Here you can find the source of gammaCdf(double a, double x)
@SuppressWarnings({ "WeakerAccess" })
public static double gammaCdf(double a, double x)
//package com.java2s; // it under the terms of the GNU General Public License as published by // public class Main { private static double r[] = { 1.253314137315500251207883, 1.193182964731915311846094, 1.137490921203604514832235, 1.085827027468003637553896, 1.037824575853726812300365, .9931557904881572182738326, .9515271920712067152786701, .9126755670832121676776603, .8763644564536923467278531, .8423810914521299997866721, .8105337152790304152036357, .7806492378708633711733062, .7525711790634080514554734, .7261578617139919103863031, .7012808218544300582109727, .6778234075911775329302582, .6556795424187984715438712, .6347526319769262711052108, .6149545961509297292775566, .5962050108690213064751457, .5784303460476310766336125, .5615632879362914156483528, .5455421356582169186076368, .5303102630712526699958747, .5158156382179633550265125, .5020103936204170322841234, .488850441527573754354743, .4762951289605100272316751, .4643069280394421644372609, .452851157630626619621641, .4418957328326000054087525, .4314109392400032535140663, .4213692292880544732249343, .4117450382989767017176231, .4025146181296716932830159, .3936558865630571131481576, .3851482907984342415801495, .3769726835829618014159496, .3691112106902638389489919, .3615472085963400644161054, .354265111329793337375764, .3472503655851968568924767, .3404893532870850071346728, .3339693208791823593693459, .3276783146905523474475952, .3216051217986084063997594, .3157392158694103491188545, .3100707075093597582907416, .304590298710103019232964, .2992892410108769288187367, .2941592970402895988586268, .2891927051332122944730683, .2843821467484925828542051, .2797207164400090390048569, .2752018941576061687414437, .2708195196759090041951434, .2665677689682234829510997, .2624411323600359552832388, .2584343943120382172559107, .2545426146965892806142785, .2507611114439652148255265, .2470854444460805703298742, .2435114006154562183725053, .2400349800063908654015814, .2366523829135604830915503, .233359997870698598664295, .2301543904788006381072361, .2270322929993801119871592, .2239905946538290863869083, .2210263325749769736284363, .2181366833614710122297952, .2153189551897363262218578, .2125705804420320545972856, .2098891088125368083169621, .2072722008565007589748572, .2047176219503302188107064, .2022232366330545215419131, .1997870033019862546952077, .1974069692375194490844627, .1950812659339918105426953, .1928081047153155616100713, .1905857726157402721374016, .1884126285076001815699527, .1862870994592909823499507, .1842076773079703381780956, .1821729154326492082990465, .1801814257143915475980612, .1782318756713315633990563, .1763229857571025870546387, .17445352681211268567823, .1726223176578507652332691, .170828222825113676267847, .1690701504076941880139726, .1673470500336553419899068, .1656579109468773975553577, .1640017601920640363366404, .1623776608968673374563811, .1607847106452193635505097, .1592220399363673265836744, .1576888107244717415286631, .1561842150339760769159709, .154707473646271358338463, .1532578348534790212960446, .1518345732754411325827937, .1504369887362691412736569, .1490644051970330214282687, .1477161697413932577413847, .1463916516111827416630501, .1450902412891308370578393, .1438113496261050352444228, .1425544070104022432905889, .1413188625767789529834851, .1401041834530502056148988, .1389098540422202650857274, .1377353753382303588480118, .1365802642735279803607799, .1354440530967635155710012, .1343262887790271962841785, .1332265324471292504019244, .132144358842515398166367, .1310793558044917945593207, .1300311237765102200812464, .128999275334337470011875, .1279834347349965694864678, .1269832374854368818978314, .1259983299299428153278645, .1250283688553503087964205, .1240730211131909094124509, .1231319632579322598468361, .1222048812005296276989127, .1212914698765461287919247, .1203914329281397110711456, .1195044823992530794107805, .1186303384433775019338515, .1177687290432979327966364, .1169193897422535131538919, .1160820633859823480155247, .1152564998751443189754465, .1144424559276431412284366, .1136396948503935650514457, .112847986320103044088645, .1120671061726592771214108, .1112968362007358601364944, .110536963959247939376068, .1097872825783083063597883, .1090475905833518904388312, .1083176917221130451719685, .1075973947981563778083775, .1068865135106744244241717, .1061848663002832119442509, .105492276200556096942253, .1048085706950511306815753, .1041335815795982142447371, .1034671448296236160489718, .1028091004723000198182652, .1021592924633203069380762, .1015175685681027854865852, .1008837802472445895049806, .1002577825460485147279854, .09963943398795665776104485, .09902859647173190962510087, .09842513517223564521296569, .09782891844465686959119527, .09723981773205465097029204, .09665770747608198672456013, .09608246503076461364872451, .09551397057921561379174917, .09495210705316911518666266, .09439676005522442883814663, .09384781778369499237091277, .09330517095996170483952101, .09276871275823452392594484, .09223833873763036123879576, .09171394677647927541850185, .09119543700877473684364846, .09068271176268733191388065, .09017567550106469857171747, .08967423476384374680079322, .08917829811230432667975505, .08868777607509647008527077, .08820258109597615778665339, .08772262748318725850402136, .0872478313604298571655505, .08677811061935764238292468, .08631338487354936400705