大数据NMaximize报错，只能在有限个数据内求解【mathematica吧】

NMaximize[{10^700 Times @@ (a7[[;; 810]]), 0 < w11 < 1, 0 < w12 < 1,
0 < w21 < 1,
0 < w22 < 1, \[Lambda]11 > 0, \[Lambda]12 > 0, \[Lambda]21 >
0, \[Lambda]22 > 0, \[Alpha]11 > 0, \[Alpha]12 > 0, \[Alpha]21 >
0, \[Alpha]22 > 0, \[Beta]11 > 0, \[Beta]12 > 0, \[Beta]21 >
0, \[Beta]22 > 0}, {w11, w12, w21,
w22, \[Lambda]11, \[Lambda]12, \[Lambda]21, \[Lambda]22, \
\[Alpha]11, \[Alpha]12, \[Alpha]21, \[Alpha]22, \[Beta]11, \[Beta]12, \
\[Beta]21, \[Beta]22}, WorkingPrecision -> 20, MaxIterations -> 200]

画风大概这样

有1999个样本似然函数，要把他们乘起来再求乘积的最大值
取前几个样本乘积进行多次尝试，超过一定数量的样本乘积最大化就报错
给乘积乘上10的k次方能起到有限的作用，让尽量多的样本乘积最大化能用NMaximize解出来，但样本大到一定程度就没用了
目前取前最多取前810个样本能解出最值，但811个就报错了

