stblinv.m

matlab alpha稳定分布

utemp = u(:);
X0 = zeros(size(utemp));
alpha = max(alpha,.1);
if beta == 1
    utemp(utemp < .1) = .1;  % bring these into table range 
end                          % since asyp. formulas don't apply if beta=1.
 
high = (utemp > .9);  
low = (utemp < .1);
middle = ~high & ~low;

% Use asymptotic formulas to guess high and low
if any(high | low)
    if alpha ~= 1 
        C = (1-alpha) / ( gamma(2 - alpha) * cos(pi*alpha/2) );
    else
        C = 2/pi;
    end
    X0(high) = ( (1-u(high))/(C * .5 * (1 + beta)) ).^(-1/alpha); 
    X0(low)  = -(u(low)/(C * .5 * (1 - beta))).^(-1/alpha);
end

% Use pre-calculated lookup table
if any(middle)
    [Alp Bet P] = meshgrid(.1:.1:2 , 0:.2:1 , .1:.1:.9 ); 
    stblfrac = zeros(6,20,9);
    stblfrac(:,1:5,1) = ...  % 
      [-1.890857122067030e+006   -1.074884919696010e+003   -9.039223076384694e+001   -2.645987890965098e+001   -1.274134564492298e+001;...
       -1.476366405440763e+005   -2.961237538429159e+002   -3.771873580263473e+001   -1.357404219788403e+001   -7.411052003232824e+000;...
       -4.686998894118387e+003   -5.145071882481552e+001   -1.151718246460839e+001   -5.524535336243413e+000   -3.611648531595958e+000;...
       -2.104710824345458e+001   -3.379418096823576e+000   -1.919928049616870e+000   -1.508399002681057e+000   -1.348510542803496e+000;...
       -1.267075422596289e-001   -2.597188113311268e-001   -4.004811495862077e-001   -5.385024279816432e-001   -6.642916520777534e-001;...
       -1.582153175255304e-001   -3.110425775503970e-001   -4.383733961816599e-001   -5.421475800719634e-001   -6.303884905318050e-001];
    stblfrac(:,6:10,1) = ...
      [-7.864009406553024e+000   -5.591791397752695e+000   -4.343949435866958e+000   -3.580521076832391e+000   -3.077683537175253e+000;...
       -4.988799898398770e+000   -3.787942909197120e+000   -3.103035515608863e+000   -2.675942594722292e+000   -2.394177022026705e+000;...
       -2.762379160216148e+000   -2.313577186902494e+000   -2.052416861482463e+000   -1.893403771865641e+000   -1.796585983161395e+000;...
       -1.284465355994317e+000   -1.267907903071982e+000   -1.279742001004255e+000   -1.309886183701422e+000   -1.349392554642457e+000;...
       -7.754208907962602e-001   -8.732998811318613e-001   -9.604322013853581e-001   -1.039287445657237e+000   -1.111986321525904e+000;...
       -7.089178961038225e-001   -7.814055112235459e-001   -8.502117698317242e-001   -9.169548634355569e-001   -9.828374636178471e-001];
    stblfrac(:,11:15,1) = ...
      [-2.729262880847457e+000   -2.479627528870857e+000   -2.297138304998905e+000   -2.162196365947914e+000   -2.061462692277420e+000;...
       -2.202290611202918e+000   -2.070075681428623e+000   -1.979193969170630e+000   -1.917168989568703e+000   -1.875099179801364e+000;...
       -1.740583121589162e+000   -1.711775396141753e+000   -1.700465158047576e+000   -1.700212465596452e+000   -1.707238269631509e+000;...
       -1.391753942957071e+000   -1.434304119387730e+000   -1.476453646904256e+000   -1.518446568503842e+000   -1.560864595722380e+000;...
       -1.180285915835185e+000   -1.245653509438976e+000   -1.309356535558631e+000   -1.372547245869795e+000   -1.436342854982504e+000;...
       -1.048835660976022e+000   -1.115815771583362e+000   -1.184614345408666e+000   -1.256100352867799e+000   -1.331235978799527e+000];
    stblfrac(:,16:20,1) = ...
       [-1.985261982958637e+000   -1.926542865732525e+000   -1.880296841910385e+000   -1.843044812063057e+000   -1.812387604873646e+000;...
       -1.846852935880107e+000   -1.828439745755405e+000   -1.817388844989596e+000   -1.812268962543248e+000   -1.812387604873646e+000;...
       -1.719534615317151e+000   -1.736176665562027e+000   -1.756931455967477e+000   -1.782079727531726e+000   -1.812387604873646e+000;...
       -1.604464355709833e+000   -1.650152416312346e+000   -1.699029550621646e+000   -1.752489822658308e+000   -1.812387604873646e+000;...
       -1.501904088536648e+000   -1.570525854475943e+000   -1.643747672313277e+000   -1.723509779436442e+000   -1.812387604873646e+000;...
       -1.411143947581252e+000   -1.497190629447853e+000   -1.591104422133556e+000   -1.695147748117837e+000   -1.812387604873646e+000];

