Java tutorial
package weka.core; /** * Class implementing some distributions, tests, etc. The code is mostly adapted * from the CERN Jet Java libraries: * * Copyright 2001 University of Waikato Copyright 1999 CERN - European * Organization for Nuclear Research. Permission to use, copy, modify, * distribute and sell this software and its documentation for any purpose is * hereby granted without fee, provided that the above copyright notice appear * in all copies and that both that copyright notice and this permission notice * appear in supporting documentation. CERN and the University of Waikato make * no representations about the suitability of this software for any purpose. It * is provided "as is" without expressed or implied warranty. * * @author peter.gedeck@pharma.Novartis.com * @author wolfgang.hoschek@cern.ch * @author Eibe Frank (eibe@cs.waikato.ac.nz) * @author Richard Kirkby (rkirkby@cs.waikato.ac.nz) * @version $Revision$ */ public class Statistics implements RevisionHandler { /** Some constants */ protected static final double MACHEP = 1.11022302462515654042E-16; protected static final double MAXLOG = 7.09782712893383996732E2; protected static final double MINLOG = -7.451332191019412076235E2; protected static final double MAXGAM = 171.624376956302725; protected static final double SQTPI = 2.50662827463100050242E0; protected static final double SQRTH = 7.07106781186547524401E-1; protected static final double LOGPI = 1.14472988584940017414; protected static final double big = 4.503599627370496e15; protected static final double biginv = 2.22044604925031308085e-16; /************************************************* * COEFFICIENTS FOR METHOD normalInverse() * *************************************************/ /* approximation for 0 <= |y - 0.5| <= 3/8 */ protected static final double P0[] = { -5.99633501014107895267E1, 9.80010754185999661536E1, -5.66762857469070293439E1, 1.39312609387279679503E1, -1.23916583867381258016E0, }; protected static final double Q0[] = { /* 1.00000000000000000000E0, */ 1.95448858338141759834E0, 4.67627912898881538453E0, 8.63602421390890590575E1, -2.25462687854119370527E2, 2.00260212380060660359E2, -8.20372256168333339912E1, 1.59056225126211695515E1, -1.18331621121330003142E0, }; /* * Approximation for interval z = sqrt(-2 log y ) between 2 and 8 i.e., y * between exp(-2) = .135 and exp(-32) = 1.27e-14. */ protected static final double P1[] = { 4.05544892305962419923E0, 3.15251094599893866154E1, 5.71628192246421288162E1, 4.40805073893200834700E1, 1.46849561928858024014E1, 2.18663306850790267539E0, -1.40256079171354495875E-1, -3.50424626827848203418E-2, -8.57456785154685413611E-4, }; protected static final double Q1[] = { /* 1.00000000000000000000E0, */ 1.57799883256466749731E1, 4.53907635128879210584E1, 4.13172038254672030440E1, 1.50425385692907503408E1, 2.50464946208309415979E0, -1.42182922854787788574E-1, -3.80806407691578277194E-2, -9.33259480895457427372E-4, }; /* * Approximation for interval z = sqrt(-2 log y ) between 8 and 64 i.e., y * between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890. */ protected static final double P2[] = { 3.23774891776946035970E0, 6.91522889068984211695E0, 3.93881025292474443415E0, 1.33303460815807542389E0, 