似然函数列表元素1999个一次发不过来，分多次发

{{11, 1.21142}, {11, 0.134916}, {11, 0.93482}, {11, 2.21504}, {12,
0.0000449634}, {21, 0.171588}, {12, 0.196705}, {21, 0.373136}, {11,
1.96068}, {11, 0.288141}, {11, 5.81077}, {12, 3.9965}, {21,
3.87772}, {11, 1.2877}, {11, 2.38795}, {11, 0.755026}, {12,
0.571993}, {21, 2.74908}, {11, 2.6275}, {11, 0.0608182}, {11,
2.0381}, {12, 0.644732}, {21, 0.176643}, {11, 2.43781}, {12,
3.73087}, {22, 1.23397}, {22, 5.20133}, {21, 0.341744}, {11,
1.02184}, {11, 1.88653}, {11, 0.391078}, {11, 1.20235}, {12,
8.48391}, {22, 0.0172368}, {21, 1.30309}, {11, 1.40668}, {11,
0.858981}, {11, 4.36707}, {11, 3.31435}, {11, 1.76995}, {12,
1.79623}, {21, 0.820006}, {12, 24.3167}, {21, 0.163109}, {11,
2.664}, {11, 0.00835634}, {11, 1.97209}, {11, 4.40456}, {11,
0.89828}, {11, 4.76014}, {12, 7.59851}, {21, 0.486628}, {12,
4.4472}, {21, 0.640175}, {11, 2.95704}, {11, 1.53197}, {11,
0.962216}, {11, 1.73751}, {11, 2.34172}, {12, 0.134509}, {22,
0.0236892}, {22, 3.47705}, {21, 1.61177}, {11, 15.117}, {11,
0.405892}, {11, 1.9005}, {11, 4.99087}, {12, 8.51797}, {22,
0.371806}, {22, 1.70347}, {22, 1.92724}, {21, 0.923827}, {11,
0.450253}, {11, 0.132281}, {12, 1.95345}, {21, 0.148901}, {11,
3.62692}, {11, 0.934814}, {11, 2.32306}, {12, 1.59361}, {21,
1.01446}, {11, 1.72504}, {12, 1.35856}, {22, 5.81172}, {21,
1.07794}, {11, 1.55729}, {11, 0.164192}, {11, 4.48205}, {11,
0.232309}, {11, 0.10922}, {11, 0.658662}, {11, 3.37}, {11,
1.70193}, {11, 2.87557}, {11, 0.99993}, {11, 3.61263}, {11,
9.45614}, {11, 2.44766}, {11, 0.608538}, {11, 0.889581}, {12,
0.632193}, {21, 1.52263}, {12, 43.2115}, {22, 1.94299}, {21,
0.439674}, {11, 4.39712}, {11, 3.0329}, {11, 0.647759}, {11,
0.103597}, {11, 1.5781}, {11, 1.63927}, {11, 3.97676}, {12,
6.26291}, {21, 2.39926}, {11, 8.11932}, {11, 0.807657}, {11,
2.70066}, {11, 4.98552}, {11, 3.62964}, {11, 0.355229}, {11,
1.5259}, {11, 0.0730312}, {11, 9.94748}, {11, 0.122783}, {11,
2.70187}, {12, 1.62495}, {22, 0.386752}, {22, 3.1621}, {22,
0.0560231}, {22, 0.0411036}, {21, 2.97539}, {11, 1.62731}, {12,
0.105329}, {22, 0.00073781}, {22, 1.57384}, {21, 0.0289233}, {11,
2.68264}, {11, 11.8124}, {11, 0.178432}, {11, 2.2905}, {11,
1.88203}, {11, 1.27634}, {12, 2.22575}, {21, 1.61087}, {11,
0.375092}, {11, 2.07886}, {12, 1.71465}, {21, 0.300758}, {11,
0.271881}, {11, 0.142078}, {11, 2.679}, {11, 0.705976}, {11,
0.89368}, {11, 2.10031}, {11, 2.80626}, {11, 2.23491}, {12,
13.2974}, {21, 0.155816}, {11, 3.22648}, {11, 3.39337}, {11,
4.27089}, {11, 1.01459}, {11, 2.39789}, {11, 0.0012786}, {11,
