x,myalpha,mybeta,mytheta,a,b,c)
first_integral = integral(@(x) eval_K(x,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x);
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
exponent_term = exp(-theta_t_ratio.^mybeta-(c.*(incomplete_gamma./n_gamma)));
numerator = first_integral.* mybeta.*incomplete_gamma.^(a-1).*...
theta_t_ratio.^(myalpha*mybeta+1).*exponent_term;
denominator = mytheta.* n_gamma.^(a+b-1).* (n_gamma-incomplete_gamma.^mybeta).^(1-b);
out = numerator./denominator;
end
function out = eval_custcdf(x,myalpha,mybeta,mytheta,a,b,c)
first_integral = integral(@(x) eval_K(x,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x);
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
second_integral = integral(@(x) eval_K(x,a,b,c),0, incomplete_gamma.^mybeta./n_gamma);
% |<----- PROBLEMATIC LINE ----->|
out = first_integral*second_integral;
end
function out = eval_K(x,a,b,c)
out = x.^(a-1).*(1-x).^(b-1).*exp(-c.*x);
end
导致问题的积分是函数 eval_custcdf() 中的第二个积分，因为它的上限是一个数组（由 PROBLEMATIC LINE 表示）。
有没有办法从数组 x 中获取单个值，使上限保持为标量？然后计算cdf使得cdf的输出是一个数组？使用 forloop，也许吧？但我似乎无法弄清楚如何实现它？
我该如何解决这个问题？
如有任何帮助，我们将不胜感激。
提前致谢。
eval_custcdf是预期 return1D array of length n的函数 给定的n数据输入。- 我使用
for loop计算给定输入的输出，然后 return 整个数组作为eval_custcdf 的输出
我一次传递一个输入数组元素
这就是 eval_custcdf 的样子
function out = eval_custcdf(x,myalpha,mybeta,mytheta,a,b,c)
out = zeros(size(x));
for i = 1: length(x)
first_integral = integral(@(w) eval_K(w,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x(i));
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
second_integral = integral(@(w) eval_K(w,a,b,c),0, incomplete_gamma.^mybeta./n_gamma);
out(i) = first_integral*second_integral;
end
end