# include <cmath>
# include <cstdlib>
# include <iostream>
# include <iomanip>

using namespace std;

# include "asa243.hpp"

//****************************************************************************80

double alnorm ( double x, bool upper )

//****************************************************************************80
//
//  Purpose:
//
//    alnorm() computes the cumulative density of the standard normal distribution.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    17 January 2008
//
//  Author:
//
//    Original FORTRAN77 version by David Hill.
//    C++ version by John Burkardt.
//
//  Reference:
//
//    David Hill,
//    Algorithm AS 66:
//    The Normal Integral,
//    Applied Statistics,
//    Volume 22, Number 3, 1973, pages 424-427.
//
//  Parameters:
//
//    Input, double X, is one endpoint of the semi-infinite interval
//    over which the integration takes place.
//
//    Input, bool UPPER, determines whether the upper or lower
//    interval is to be integrated:
//    .TRUE.  => integrate from X to + Infinity;
//    .FALSE. => integrate from - Infinity to X.
//
//    Output, double ALNORM, the integral of the standard normal
//    distribution over the desired interval.
//
{
  double a1 = 5.75885480458;
  double a2 = 2.62433121679;
  double a3 = 5.92885724438;
  double b1 = -29.8213557807;
  double b2 = 48.6959930692;
  double c1 = -0.000000038052;
  double c2 = 0.000398064794;
  double c3 = -0.151679116635;
  double c4 = 4.8385912808;
  double c5 = 0.742380924027;
  double c6 = 3.99019417011;
  double con = 1.28;
  double d1 = 1.00000615302;
  double d2 = 1.98615381364;
  double d3 = 5.29330324926;
  double d4 = -15.1508972451;
  double d5 = 30.789933034;
  double ltone = 7.0;
  double p = 0.398942280444;
  double q = 0.39990348504;
  double r = 0.398942280385;
  bool up;
  double utzero = 18.66;
  double value;
  double y;
  double z;

  up = upper;
  z = x;

  if ( z < 0.0 )
  {
    up = !up;
    z = - z;
  }

  if ( ltone < z && ( ( !up ) || utzero < z ) )
  {
    if ( up )
    {
      value = 0.0;
    }
    else
    {
      value = 1.0;
    }
    return value;
  }

  y = 0.5 * z * z;

  if ( z <= con )
  {
    value = 0.5 - z * ( p - q * y
      / ( y + a1 + b1
      / ( y + a2 + b2
      / ( y + a3 ))));
  }
  else
  {
    value = r * exp ( - y )
      / ( z + c1 + d1
      / ( z + c2 + d2
      / ( z + c3 + d3
      / ( z + c4 + d4
      / ( z + c5 + d5
      / ( z + c6 ))))));
  }

  if ( !up )
  {
    value = 1.0 - value;
  }

  return value;
}
//****************************************************************************80

double betain ( double x, double p, double q, double beta, int *ifault )

//****************************************************************************80
//
//  Purpose:
//
//    betain() computes the incomplete Beta function ratio.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    23 January 2008
//
//  Author:
//
//    Original FORTRAN77 version by KL Majumder, GP Bhattacharjee.
//    C++ version by John Burkardt.
//
//  Reference:
//
//    KL Majumder, GP Bhattacharjee,
//    Algorithm AS 63:
//    The incomplete Beta Integral,
//    Applied Statistics,
//    Volume 22, Number 3, 1973, pages 409-411.
//
//  Parameters:
//
//    Input, double X, the argument, between 0 and 1.
//
//    Input, double P, Q, the parameters, which
//    must be positive.
//
//    Input, double BETA, the logarithm of the complete
//    beta function.
//
//    Output, int *IFAULT, error flag.
//    0, no error.
//    nonzero, an error occurred.
//
//    Output, double BETAIN, the value of the incomplete
//    Beta function ratio.
//
{
  double acu = 0.1E-14;
  double ai;
  double cx;
  bool indx;
  int ns;
  double pp;
  double psq;
  double qq;
  double rx;
  double temp;
  double term;
  double value;
  double xx;

  value = x;
  *ifault = 0;
//
//  Check the input arguments.
//
  if ( p <= 0.0 || q <= 0.0 )
  {
    *ifault = 1;
    return value;
  }

  if ( x < 0.0 || 1.0 < x )
  {
    *ifault = 2;
    return value;
  }
//
//  Special cases.
//
  if ( x == 0.0 || x == 1.0 )
  {
    return value;
  }
//
//  Change tail if necessary and determine S.
//
  psq = p + q;
  cx = 1.0 - x;

  if ( p < psq * x )
  {
    xx = cx;
    cx = x;
    pp = q;
    qq = p;
    indx = true;
  }
  else
  {
    xx = x;
    pp = p;
    qq = q;
    indx = false;
  }