2.01485389549179081538E-1, 1.23716634817820021358E-2, 3.01581553508235416007E-4, 2.65806974686737550832E-6, 6.23974539184983293730E-9, }; protected static final double Q2[] = { /* 1.00000000000000000000E0, */ 6.02427039364742014255E0, 3.67983563856160859403E0, 1.37702099489081330271E0, 2.16236993594496635890E-1, 1.34204006088543189037E-2, 3.28014464682127739104E-4, 2.89247864745380683936E-6, 6.79019408009981274425E-9, }; /** * Computes standard error for observed values of a binomial random variable. * * @param p the probability of success * @param n the size of the sample * @return the standard error */ public static double binomialStandardError(double p, int n) { if (n == 0) { return 0; } return Math.sqrt((p * (1 - p)) / n); } /** * Returns chi-squared probability for given value and degrees of freedom. * (The probability that the chi-squared variate will be greater than x for * the given degrees of freedom.) * * @param x the value * @param v the number of degrees of freedom * @return the chi-squared probability */ public static double chiSquaredProbability(double x, double v) { if (x < 0.0 || v < 1.0) { return 0.0; } return incompleteGammaComplement(v / 2.0, x / 2.0); } /** * Computes probability of F-ratio. * * @param F the F-ratio * @param df1 the first number of degrees of freedom * @param df2 the second number of degrees of freedom * @return the probability of the F-ratio. */ public static double FProbability(double F, int df1, int df2) { return incompleteBeta(df2 / 2.0, df1 / 2.0, df2 / (df2 + df1 * F)); } /** * Returns the area under the Normal (Gaussian) probability density function, * integrated from minus infinity to <tt>x</tt> (assumes mean is zero, * variance is one). * * <pre> * x * - * 1 | | 2 * normal(x) = --------- | exp( - t /2 ) dt * sqrt(2pi) | | * - * -inf. * * = ( 1 + erf(z) ) / 2 * = erfc(z) / 2 * </pre> * * where <tt>z = x/sqrt(2)</tt>. Computation is via the functions * <tt>errorFunction</tt> and <tt>errorFunctionComplement</tt>. * * @param a the z-value * @return the probability of the z value according to the normal pdf */ public static double normalProbability(double a) { double x, y, z; x = a * SQRTH; z = Math.abs(x); if (z < SQRTH) { y = 0.5 + 0.5 * errorFunction(x); } else { y = 0.5 * errorFunctionComplemented(z); if (x > 0) { y = 1.0 - y; } } return y; } /** * Returns the value, <tt>x</tt>, for which the area under the Normal * (Gaussian) probability density function (integrated from minus infinity to * <tt>x</tt>) is equal to the argument <tt>y</tt> (assumes mean is zero, * variance is one). * <p> * For small arguments <tt>0 < y < exp(-2)</tt>, the program computes * <tt>z = sqrt( -2.0 * log(y) )</tt>; then the approximation is * <tt>x = z - log(z)/z - (1/z) P(1/z) / Q(1/z)</tt>. There are two rational * functions P/Q, one for <tt>0 < y < exp(-32)</tt> and the other for * <tt>y</tt> up to <tt>exp(-2)</tt>. For larger arguments, * <tt>w = y - 0.5</tt>, and <tt>x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2))</tt>. * * @param y0 the area under the normal pdf * @return the z-value */ public static double normalInverse(double y0) { double x, y, z, y2, x0, x1; int code; final double s2pi = Math.sqrt(2.0 * Math.PI); if (y0 <= 0.0) { throw new