0.256162}, {11, 7.57796}, {11, 0.137777}, {11, 0.0188366}, {11,
2.37417}, {11, 0.0766399}, {11, 3.41056}, {12, 3.41023}, {22,
8.13503}, {22, 0.0619812}, {22, 1.13408}, {21, 0.883206}, {11,
1.81183}, {11, 3.59401}, {11, 0.459683}, {11, 2.35166}, {11,
0.171278}, {12, 1.33482}, {21, 0.481108}, {12, 1.05658}, {21,
3.24673}, {11, 0.905575}, {11, 4.60674}, {11, 16.4169}, {11,
2.39446}, {12, 1.49601}, {22, 2.98946}, {21, 0.072528}, {11,
3.03993}, {12, 1.37253}, {22, 4.51084}, {21, 0.371153}, {11,
0.834973}, {12, 2.58053}, {21, 0.682489}, {11, 1.11645}, {11,
2.36627}, {11, 0.452739}, {12, 0.51225}, {22, 8.51098}, {21,
0.668063}, {12, 9.57352}, {21, 5.83167}, {11, 0.283811}, {11,
2.51739}, {11, 0.711098}, {12, 3.13439}, {21, 1.12271}, {12,
4.39267}, {22, 1.36729}, {22, 1.45951}, {22, 2.67773}, {21,
0.375948}, {11, 1.92386}, {11, 1.23622}, {12, 0.108389}, {21,
0.3705}, {12, 2.29331}, {22, 0.438194}, {21, 0.525701}, {11,
0.598552}, {11, 8.81839}, {12, 5.2682}, {21, 1.81377}, {12,
1.40081}, {21, 1.77492}, {11, 0.40669}, {11, 1.16598}, {11,
4.28619}, {12, 0.643}, {21, 2.47406}, {11, 2.63866}, {11,
3.43174}, {11, 4.30963}, {11, 1.85623}, {11, 0.353329}, {11,
1.87754}, {11, 1.3218}, {11, 0.665675}, {11, 4.20858}, {11,
4.15347}, {12, 2.34624}, {21, 0.731575}, {11, 1.15241}, {11,
0.0414488}, {11, 3.83999}, {12, 2.53748}, {22, 1.72036}, {22,
1.54993}, {21, 0.0634516}, {11, 0.0967158}, {11, 3.08902}, {11,
0.169984}, {11, 2.59665}, {11, 1.8113}, {11, 1.15592}, {11,
0.432256}, {12, 0.112454}, {21, 0.0925832}, {11, 5.54543}, {11,
1.82186}, {11, 0.0307038}, {11, 0.136141}, {11, 1.97385}, {11,
0.89142}, {11, 0.677233}, {11, 3.16198}, {11, 1.82287}, {11,
1.56418}, {12, 1.0886}, {21, 2.06019}, {12, 0.647606}, {21,
0.41147}, {11, 2.72057}, {11, 1.04468}, {11, 2.84094}, {11,
0.384157}, {11, 1.4603}, {12, 15.2212}, {22, 3.0392}, {22,
0.723344}, {21, 3.38961}, {12, 2.91617}, {22, 3.44695}, {22,
2.09559}, {21, 2.10573}, {11, 1.44079}, {11, 4.86781}, {11,
0.520662}, {11, 0.746715}, {11, 0.306281}, {11, 5.09198}, {11,
0.71536}, {11, 2.41427}, {11, 0.0881861}, {11, 5.03889}, {12,
1.95982}, {21, 0.00813682}, {11, 0.717399}, {11, 2.19969}, {11,
3.90254}, {11, 0.618343}, {11, 1.46609}, {12, 1.64411}, {21,
0.174679}, {11, 1.579}, {11, 1.04525}, {11, 2.5956}, {11,
14.299}, {11, 8.70876}, {12, 60.6318}, {21, 0.378533}, {12,
4.88898}, {21, 0.324341}, {12, 5.45187}, {21, 0.259556}, {11,
1.0732}, {11, 2.43815}, {11, 2.05789}, {11, 0.783846}, {11,
3.11615}, {11, 3.7054}, {12, 2.22448}, {21, 0.294525}, {11,
0.0761907}, {11, 0.819215}, {11, 6.0825}, {11, 0.463129}, {11,