  term = 1.0;
  ai = 1.0;
  value = 1.0;
  ns = ( int ) ( qq + cx * psq );
//
//  Use the Soper reduction formula.
//
  rx = xx / cx;
  temp = qq - ai;
  if ( ns == 0 )
  {
    rx = xx;
  }

  for ( ; ; )
  {
    term = term * temp * rx / ( pp + ai );
    value = value + term;;
    temp = fabs ( term );

    if ( temp <= acu && temp <= acu * value )
    {
      value = value * exp ( pp * log ( xx )
      + ( qq - 1.0 ) * log ( cx ) - beta ) / pp;

      if ( indx )
      {
        value = 1.0 - value;
      }
      break;
    }

    ai = ai + 1.0;
    ns = ns - 1;

    if ( 0 <= ns )
    {
      temp = qq - ai;
      if ( ns == 0 )
      {
        rx = xx;
      }
    }
    else
    {
      temp = psq;
      psq = psq + 1.0;
    }
  }

  return value;
}
//****************************************************************************80

void student_noncentral_cdf_values ( int *n_data, int *df, double *lambda,
  double *x, double *fx )

//****************************************************************************80
//
//  Purpose:
//
//    student_noncentral_cdf_values() returns values of the noncentral Student CDF.
//
//  Discussion:
//
//    In Mathematica, the function can be evaluated by:
//
//      Needs["Statistics`ContinuousDistributions`"]
//      dist = NoncentralStudentTDistribution [ df, lambda ]
//      CDF [ dist, x ]
//
//    Mathematica seems to have some difficulty computing this function
//    to the desired number of digits.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    01 September 2004
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Milton Abramowitz, Irene Stegun,
//    Handbook of Mathematical Functions,
//    National Bureau of Standards, 1964,
//    ISBN: 0-486-61272-4,
//    LC: QA47.A34.
//
//    Stephen Wolfram,
//    The Mathematica Book,
//    Fourth Edition,
//    Cambridge University Press, 1999,
//    ISBN: 0-521-64314-7,
//    LC: QA76.95.W65.
//
//  Parameters:
//
//    Input/output, int *N_DATA.  The user sets N_DATA to 0 before the
//    first call.  On each call, the routine increments N_DATA by 1, and
//    returns the corresponding data; when there is no more data, the
//    output value of N_DATA will be 0 again.
//
//    Output, int *DF, double *LAMBDA, the parameters of the
//    function.
//
//    Output, double *X, the argument of the function.
//
//    Output, double *FX, the value of the function.
//
{
# define N_MAX 30

  int df_vec[N_MAX] = {
     1,  2,  3,
     1,  2,  3,
     1,  2,  3,
     1,  2,  3,
     1,  2,  3,
    15, 20, 25,
     1,  2,  3,
    10, 10, 10,
    10, 10, 10,
    10, 10, 10 };

  double fx_vec[N_MAX] = {
     0.8975836176504333E+00,
     0.9522670169E+00,
     0.9711655571887813E+00,
     0.8231218864E+00,
     0.9049021510E+00,
     0.9363471834E+00,
     0.7301025986E+00,
     0.8335594263E+00,
     0.8774010255E+00,
     0.5248571617E+00,
     0.6293856597E+00,
     0.6800271741E+00,
     0.20590131975E+00,
     0.2112148916E+00,
     0.2074730718E+00,
     0.9981130072E+00,
     0.9994873850E+00,
     0.9998391562E+00,
     0.168610566972E+00,
     0.16967950985E+00,
     0.1701041003E+00,
     0.9247683363E+00,
     0.7483139269E+00,
     0.4659802096E+00,
     0.9761872541E+00,
     0.8979689357E+00,
     0.7181904627E+00,
     0.9923658945E+00,
     0.9610341649E+00,
     0.8688007350E+00 };

  double lambda_vec[N_MAX] = {
     0.0E+00,
     0.0E+00,
     0.0E+00,
     0.5E+00,
     0.5E+00,
     0.5E+00,
     1.0E+00,
     1.0E+00,
     1.0E+00,
     2.0E+00,
     2.0E+00,
     2.0E+00,
     4.0E+00,
     4.0E+00,
     4.0E+00,
     7.0E+00,
     7.0E+00,
     7.0E+00,
     1.0E+00,
     1.0E+00,
     1.0E+00,
     2.0E+00,
     3.0E+00,
     4.0E+00,
     2.0E+00,
     3.0E+00,
     4.0E+00,
     2.0E+00,
     3.0E+00,
     4.0E+00 };