IllegalArgumentException(); } if (y0 >= 1.0) { throw new IllegalArgumentException(); } code = 1; y = y0; if (y > (1.0 - 0.13533528323661269189)) { /* 0.135... = exp(-2) */ y = 1.0 - y; code = 0; } if (y > 0.13533528323661269189) { y = y - 0.5; y2 = y * y; x = y + y * (y2 * polevl(y2, P0, 4) / p1evl(y2, Q0, 8)); x = x * s2pi; return (x); } x = Math.sqrt(-2.0 * Math.log(y)); x0 = x - Math.log(x) / x; z = 1.0 / x; if (x < 8.0) { x1 = z * polevl(z, P1, 8) / p1evl(z, Q1, 8); } else { x1 = z * polevl(z, P2, 8) / p1evl(z, Q2, 8); } x = x0 - x1; if (code != 0) { x = -x; } return (x); } /** * Returns natural logarithm of gamma function. * * @param x the value * @return natural logarithm of gamma function */ public static double lnGamma(double x) { double p, q, w, z; double A[] = { 8.11614167470508450300E-4, -5.95061904284301438324E-4, 7.93650340457716943945E-4, -2.77777777730099687205E-3, 8.33333333333331927722E-2 }; double B[] = { -1.37825152569120859100E3, -3.88016315134637840924E4, -3.31612992738871184744E5, -1.16237097492762307383E6, -1.72173700820839662146E6, -8.53555664245765465627E5 }; double C[] = { /* 1.00000000000000000000E0, */ -3.51815701436523470549E2, -1.70642106651881159223E4, -2.20528590553854454839E5, -1.13933444367982507207E6, -2.53252307177582951285E6, -2.01889141433532773231E6 }; if (x < -34.0) { q = -x; w = lnGamma(q); p = Math.floor(q); if (p == q) { throw new ArithmeticException("lnGamma: Overflow"); } z = q - p; if (z > 0.5) { p += 1.0; z = p - q; } z = q * Math.sin(Math.PI * z); if (z == 0.0) { throw new ArithmeticException("lnGamma: Overflow"); } z = LOGPI - Math.log(z) - w; return z; } if (x < 13.0) { z = 1.0; while (x >= 3.0) { x -= 1.0; z *= x; } while (x < 2.0) { if (x == 0.0) { throw new ArithmeticException("lnGamma: Overflow"); } z /= x; x += 1.0; } if (z < 0.0) { z = -z; } if (x == 2.0) { return Math.log(z); } x -= 2.0; p = x * polevl(x, B, 5) / p1evl(x, C, 6); return (Math.log(z) + p); } if (x > 2.556348e305) { throw new ArithmeticException("lnGamma: Overflow"); } q = (x - 0.5) * Math.log(x) - x + 0.91893853320467274178; if (x > 1.0e8) { return (q); } p = 1.0 / (x * x); if (x >= 1000.0) { q += ((7.9365079365079365079365e-4 * p - 2.7777777777777777777778e-3) * p + 0.0833333333333333333333) / x; } else { q += polevl(p, A, 4) / x; } return q; } /** * Returns the error function of the normal distribution. The integral is * * <pre> * x * - * 2 | | 2 * erf(x) = -------- | exp( - t ) dt. * sqrt(pi) | | * - * 0 * </pre> * * <b>Implementation:</b> For * <tt>0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2)</tt>; otherwise * <tt>erf(x) = 1 - erfc(x)</tt>. * <p> * Code adapted from the <A * HREF="http://www.sci.usq.edu.au/staff/leighb/graph/Top.html"> Java 2D Graph * Package 2.4</A>, which in turn is a port from the <A * HREF="http://people.ne.mediaone.net/moshier/index.html#Cephes">Cephes * 2.2</A> Math Library (C). * * @param a the argument to the function. */ public static double errorFunction(double x) { double y, z; final double T[] = { 9.60497373987051638749E0, 9.00260197203842689217E1, 2.23200534594684319226E3, 7.00332514112805075473E3, 5.55923013010394962768E4 }; final double U[] = { // 1.00000000000000000000E0, 3.35617141647503099647E1, 5.21357949780152679795E2, 