    stblfrac(:,1:5,2) = ...
       [-4.738866777987500e+002   -1.684460387562537e+001   -5.619926961081743e+000   -3.281734135829228e+000   -2.397479160864619e+000;...
       -2.185953347160669e+001   -3.543320127025984e+000   -1.977029667649595e+000   -1.507632281031653e+000   -1.303310228044346e+000;...
       -2.681009914911080e-001   -4.350930213152404e-001   -5.305212880041126e-001   -6.015232065896753e-001   -6.620641788021128e-001;...
       -9.503065419472154e-002   -1.947070824738389e-001   -2.987136341021804e-001   -3.973064532664002e-001   -4.838698271554803e-001;...
       -1.264483719244014e-001   -2.437377726529247e-001   -3.333750988387906e-001   -4.016893641684894e-001   -4.577316520822721e-001;...
       -1.526287733702501e-001   -2.498255243669921e-001   -3.063859169446500e-001   -3.504924054764082e-001   -3.911254396222550e-001];
    stblfrac(:,6:10,2) = ...
       [-1.959508008521143e+000   -1.708174380583835e+000   -1.550822278332538e+000   -1.447013328833974e+000   -1.376381920471173e+000;...
       -1.199548019673933e+000   -1.144166826374866e+000   -1.115692821970145e+000   -1.103448361903579e+000   -1.101126400280696e+000;...
       -7.174026993828067e-001   -7.694003004766365e-001   -8.178267862332173e-001   -8.615585464741182e-001   -9.003104216523169e-001;...
       -5.579448431371428e-001   -6.215822273361273e-001   -6.771753949313707e-001   -7.267793058476849e-001   -7.720164852674839e-001;...
       -5.069548741156986e-001   -5.523620701546919e-001   -5.956554729327528e-001   -6.378655338388568e-001   -6.796745661620428e-001;...
       -4.309657384679277e-001   -4.709130419301468e-001   -5.113624096299824e-001   -5.525816075847192e-001   -5.948321009341774e-001];
    stblfrac(:,11:15,2) = ...
      [-1.327391983207241e+000   -1.292811209009340e+000   -1.267812588403031e+000   -1.249132310044230e+000   -1.234616432819130e+000;...
       -1.104531584444055e+000   -1.110930462397609e+000   -1.118760810700929e+000   -1.127268239360369e+000   -1.136171639806347e+000;...
       -9.347554970493899e-001   -9.658656088352816e-001   -9.945788535033495e-001   -1.021718797792234e+000   -1.048005562158225e+000;...
       -8.141486817740096e-001   -8.541760575495752e-001   -8.929234555236560e-001   -9.311104141820112e-001   -9.694099704722252e-001;...
       -7.215886443544494e-001   -7.640354693071291e-001   -8.074261467088205e-001   -8.522003643607233e-001   -8.988670244927735e-001;...
       -6.384119892912432e-001   -6.836776839822375e-001   -7.310612144698296e-001   -7.810921001396979e-001   -8.344269070778757e-001];
    stblfrac(:,16:20,2) = ...
       [-1.222879780072203e+000   -1.213041554808853e+000   -1.204541064608597e+000   -1.197016952370690e+000   -1.190232162899989e+000;...
       -1.145449097190615e+000   -1.155224344271089e+000   -1.165719407748303e+000   -1.177246763148178e+000   -1.190232162899989e+000;...
       -1.074094694885961e+000   -1.100624477495892e+000   -1.128270402039747e+000   -1.157812818875688e+000   -1.190232162899989e+000;...
       -1.008502023575024e+000   -1.049129636922346e+000   -1.092166845038550e+000   -1.138712425453996e+000   -1.190232162899989e+000;...
       -9.480479125009214e-001   -1.000533792677121e+000   -1.057363229272293e+000   -1.119941850176443e+000   -1.190232162899989e+000;...
       -8.918931068397437e-001   -9.545526172382969e-001   -1.023797332562095e+000   -1.101496412960141e+000   -1.190232162899989e+000];