9.39858}, {11, 2.21535}, {12, 3.27443}, {22, 1.79496}, {22,
1.91479}, {21, 0.0244553}, {11, 3.2986}, {11, 0.947061}, {11,
8.99542}, {12, 18.2325}, {22, 40.0858}, {21, 0.888141}, {12,
5.83575}, {21, 4.5691}, {11, 0.209406}, {11, 1.45323}, {11,
0.858814}, {12, 1.62626}, {21, 0.0323131}, {12, 1.9379}, {21,
0.114223}, {11, 0.914693}, {11, 1.2745}, {11, 0.860423}, {11,
2.48966}, {11, 6.01146}, {12, 3.60139}, {21, 3.17734}, {11,
1.13914}, {11, 23.0131}, {11, 3.01658}, {11, 0.44302}, {11,
3.09507}, {12, 2.67898}, {22, 4.5478}, {21, 3.11333}, {12,
220.223}, {22, 0.947471}, {21, 0.73805}, {12, 0.229876}, {21,
0.0334121}, {11, 0.646208}, {11, 0.763161}, {12, 1.61841}, {21,
3.26481}, {11, 2.59895}, {11, 5.5951}, {11, 1.96849}, {11,
1.82076}, {11, 0.729646}, {11, 2.86477}, {12, 6.60307}, {22,
3.0114}, {21, 2.44649}, {11, 1.33681}, {12, 0.30028}, {21,
4.85319}, {11, 2.52322}, {11, 0.937138}, {11, 2.85908}, {12,
1.66298}, {22, 2.50931}, {22, 4.93735}, {21, 3.32006}, {12,
0.00228936}, {21, 0.656371}, {11, 1.19071}, {12, 0.510094}, {21,
0.743319}, {11, 4.02809}, {11, 1.04496}, {11, 1.62482}, {11,
0.862675}, {11, 2.86354}, {11, 2.36819}, {11, 0.62228}, {11,
2.95324}, {11, 2.05741}, {11, 0.269327}, {11, 0.954059}, {11,
0.492027}, {12, 40.2807}, {21, 1.18365}, {11, 6.55213}, {11,
5.97111}, {11, 3.43927}, {12, 0.192273}, {21, 1.49062}, {11,
0.770907}, {11, 0.175105}, {11, 6.27714}, {11, 5.61819}, {11,
0.918489}, {11, 0.287903}, {12, 1.0136}, {21, 0.504477}, {11,
3.34961}, {11, 3.109}, {11, 0.000940908}, {11, 1.23368}, {11,
26.3921}, {11, 2.08089}, {11, 0.295977}, {12, 30.3913}, {22,
0.76397}, {21, 0.231084}, {11, 0.277827}, {11, 0.714355}, {11,
1.32373}, {11, 2.19623}, {11, 2.00104}, {11, 0.663317}, {11,
1.34304}, {12, 0.00606519}, {21, 3.9485}, {12, 0.311826}, {21,
2.38436}, {11, 0.0891827}, {12, 1.86986}, {21, 0.369234}, {11,
4.05934}, {11, 3.96586}, {12, 1.36259}, {21, 0.680238}, {11,
0.0624457}, {11, 0.291489}, {11, 2.29941}, {11, 0.821843}, {11,
0.310665}, {11, 2.47296}, {11, 0.351705}, {11, 0.68359}, {11,
3.82825}, {11, 0.0117543}, {12, 12.1905}, {21, 0.118971}, {11,
1.20009}, {12, 5.9188}, {21, 0.414438}, {11, 4.59963}, {11,
0.586125}, {11, 9.8659}, {12, 0.928261}, {22, 10.862}, {21,
4.0916}, {11, 0.162617}, {11, 1.43906}, {11, 1.0653}, {11,
0.0191653}, {11, 0.029664}, {11, 0.793592}, {11, 10.9403}, {11,
0.443276}, {11, 1.79034}, {12, 2.96605}, {21, 0.271376}, {11,
10.3482}, {11, 1.01124}, {12, 0.0186686}, {21, 0.0212673}, {11,
3.30284}, {11, 2.29006}, {11, 0.265414}, {11, 0.179482}, {11,
5.38253}, {11, 6.03381}, {11, 5.36193}, {12, 0.0214731}}