4.59432382970980127987E3, 2.26290000613890934246E4, 4.92673942608635921086E4 }; if (Math.abs(x) > 1.0) { return (1.0 - errorFunctionComplemented(x)); } z = x * x; y = x * polevl(z, T, 4) / p1evl(z, U, 5); return y; } /** * Returns the complementary Error function of the normal distribution. * * <pre> * 1 - erf(x) = * * inf. * - * 2 | | 2 * erfc(x) = -------- | exp( - t ) dt * sqrt(pi) | | * - * x * </pre> * * <b>Implementation:</b> For small x, <tt>erfc(x) = 1 - erf(x)</tt>; * otherwise rational approximations are computed. * <p> * Code adapted from the <A * HREF="http://www.sci.usq.edu.au/staff/leighb/graph/Top.html"> Java 2D Graph * Package 2.4</A>, which in turn is a port from the <A * HREF="http://people.ne.mediaone.net/moshier/index.html#Cephes">Cephes * 2.2</A> Math Library (C). * * @param a the argument to the function. */ public static double errorFunctionComplemented(double a) { double x, y, z, p, q; double P[] = { 2.46196981473530512524E-10, 5.64189564831068821977E-1, 7.46321056442269912687E0, 4.86371970985681366614E1, 1.96520832956077098242E2, 5.26445194995477358631E2, 9.34528527171957607540E2, 1.02755188689515710272E3, 5.57535335369399327526E2 }; double Q[] = { // 1.0 1.32281951154744992508E1, 8.67072140885989742329E1, 3.54937778887819891062E2, 9.75708501743205489753E2, 1.82390916687909736289E3, 2.24633760818710981792E3, 1.65666309194161350182E3, 5.57535340817727675546E2 }; double R[] = { 5.64189583547755073984E-1, 1.27536670759978104416E0, 5.01905042251180477414E0, 6.16021097993053585195E0, 7.40974269950448939160E0, 2.97886665372100240670E0 }; double S[] = { // 1.00000000000000000000E0, 2.26052863220117276590E0, 9.39603524938001434673E0, 1.20489539808096656605E1, 1.70814450747565897222E1, 9.60896809063285878198E0, 3.36907645100081516050E0 }; if (a < 0.0) { x = -a; } else { x = a; } if (x < 1.0) { return 1.0 - errorFunction(a); } z = -a * a; if (z < -MAXLOG) { if (a < 0) { return (2.0); } else { return (0.0); } } z = Math.exp(z); if (x < 8.0) { p = polevl(x, P, 8); q = p1evl(x, Q, 8); } else { p = polevl(x, R, 5); q = p1evl(x, S, 6); } y = (z * p) / q; if (a < 0) { y = 2.0 - y; } if (y == 0.0) { if (a < 0) { return 2.0; } else { return (0.0); } } return y; } /** * Evaluates the given polynomial of degree <tt>N</tt> at <tt>x</tt>. * Evaluates polynomial when coefficient of N is 1.0. Otherwise same as * <tt>polevl()</tt>. * * <pre> * 2 N * y = C + C x + C x +...+ C x * 0 1 2 N * * Coefficients are stored in reverse order: * * coef[0] = C , ..., coef[N] = C . * N 0 * </pre> * * The function <tt>p1evl()</tt> assumes that <tt>coef[N] = 1.0</tt> and is * omitted from the array. Its calling arguments are otherwise the same as * <tt>polevl()</tt>. * <p> * In the interest of speed, there are no checks for out of bounds arithmetic. * * @param x argument to the polynomial. * @param coef the coefficients of the polynomial. * @param N the degree of the polynomial. */ public static double p1evl(double x, double coef[], int N) { double ans; ans = x + coef[0]; for (int i = 1; i < N; i++) { ans = ans * x + coef[i]; } return ans; } /** * Evaluates the given polynomial of degree <tt>N</tt> at <tt>x</tt>. * * <pre> * 2 N * y = C + C x + C x +...