  double x_vec[N_MAX] = {
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
      3.00E+00,
     15.00E+00,
     15.00E+00,
     15.00E+00,
      0.05E+00,
      0.05E+00,
      0.05E+00,
      4.00E+00,
      4.00E+00,
      4.00E+00,
      5.00E+00,
      5.00E+00,
      5.00E+00,
      6.00E+00,
      6.00E+00,
      6.00E+00 };

  if ( *n_data < 0 )
  {
    *n_data = 0;
  }

  *n_data = *n_data + 1;

  if ( N_MAX < *n_data )
  {
    *n_data = 0;
    *df = 0;
    *lambda = 0.0;
    *x = 0.0;
    *fx = 0.0;
  }
  else
  {
    *df = df_vec[*n_data-1];
    *lambda = lambda_vec[*n_data-1];
    *x = x_vec[*n_data-1];
    *fx = fx_vec[*n_data-1];
  }

  return;
# undef N_MAX
}
//****************************************************************************80

double tnc ( double t, double df, double delta, int *ifault )

//****************************************************************************80
//
//  Purpose:
//
//    tnc() computes the tail of the noncentral T distribution.
//
//  Discussion:
//
//    This routine computes the cumulative probability at T of the
//    non-central T-distribution with DF degrees of freedom (which may
//    be fractional) and non-centrality parameter DELTA.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    25 January 2008
//
//  Author:
//
//    Original FORTRAN77 version by Russell Lenth.
//    C++ version by John Burkardt.
//
//  Reference:
//
//    Russell Lenth,
//    Algorithm AS 243:
//    Cumulative Distribution Function of the Non-Central T Distribution,
//    Applied Statistics,
//    Volume 38, Number 1, 1989, pages 185-189.
//
//    William Guenther,
//    Evaluation of probabilities for the noncentral distributions and
//    difference of two T-variables with a desk calculator,
//    Journal of Statistical Computation and Simulation,
//    Volume 6, Number 3-4, 1978, pages 199-206.
//
//  Parameters:
//
//    Input, double T, the point whose cumulative probability
//    is desired.
//
//    Input, double DF, the number of degrees of freedom.
//
//    Input, double DELTA, the noncentrality parameter.
//
//    Output, int *IFAULT, error flag.
//    0, no error.
//    nonzero, an error occcurred.
//
//    Output, double TNC, the tail of the noncentral
//    T distribution.
//
{
  double a;
  double albeta;
  double alnrpi = 0.57236494292470008707;
  double b;
  double del;
  double en;
  double errbd;
  double errmax = 1.0E-10;
  double geven;
  double godd;
  int itrmax = 100;
  double lambda;
  bool negdel;
  double p;
  double q;
  double r2pi = 0.79788456080286535588;
  double rxb;
  double s;
  double tt;
  double value;;
  double x;
  double xeven;
  double xodd;

  value = 0.0;

  if ( df <= 0.0 )
  {
    *ifault = 2;
    return value;
  }

  *ifault = 0;

  tt = t;
  del = delta;
  negdel = false;

  if ( t < 0.0 )
  {
    negdel = true;
    tt = - tt;
    del = - del;
  }
//
//  Initialize twin series.
//
  en = 1.0;
  x = t * t / ( t * t + df );

  if ( x <= 0.0 )
  {
    *ifault = 0;
    value = value + alnorm ( del, true );

    if ( negdel )
    {
      value = 1.0 - value;
    }
    return value;
  }

  lambda = del * del;
  p = 0.5 * exp ( - 0.5 * lambda );
  q = r2pi * p * del;
  s = 0.5 - p;
  a = 0.5;
  b = 0.5 * df;
  rxb = pow ( 1.0 - x, b );
  albeta = alnrpi + lgamma ( b ) - lgamma ( a + b );
  xodd = betain ( x, a, b, albeta, ifault );
  godd = 2.0 * rxb * exp ( a * log ( x ) - albeta );
  xeven = 1.0 - rxb;
  geven = b * x * rxb;
  value = p * xodd + q * xeven;
//
//  Repeat until convergence.
//
  for ( ; ; )
  {
    a = a + 1.0;
    xodd = xodd - godd;
    xeven = xeven - geven;
    godd = godd * x * ( a + b - 1.0 ) / a;
    geven = geven * x * ( a + b - 0.5 ) / ( a + 0.5 );
    p = p * lambda / ( 2.0 * en );
    q = q * lambda / ( 2.0 * en + 1.0 );
    s = s - p;
    en = en + 1.0;
    value = value + p * xodd + q * xeven;
    errbd = 2.0 * s * ( xodd - godd );

    if ( errbd <= errmax )
    {
      *ifault = 0;
      break;
    }

    if ( itrmax < en )
    {
      *ifault = 1;
      break;
    }
  }

  value = value + alnorm ( del, true );

  if ( negdel )
  {
    value = 1.0 - value;
  }

  return value;
}