    stblfrac(:,1:5,3) = ...
       [-1.354883142615948e+000   -8.855778500552980e-001   -7.773858277863260e-001   -7.357727812399337e-001   -7.181850957003714e-001;...
       -5.193811327974376e-002   -1.633949875159595e-001   -2.617724006156590e-001   -3.392619822712012e-001   -4.018554923458003e-001;...
       -6.335376612981386e-002   -1.297738965263227e-001   -1.985319371835911e-001   -2.624863717000360e-001   -3.174865471926985e-001;...
       -9.460338726038994e-002   -1.756165596280472e-001   -2.282691311262980e-001   -2.638458905915733e-001   -2.918110046315503e-001;...
       -1.158003423724520e-001   -1.620942232133271e-001   -1.790483132028017e-001   -1.937097725890709e-001   -2.109729530977958e-001;...
       -5.695213481951577e-002   -2.485009114767256e-002   -2.455774348005581e-002   -4.243720620421176e-002   -6.906960852184874e-002];
    stblfrac(:,6:10,3) = ...
       [ -7.120493514301658e-001   -7.121454153857569e-001   -7.157018373526386e-001   -7.209253714350538e-001   -7.265425280053609e-001;...
       -4.539746445467862e-001   -4.979328472153985e-001   -5.348184073267474e-001   -5.654705188376931e-001   -5.909430146259388e-001;...
       -3.637544360366539e-001   -4.030045272659678e-001   -4.369896090801292e-001   -4.671253359013797e-001   -4.944847533335236e-001;...
       -3.167744873288179e-001   -3.408290016876749e-001   -3.649204420006245e-001   -3.894754728525021e-001   -4.146904022890949e-001;...
       -2.311198638992638e-001   -2.537077422985343e-001   -2.783252370301364e-001   -3.047045003309861e-001   -3.327092628454751e-001;...
       -1.000745485866474e-001   -1.334091111747126e-001   -1.681287272131953e-001   -2.038409527302062e-001   -2.404547731975402e-001];
    stblfrac(:,11:15,3) = ...
       [-7.317075569303094e-001   -7.359762286696208e-001   -7.392122467978279e-001   -7.414607677550720e-001   -7.428480570989012e-001;...
       -6.123665499489599e-001   -6.307488506465194e-001   -6.469130897780404e-001   -6.615145568123281e-001   -6.750798357120451e-001;...
       -5.198770070249209e-001   -5.439265161390062e-001   -5.671356857543234e-001   -5.899325077218274e-001   -6.127077038151078e-001;...
       -4.406707089221509e-001   -4.675033009839270e-001   -4.952960990683358e-001   -5.242037261193876e-001   -5.544463409264927e-001;...
       -3.623063449447594e-001   -3.935470145089454e-001   -4.265595391976379e-001   -4.615525703717921e-001   -4.988293297210071e-001;...
       -2.780623638274261e-001   -3.168837529800063e-001   -3.572466721186688e-001   -3.995862986780706e-001   -4.444626893956575e-001];
    stblfrac(:,16:20,3) = ...
      [-7.435216571211187e-001   -7.436225251216279e-001   -7.432733099840527e-001   -7.425762029730668e-001   -7.416143171871161e-001;...
       -6.880470899358724e-001   -7.008026232247697e-001   -7.137148222421971e-001   -7.271697520465581e-001   -7.416143171871161e-001;...
       -6.358474023877762e-001   -6.597648782206755e-001   -6.849381555866478e-001   -7.119602076523737e-001   -7.416143171871161e-001;...
       -5.863313160876512e-001   -6.202819599064874e-001   -6.568811178840162e-001   -6.969403639254603e-001   -7.416143171871159e-001;...
       -5.388134824040952e-001   -5.820906647738434e-001   -6.294732446564461e-001   -6.821024214831549e-001   -7.416143171871159e-001;...
       -4.925935308416445e-001   -5.449092276644302e-001   -6.026377433551201e-001   -6.674379829825384e-001   -7.416143171871159e-001];