{{21, 1.40679}, {11, 1.93441}, {12, 4.63318}, {22, 46.496}, {21,
3.32509}, {12, 1.79442}, {22, 6.10555}, {21, 0.83035}, {11,
1.77595}, {11, 9.68321}, {11, 0.942905}, {11, 0.431747}, {11,
0.724573}, {11, 3.36428}, {11, 0.671109}, {11, 3.36826}, {11,
3.96065}, {11, 0.856256}, {11, 6.08217}, {12, 3.37772}, {21,
1.84991}, {11, 3.93281}, {11, 3.92168}, {12, 11.0214}, {21,
0.607707}, {11, 0.568509}, {11, 0.226295}, {12, 0.065158}, {21,
1.96438}, {11, 2.74094}, {12, 18.0162}, {21, 0.635886}, {11,
1.49167}, {11, 1.80937}, {11, 5.42505}, {11, 6.37474}, {11,
2.87062}, {11, 2.86664}, {11, 0.203184}, {11, 0.574386}, {12,
2.44281}, {21, 1.24903}, {12, 0.0466638}, {22, 0.159081}, {22,
0.0422183}, {21, 1.38484}, {11, 1.57368}, {11, 0.108739}, {11,
1.59221}, {11, 8.40024}, {12, 0.38737}, {21, 2.49035}, {11,
1.32185}, {12, 2.12832}, {21, 1.22332}, {11, 0.00719662}, {11,
10.8008}, {11, 2.39068}, {11, 1.0415}, {11, 9.965}, {11,
0.384449}, {11, 2.0032}, {11, 0.479976}, {11, 0.784839}, {11,
0.00197985}, {11, 0.117584}, {12, 4.94818}, {21, 1.42456}, {11,
3.24443}, {11, 5.30823}, {11, 2.68755}, {11, 1.24694}, {11,
5.77435}, {11, 6.81148}, {11, 2.46485}, {11, 0.819767}, {12,
1.92909}, {21, 1.51619}, {12, 0.275036}, {22, 3.12242}, {22,
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5.34809}, {11, 2.16714}, {12, 20.3934}, {21, 2.58429}, {12,
0.982478}, {21, 0.96555}, {11, 1.8061}, {12, 3.13771}, {22,
0.193815}, {21, 0.167285}, {11, 0.0702887}, {11, 8.87907}, {12,
0.000842967}, {21, 0.0271382}, {11, 1.97738}, {12, 2.37507}, {21,
1.24559}, {11, 0.0119}, {12, 3.28408}, {21, 3.72507}, {12,
8.85587}, {21, 3.60479}, {11, 4.7883}, {11, 0.808183}, {11,
0.819872}, {11, 15.7243}, {11, 5.81794}, {11, 0.261655}, {11,
1.01092}, {11, 1.70611}, {11, 0.192521}, {11, 1.26826}, {11,
2.03495}, {11, 0.484149}, {11, 0.780455}, {11, 0.152741}, {12,
1.1444}, {22, 10.3844}, {21, 0.180593}, {11, 0.781895}, {11,
0.357182}, {11, 0.860676}, {11, 1.02211}, {11, 2.6353}, {12,
5.16386}, {22, 0.490932}, {21, 1.08401}, {11, 1.93301}, {11,
0.892317}, {11, 2.29316}, {12, 0.0417666}, {22, 91.1599}, {21,
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3.31679}, {21, 0.0605242}, {11, 6.53299}, {11, 0.993486}, {12,
12.295}, {22, 26.3368}, {21, 0.541946}, {11, 2.02805}, {11,
1.11008}, {11, 0.369521}, {11, 0.631506}, {12, 0.0341794}, {22,
3.38266}, {22, 2.10728}, {21, 0.632345}, {11, 1.38166}, {12,
0.802346}, {21, 0.330738}, {11, 10.8836}, {11, 1.92341}, {11,
3.18795}, {11, 0.324107}, {11, 0.303734}, {12, 3.09965}, {21,
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0.851523}, {21, 0.224333}, {11, 0.790603}, {11, 4.22296}, {11,
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2.14954}, {12, 12.4081}, {22, 1.07027}, {21, 0.41787}, {11,
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0.346638}, {11, 1.024}, {11, 3.6366}, {11, 3.14778}, {11,
1.76417}, {12, 1.86509}, {21, 0.333264}, {11, 0.0585468}, {11,
1.08582}, {11, 2.20401}, {12, 5.39257}, {21, 0.0978229}, {11,
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1.31633}, {11, 2.98747}, {12, 0.02608}, {21, 2.35025}, {11,
4.75365}, {12, 26.2802}, {22, 3.387}, {21, 0.706056}, {11,
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1.63082}, {21, 0.32223}, {11, 1.43161}, {11, 0.22785}, {11,
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3.31052}, {12, 3.787}, {21, 2.79543}, {11, 0.541556}, {11,
0.485166}, {11, 0.122183}, {11, 4.76756}, {11, 1.46694}, {11,
0.341336}, {11, 0.396161}, {11, 2.15552}, {11, 0.919227}, {11,
8.83382}, {12, 4.17046}, {21, 1.52963}, {11, 4.00444}, {12,
3.98975}, {21, 0.803004}, {11, 0.61918}, {11, 1.12726}, {11,
0.703332}, {11, 2.20456}, {11, 0.65832}, {12, 2.53529}, {21,
0.552773}, {11, 0.752771}, {12, 0.648891}, {22, 2.33094}, {21,
1.07172}, {11, 1.22272}, {12, 1.9882}, {21, 0.383318}, {11,
2.47532}, {11, 0.958663}, {11, 0.810984}, {11, 1.77818}, {11,
4.2106}, {11, 0.187203}, {12, 11.4189}, {21, 0.858178}, {11,
1.89701}, {11, 1.6224}, {11, 0.418025}, {11, 0.470917}, {11,
0.929235}, {11, 3.69097}, {11, 0.41849}, {11, 1.1358}, {11,
1.33364}, {11, 0.528337}, {11, 9.15382}, {11, 1.23739}, {11,
0.10116}, {11, 0.453442}, {11, 4.05979}, {11, 0.000287956}, {11,
0.779157}, {11, 1.1194}, {11, 0.217777}, {12, 27.8495}, {21,
1.99525}, {11, 0.160386}, {11, 1.06986}, {12, 2.97524}, {22,
2.30908}, {21, 1.15799}, {11, 0.205706}, {12, 0.74}, {21,
0.227861}, {12, 1.23454}, {22, 2.5918}, {21, 0.0770961}, {12,
0.0322104}, {22, 1.94694}, {21, 0.822924}, {11, 8.25114}, {11,
2.21538}, {11, 2.61864}, {11, 3.09168}, {11, 1.18344}, {11,
1.18772}, {11, 2.71255}, {12, 0.579122}, {21, 1.22323}, {11,
0.442461}, {11, 3.65648}, {11, 0.473265}, {11, 1.20711}, {11,
2.46904}, {11, 2.04034}, {11, 1.21709}, {11, 22.8938}, {11,
0.405652}, {11, 13.3665}, {11, 0.206861}, {11, 3.90875}, {11,
1.34437}, {11, 3.30651}, {11, 2.07061}, {11, 1.4659}, {11,
5.50851}, {11, 7.53881}, {12, 2.34253}, {21, 5.94549}, {11,
3.70878}, {11, 1.50296}, {11, 0.851377}, {12, 0.000665337}, {21,
0.487052}, {11, 2.23259}, {12, 2.05711}, {21, 2.54216}, {11,
2.31364}, {12, 0.191588}, {22, 4.40801}, {21, 0.693429}, {11,
2.18728}, {12, 1.76642}, {22, 2.00576}, {21, 0.902264}, {11,
1.72401}, {11, 0.0178434}, {12, 3.05314}, {22, 4.76749}, {21,
0.427456}, {12, 3.73905}, {21, 1.01928}, {11, 2.3834}, {11,
0.604941}, {11, 4.58362}, {11, 0.456101}, {11, 0.317502}, {11,
0.448837}, {11, 1.06587}, {11, 0.323111}, {11, 1.91542}}