+ C x * 0 1 2 N * * Coefficients are stored in reverse order: * * coef[0] = C , ..., coef[N] = C . * N 0 * </pre> * * In the interest of speed, there are no checks for out of bounds arithmetic. * * @param x argument to the polynomial. * @param coef the coefficients of the polynomial. * @param N the degree of the polynomial. */ public static double polevl(double x, double coef[], int N) { double ans; ans = coef[0]; for (int i = 1; i <= N; i++) { ans = ans * x + coef[i]; } return ans; } /** * Returns the Incomplete Gamma function. * * @param a the parameter of the gamma distribution. * @param x the integration end point. */ public static double incompleteGamma(double a, double x) { double ans, ax, c, r; if (x <= 0 || a <= 0) { return 0.0; } if (x > 1.0 && x > a) { return 1.0 - incompleteGammaComplement(a, x); } /* Compute x**a * exp(-x) / gamma(a) */ ax = a * Math.log(x) - x - lnGamma(a); if (ax < -MAXLOG) { return (0.0); } ax = Math.exp(ax); /* power series */ r = a; c = 1.0; ans = 1.0; do { r += 1.0; c *= x / r; ans += c; } while (c / ans > MACHEP); return (ans * ax / a); } /** * Returns the Complemented Incomplete Gamma function. * * @param a the parameter of the gamma distribution. * @param x the integration start point. */ public static double incompleteGammaComplement(double a, double x) { double ans, ax, c, yc, r, t, y, z; double pk, pkm1, pkm2, qk, qkm1, qkm2; if (x <= 0 || a <= 0) { return 1.0; } if (x < 1.0 || x < a) { return 1.0 - incompleteGamma(a, x); } ax = a * Math.log(x) - x - lnGamma(a); if (ax < -MAXLOG) { return 0.0; } ax = Math.exp(ax); /* continued fraction */ y = 1.0 - a; z = x + y + 1.0; c = 0.0; pkm2 = 1.0; qkm2 = x; pkm1 = x + 1.0; qkm1 = z * x; ans = pkm1 / qkm1; do { c += 1.0; y += 1.0; z += 2.0; yc = y * c; pk = pkm1 * z - pkm2 * yc; qk = qkm1 * z - qkm2 * yc; if (qk != 0) { r = pk / qk; t = Math.abs((ans - r) / r); ans = r; } else { t = 1.0; } pkm2 = pkm1; pkm1 = pk; qkm2 = qkm1; qkm1 = qk; if (Math.abs(pk) > big) { pkm2 *= biginv; pkm1 *= biginv; qkm2 *= biginv; qkm1 *= biginv; } } while (t > MACHEP); return ans * ax; } /** * Returns the Gamma function of the argument. */ public static double gamma(double x) { double P[] = { 1.60119522476751861407E-4, 1.19135147006586384913E-3, 1.04213797561761569935E-2, 4.76367800457137231464E-2, 2.07448227648435975150E-1, 4.94214826801497100753E-1, 9.99999999999999996796E-1 }; double Q[] = { -2.31581873324120129819E-5, 5.39605580493303397842E-4, -4.45641913851797240494E-3, 1.18139785222060435552E-2, 3.58236398605498653373E-2, -2.34591795718243348568E-1, 7.14304917030273074085E-2, 1.00000000000000000320E0 }; double p, z; double q = Math.abs(x); if (q > 33.0) { if (x < 0.0) { p = Math.floor(q); if (p == q) { throw new ArithmeticException("gamma: overflow"); } z = q - p; if (z > 0.5) { p += 1.0; z = q - p; } z = q * Math.sin(Math.PI * z); if (z == 0.0) { throw new ArithmeticException("gamma: overflow"); } z = Math.abs(z); z = Math.PI / (z * stirlingFormula(q)); return -z; } else { return stirlingFormula(x); } } z = 1.0; while (x >= 3.0) { x -= 1.0; z *= x; } while (x < 0.0) { if (x == 0.0) { throw new ArithmeticException("gamma: singular"); } else if (x > -1.E-9) { return (z / ((1.0 + 0.5772156649015329 * x) * x)); } z /= x; x += 1.0; } while (x < 2.0) { if (x == 0.0) { throw