    stblfrac(:,1:5,4) = ...
       [-4.719005698760254e-003   -5.039419714218448e-002   -1.108600074872916e-001   -1.646393852283324e-001   -2.088895889525075e-001;...
       -3.167687806490741e-002   -6.488347295237770e-002   -9.913854730442322e-002   -1.306663969875579e-001   -1.574578108363950e-001;...
       -6.256908981229170e-002   -1.058190431028687e-001   -1.215669874255146e-001   -1.261149689648148e-001   -1.284283108027729e-001;...
       -7.132464704948761e-002   -5.885471032381771e-002   -3.846810486653290e-002   -2.801768649688129e-002   -2.615407079824540e-002;...
        1.186775035989228e-001    1.847231744541209e-001    1.899666578065291e-001    1.756596652192159e-001    1.538218851318199e-001;...
        1.359937191266603e+000    7.928324704017256e-001    6.068350758065271e-001    4.949176895753282e-001    4.117787224185477e-001];
    stblfrac(:,6:10,4) = ...
       [-2.445873831127209e-001   -2.729819770922066e-001   -2.951510874462016e-001   -3.121233685073350e-001   -3.249196962329062e-001;...
       -1.797875581290475e-001   -1.986122400020671e-001   -2.148458045681510e-001   -2.292024720743768e-001   -2.422125650878785e-001;...
       -1.318108373643454e-001   -1.372885008966837e-001   -1.450218673440198e-001   -1.548461140242879e-001   -1.664940537646226e-001;...
       -3.037902421859952e-002   -3.894619676380785e-002   -5.076849313651704e-002   -6.518223105549245e-002   -8.178056142331483e-002;...
        1.287679439328719e-001    1.022243387982872e-001    7.488543991005173e-002    4.698265181928261e-002    1.852002327642577e-002;...
        3.435869264264112e-001    2.844376471729288e-001    2.312306852681522e-001    1.820841981890349e-001    1.357181057787019e-001];
    stblfrac(:,11:15,4) = ...
       [-3.344714240325961e-001   -3.415532212363377e-001   -3.467713617249639e-001   -3.505859000173167e-001   -3.533413466958321e-001;...
       -2.542699931601989e-001   -2.656748454748664e-001   -2.766656461455947e-001   -2.874428940341864e-001   -2.981872822548070e-001;...
       -1.796994139325742e-001   -1.942454974557965e-001   -2.099854734361004e-001   -2.268483937252861e-001   -2.448403779828917e-001;...
       -1.003134231215546e-001   -1.206343411798188e-001   -1.426762955132322e-001   -1.664453845103147e-001   -1.920257997377931e-001;...
       -1.062008675791458e-002   -4.062891141128176e-002   -7.175196683590498e-002   -1.042870733773311e-001   -1.385948877988075e-001;...
        9.117291945474759e-002    4.766184332000264e-002    4.481886485253039e-003   -3.904933750228177e-002   -8.364689014849616e-002];
    stblfrac(:,16:20,4) = ...
       [-3.552947623689004e-001   -3.566384591258251e-001   -3.575167387322836e-001   -3.580387843935552e-001   -3.582869092425832e-001;...
       -3.090746307371333e-001   -3.202900038682522e-001   -3.320450798333745e-001   -3.445973947956370e-001   -3.582869092425832e-001;...
       -2.640470286750166e-001   -2.846415660837839e-001   -3.069024734642628e-001   -3.312464672828315e-001   -3.582869092425832e-001;...
       -2.195942670864279e-001   -2.494428999135824e-001   -2.820166786810741e-001   -3.179740384308457e-001   -3.582869092425832e-001;...
       -1.751227987938045e-001   -2.144432379167035e-001   -2.573138196343415e-001   -3.047716553689650e-001   -3.582869092425832e-001;...
       -1.301133939768983e-001   -1.794049920724848e-001   -2.327202766583559e-001   -2.916310469293936e-001   -3.582869092425832e-001];

    stblfrac(:,1:5,5) = ...
      [                      0                         0                         0                         0                         0;...
       -2.998229841415443e-002   -3.235136568035350e-002   -1.058934315424071e-002    1.472786013654386e-002    3.649529125352272e-002;...
       -4.911181618214269e-004    7.928758678692660e-002    1.295711243349632e-001    1.575625247967377e-001    1.726794061650541e-001;...
        6.444732609572413e-001    5.412205715497974e-001    4.864603927210872e-001    4.457073928551408e-001    4.118964225372133e-001;...
        4.884639795042095e+000    1.686842470765597e+000    1.132342494635284e+000    8.944978064032267e-001    7.538011200000044e-001;...
        2.410567057697245e+001    4.005534670805399e+000    2.144263118197206e+000    1.518214626927320e+000    1.198109338317733e+000];
    stblfrac(:,6:10,5) = ...
     [                      0                         0                         0                         0                         0;...
        5.320761222262883e-002    6.497369053185199e-002    7.235439352353751e-002    7.603800885095309e-002    7.671459793802817e-002;...
        1.799982238321182e-001    1.821699713013862e-001    1.806145618464317e-001    1.761248753943454e-001    1.691770293512301e-001;...
        3.823074983529713e-001    3.554905959697276e-001    3.305043126978712e-001    3.066571802106021e-001    2.834017043112906e-001;...
        6.558265419066330e-001    5.806408912949470e-001    5.191065509143589e-001    4.663489244354866e-001    4.194539705064985e-001;...
        9.966378800612080e-001    8.532685386168033e-001    7.427048697651345e-001    6.524693172360032e-001    5.756299950589361e-001];
    stblfrac(:,11:15,5) = ...
      [                      0                         0                         0                         0                         0;...