Disth[11] =
MixtureDistribution[{w11,
1 - w11}, {ExponentialDistribution[\[Lambda]11],
WeibullDistribution[\[Alpha]11, \[Beta]11]}];
Disth[12] =
MixtureDistribution[{w12,
1 - w12}, {ExponentialDistribution[\[Lambda]12],
WeibullDistribution[\[Alpha]12, \[Beta]12]}];
Disth[21] =
MixtureDistribution[{w21,
1 - w21}, {ExponentialDistribution[\[Lambda]21],
WeibullDistribution[\[Alpha]21, \[Beta]21]}];
Disth[22] =
MixtureDistribution[{w22,
1 - w22}, {ExponentialDistribution[\[Lambda]22],
WeibullDistribution[\[Alpha]22, \[Beta]22]}];
a7 = PDF[Disth[#[[1]]], x] /. x -> #[[2]] & /@ a6

似乎直接原因是beta12太接近0

想了一个不太好的办法，参数限制>0改成>0.001，就能跑出来了，但是结果和真实值相差太大了，但明明真实值也>0.001，为什么估计出来的参数和>0的限制差距这么大

换了FindMaximin，至少没中途报错，但跑了一个小时没结果，放弃了

四个Disth函数如果是互不相关的，为什么不把数据分成四组分别求最大值最后再乘起来？

NMaximize[{Total@(Log[PDF[Disth[11],#]&/@Cases[a6,{11,x_}:>x]]),0<w11<1,\[Lambda]11>0,\[Alpha]11>0,\[Beta]11>0},{w11,\[Lambda]11,\[Alpha]11,\[Beta]11},WorkingPrecision->20,MaxIterations->50]
NMaximize[{Total@(Log[PDF[Disth[12],#]&/@Cases[a6,{12,x_}:>x]]),0<w12<1,\[Lambda]12>0,\[Alpha]12>0,\[Beta]12>0},{w12,\[Lambda]12,\[Alpha]12,\[Beta]12},WorkingPrecision->20,MaxIterations->50]
NMaximize[{Total@(Log[PDF[Disth[21],#]&/@Cases[a6,{21,x_}:>x]]),0<w21<1,\[Lambda]21>0,\[Alpha]21>0,\[Beta]21>0},{w21,\[Lambda]21,\[Alpha]21,\[Beta]21},WorkingPrecision->20,MaxIterations->50]
NMaximize[{Total@(Log[PDF[Disth[22],#]&/@Cases[a6,{22,x_}:>x]]),0<w22<1,\[Lambda]22>0,\[Alpha]22>0,\[Beta]22>0},{w22,\[Lambda]22,\[Alpha]22,\[Beta]22},WorkingPrecision->20,MaxIterations->50]
总之算出来了一些结果，但还是有很多warning，lz自己对一下是不是在合理范围吧

测试我就不测了。只说两点：
1. 最优化问题本来就是变量越多不好办。
2. "DifferentialEvolution"偶尔会有奇效，试过了吗？

有些回复我在个人中心看到一部分，反而在帖子里面显示不出来，是不是有毒

日	一	二	三	四	五	六

大数据NMaximize报错，只能在有限个数据内求解

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