new ArithmeticException("gamma: singular"); } else if (x < 1.e-9) { return (z / ((1.0 + 0.5772156649015329 * x) * x)); } z /= x; x += 1.0; } if ((x == 2.0) || (x == 3.0)) { return z; } x -= 2.0; p = polevl(x, P, 6); q = polevl(x, Q, 7); return z * p / q; } /** * Returns the Gamma function computed by Stirling's formula. The polynomial * STIR is valid for 33 <= x <= 172. */ public static double stirlingFormula(double x) { double STIR[] = { 7.87311395793093628397E-4, -2.29549961613378126380E-4, -2.68132617805781232825E-3, 3.47222221605458667310E-3, 8.33333333333482257126E-2, }; double MAXSTIR = 143.01608; double w = 1.0 / x; double y = Math.exp(x); w = 1.0 + w * polevl(w, STIR, 4); if (x > MAXSTIR) { /* Avoid overflow in Math.pow() */ double v = Math.pow(x, 0.5 * x - 0.25); y = v * (v / y); } else { y = Math.pow(x, x - 0.5) / y; } y = SQTPI * y * w; return y; } /** * Returns the Incomplete Beta Function evaluated from zero to <tt>xx</tt>. * * @param aa the alpha parameter of the beta distribution. * @param bb the beta parameter of the beta distribution. * @param xx the integration end point. */ public static double incompleteBeta(double aa, double bb, double xx) { double a, b, t, x, xc, w, y; boolean flag; if (aa <= 0.0 || bb <= 0.0) { throw new ArithmeticException("ibeta: Domain error!"); } if ((xx <= 0.0) || (xx >= 1.0)) { if (xx == 0.0) { return 0.0; } if (xx == 1.0) { return 1.0; } throw new ArithmeticException("ibeta: Domain error!"); } flag = false; if ((bb * xx) <= 1.0 && xx <= 0.95) { t = powerSeries(aa, bb, xx); return t; } w = 1.0 - xx; /* Reverse a and b if x is greater than the mean. */ if (xx > (aa / (aa + bb))) { flag = true; a = bb; b = aa; xc = xx; x = w; } else { a = aa; b = bb; xc = w; x = xx; } if (flag && (b * x) <= 1.0 && x <= 0.95) { t = powerSeries(a, b, x); if (t <= MACHEP) { t = 1.0 - MACHEP; } else { t = 1.0 - t; } return t; } /* Choose expansion for better convergence. */ y = x * (a + b - 2.0) - (a - 1.0); if (y < 0.0) { w = incompleteBetaFraction1(a, b, x); } else { w = incompleteBetaFraction2(a, b, x) / xc; } /* * Multiply w by the factor a b _ _ _ x (1-x) | (a+b) / ( a | (a) | (b) ) . */ y = a * Math.log(x); t = b * Math.log(xc); if ((a + b) < MAXGAM && Math.abs(y) < MAXLOG && Math.abs(t) < MAXLOG) { t = Math.pow(xc, b); t *= Math.pow(x, a); t /= a; t *= w; t *= gamma(a + b) / (gamma(a) * gamma(b)); if (flag) { if (t <= MACHEP) { t = 1.0 - MACHEP; } else { t = 1.0 - t; } } return t; } /* Resort to logarithms. */ y += t + lnGamma(a + b) - lnGamma(a) - lnGamma(b); y += Math.log(w / a); if (y < MINLOG) { t = 0.0; } else { t = Math.exp(y); } if (flag) { if (t <= MACHEP) { t = 1.0 - MACHEP; } else { t = 1.0 - t; } } return t; } /** * Continued fraction expansion #1 for incomplete beta integral. */ public static double incompleteBetaFraction1(double a, double b, double x) { double xk, pk, pkm1, pkm2, qk, qkm1, qkm2; double k1, k2, k3, k4, k5, k6, k7, k8; double r, t, ans, thresh; int n; k1 = a; k2 = a + b; k3 = a; k4 = a + 1.0; k5 = 1.0; k6 = b - 1.0; k7 = k4; k8 = a + 2.0; pkm2 = 0.0; qkm2 = 1.0; pkm1 = 1.0; qkm1 = 1.0; ans = 1.0; r = 1.0; n = 0; thresh = 3.0 * MACHEP; do { xk = -(x * k1 * k2) / (k3 * k4); pk = pkm1 + pkm2 * xk; qk = qkm1 + qkm2 * xk; pkm2 = pkm1; pkm1 = pk; qkm2 = qkm1; qkm1 = qk; xk = (x * k5 * k6) / (k7 * k8); pk = pkm1 + pkm2 * xk; qk = qkm1 + qkm2 * xk; pkm2 = pkm1; pkm1 = pk; qkm2 = qkm1; qkm1 = qk; if (qk != 0) { r = pk / qk; } if (r != 0) { t = Math.abs((ans - r) / r); ans = r; } else { t = 1.0; } if (t < thresh) { return ans; } k1 += 1.0; k2 += 1.0; k3 += 2.0; k4 += 2.0; k5 += 1.0; k6 -= 1.0; k7 += 2.0; k8 += 2.0; if ((Math.abs(qk) + Math.abs(pk)) > big) { pkm2 *= biginv; pkm1 *= biginv; qkm2 *= biginv; qkm1 *= biginv; } if ((Math.abs(qk) < biginv) || (Math.abs(pk) < biginv)) { pkm2 *= big; pkm1 *= big; qkm2 *= big; qkm1 *= big; } } while (++n < 300); return ans; } /** * Continued fraction expansion #2 for incomplete beta integral. */ public static double incompleteBetaFraction2(double a, double b, double x) { double xk, pk, pkm1, pkm2, qk, qkm1, qkm2; double k1, k2, k3, k4, k5, k6, k7, k8; double r, t, ans, z, thresh; int n; k1 = a; k2 = b - 1.0; k3 = a; k4 = a + 1.0; k5 = 1.0; k6 = a + b; k7 = a + 1.0; ; k8 = a + 2.0; pkm2 = 0.0; qkm2 = 1.0; pkm1 = 1.0; qkm1 = 1.0; z = x / (1.0 - x); ans = 1.0; r = 1.0; n = 0; thresh = 3.0 * MACHEP; do { xk = -(z * k1 * k2) / (k3 * k4); pk = pkm1 + pkm2 * xk; qk = qkm1 + qkm2 * xk; pkm2 = pkm1; pkm1 = pk; qkm2 = qkm1; qkm1 = qk; xk = (z * k5 * k6) / (k7 * k8); pk = pkm1 + pkm2 * xk; qk = qkm1 + qkm2 * xk; pkm2 = pkm1; pkm1 = pk; qkm2 = qkm1; qkm1 = qk; if (qk != 0) { r = pk / qk; } if (r != 0) { t = Math.abs((ans - r) / r); ans = r; } else { t = 1.0; } if (t < thresh) { return ans; } k1 += 1.0; k2 -= 1.0; k3 += 2.0; k4 += 2.0; k5 += 1.0; k6 += 1.0; k7 += 2.0; k8 += 2.0; if ((Math.abs(qk) + Math.abs(pk)) > big) { pkm2 *= biginv; pkm1 *= biginv; qkm2 *= biginv; qkm1 *= biginv; } if ((Math.abs(qk) < biginv) || (Math.abs(pk) < biginv)) { pkm2 *= big; pkm1 *= big; qkm2 *= big; qkm1 *= big; } } while (++n < 300); return ans; } /** * Power series for incomplete beta integral. Use when b*x is small and x not * too close to 1. */ public static double powerSeries(double a, double b, double x) { double s, t, u, v, n, t1, z, ai; ai = 1.0 / a; u = (1.0 - b) * x; v = u / (a + 1.0); t1 = v; t = u; n = 2.0; s = 0.0; z = MACHEP * ai; while (Math.abs(v) > z) { u = (n - b) * x / n; t *= u; v = t / (a + n); s += v; n += 1.0; } s += t1; s += ai; u = a * Math.log(x); if ((a + b) < MAXGAM && Math.abs(u) < MAXLOG) { t = gamma(a + b) / (gamma(a) * gamma(b)); s = s * t * Math.pow(x, a); } else { t = lnGamma(a + b) - lnGamma(a) - lnGamma(b) + u + Math.log(s); if (t < MINLOG) { s = 0.0; } else { s = Math.exp(t); } } return s; } /** * Returns the revision string. * * @return the revision */ @Override public String getRevision() { return RevisionUtils.extract("$Revision$"); } /** * Main method for testing this class. */ public static void main(String[] ops) { System.out.println("Binomial standard error (0.5, 100): " + Statistics.binomialStandardError(0.5, 100)); System.out.println("Chi-squared probability (2.558, 10): " + Statistics.chiSquaredProbability(2.558, 10)); System.out.println("Normal probability (0.2): " + Statistics.normalProbability(0.2)); System.out.println("F probability (5.1922, 4, 5): " + Statistics.FProbability(5.1922, 4, 5)); System.out.println("lnGamma(6): " + Statistics.lnGamma(6)); } }