558, .0858535754139016061424034, .08539860516539225449532534, .08494839864516607442904103, .08450288192189570024131742, .08406198257637363654606902, .08362562966329130783291586, .08319375367416516011749277, .0827662865013691388259681, .08234316140323582329192271, .08192431297018950814835363, .08150967709187601159489754, .08109919092525534990138904, .08069279286362471847049943, .0802904225065404650858022, .07989202063060893323638823, .07949752916111719512006792, .07910689114447578744239717, .0787200507214466106865758, .07833695310113015625477634, .07795754453568718779269906, .07758177229577092502292493, .07720958464664666235002043, .07684093082497660209183881, .07647576101624849508185813, .07611402633282746114038384, .07575567879261111001491475, .07540067129826880125610838, .07504895761704657047089306, .07470049236111991075842844, .07435523096847723310605399, .07401312968431743926073765, .07367414554294562620094298, .07333823635015150386570458, .0730053606660556482535154, .07267547778840923133747565, .07234854773633336836416045, .07202453123448470287828978, .07170338969763431106948403, .07138508521564745055865869, .07106958053885214609220417, .07075683906378472602241689, .07044682481930169454732137, .07013950245304622696078506, .06983483721825943539080115, .06953279496092599670031216, .06923334210724437899739519, .06893644565141218490800048, .06864207314371744366250278, .06835019267892698635104373, .06806077288496332988399061, .06777378291186177570382577, .06748919242099969956446575, .06720697157459026913544459, .06692709102543307719554012, .06664952190691442013000059, .06637423582325018469784634 }; private static final double[] cof = { 76.18009172947146, -86.50532032941677, 24.01409824083091, -1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5 }; private static final double EPSILON = 1.0e-14, LARGE_A = 10000.0; private static final int ITMAX = 1000; private static final double a0 = 2.50662823884; private static final double a1 = -18.61500062529; private static final double b1 = -8.47351093090; /**//from w w w . j a va 2s .c o m * compute complementary gamma cdf by its continued fraction expansion */ @SuppressWarnings({ "WeakerAccess" }) public static double gammaCdf(double a, double x) { double gln /*, p*/; if ((x <= 0.0) || (a <= 0.0)) { return Double.NaN; } else if (a > LARGE_A) { return gnorm(a, x); } else { gln = lngamma(a); if (x < (a + 1.0)) { return gser(a, x, gln); } else { return (1.0 - gcf(a, x, gln)); } } } /** * Compute gamma cdf by a normal approximation */ private static double gnorm(double a, double x) { double /*p, */sx; if ((x <= 0.0) || (a <= 0.0)) { return 0.0; } else { sx = Math.sqrt(a) * 3.0 * (Math.pow(x / a, 1.0 / 3.0) + 1.0 / (a * 9.0) - 1.0); return normalCdf(sx); } } /** * This is a more literal (that is, exact) copy of the log gamma method from * Numerical Recipes than the following one. It was created by cutting and * pasting from the PDF version of the book and then converting C syntax to * Java. </p> The static double array above goes with this. </p> Converted * to Java by Frank Wimberly * * @param xx * @return the value ln[?(xx)] for xx > 0 */ public static double lngamma(double xx) { //Returns the value ln[?(xx)] for xx > 0. if (xx <= 0) return Double.NaN; //Internal arithmetic will be done in double precision, a nicety that you can omit if ?ve-?gure //accuracy is good enough. double x, y, tmp, ser; int j; y = x = xx; tmp = x + 5.5; tmp -= (x + 0.5) * Math.log(tmp); ser = 1.000000000190015; for (j = 0; j <= 5; j++) { ser += cof[j] / ++y; } return -tmp + Math.log(2.5066282746310005 * ser / x); } private static double gser(double a, double x, double gln) { double p, sum, del, ap; int n; boolean done = false; if ((x <= 0.0) || (a <= 0.0)) { p = 0.0; } else { ap = a; del = 1.0 / a; sum = del; for (n = 1; (!done) && (n < ITMAX); n++) { ap += 1.0; del *= x / ap; sum += del; if (Math.abs(del) < EPSILON) { done = true; } } p = sum * Math.exp(-x + a * Math.log(x) - gln); } return p; } /** * compute gamma cdf by its series representation */ private static double gcf(double a, double x, double gln) { double gold = 0.0, g, fac = 1.0, b1 = 1.0; double b0 = 0.0, anf, ana, an, a1, a0 = 1.0; double p; boolean done = false; a1 = x; p = 0.0; for (an = 1.0; (!done) && (an <= ITMAX); an += 1.0) { ana = an - a; a0 = (a1 + a0 * ana) * fac; b0 = (b1 + b0 * ana) * fac; anf = an * fac; a1 = x * a0 + anf * a1; b1 = x * b0 + anf * b1; if (a1 != 0.0) { fac = 1.0 / a1; g = b1 * fac; if (Math.abs((g - gold) / g) < EPSILON) { p = Math.exp(-x + a * Math.log(x) - gln) * g; done = true; } gold = g; } } return p; } /** * Normal cumulative distribution function (the value which results by * integrating the normal distribution function from negative infinity up to * y). * * @param y the upper limit of integration. * @return the area accumulated in the integration. */ @SuppressWarnings({ "SuspiciousNameCombination" }) public static double normalCdf(double y) { double f, h; int j; double dcphi, x, z, f1, f2, f3, f4, f5; x = y; if (Math.abs(x) > 15.) { dcphi = 0.; } else { j = (int) Math.floor(Math.abs(x) * 16. + .5); z = j * .0625; h = Math.abs(x) - z; f = r[j]; f1 = f * z - 1; f2 = f + z * f1; f3 = f1 * 2. + z * f2; f4 = f2 * 3 + z * f3; f5 = f3 * 4 + z * f4; dcphi = f + h * (f1 * 120. + h * (f2 * 60. + h * (f3 * 20. + h * (f4 * 5. + h * f5)))) / 120.; dcphi = dcphi * .3989422804014326779 * Math.exp(x * -.5 * x); } if (x < 0.) { return dcphi; } else { return (1.0 - dcphi); } } }