studenttdistr.cs

数理统计Stutent s检验源代码

/*************************************************************************
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from C to
      pseudocode.

See subroutines comments for additional copyrights.

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  contributors may be used to endorse or promote products derived from
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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*************************************************************************/

using System;

class studenttdistr
{
    /*************************************************************************
    Student's t distribution

    Computes the integral from minus infinity to t of the Student
    t distribution with integer k > 0 degrees of freedom:

                                         t
                                         -
                                        | |
                 -                      |         2   -(k+1)/2
                | ( (k+1)/2 )           |  (     x   )
          ----------------------        |  ( 1 + --- )        dx
                        -               |  (      k  )
          sqrt( k pi ) | ( k/2 )        |
                                      | |
                                       -
                                      -inf.

    Relation to incomplete beta integral:

           1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
    where
           z = k/(k + t**2).

    For t < -2, this is the method of computation.  For higher t,
    a direct method is derived from integration by parts.
    Since the function is symmetric about t=0, the area under the
    right tail of the density is found by calling the function
    with -t instead of t.

    ACCURACY:

    Tested at random 1 <= k <= 25.  The "domain" refers to t.
                         Relative error:
    arithmetic   domain     # trials      peak         rms
       IEEE     -100,-2      50000       5.9e-15     1.4e-15
       IEEE     -2,100      500000       2.7e-15     4.9e-17

    Cephes Math Library Release 2.8:  June, 2000
    Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
    *************************************************************************/
    public static double studenttdistribution(int k,
        double t)
    {
        double result = 0;
        double x = 0;
        double rk = 0;
        double z = 0;
        double f = 0;
        double tz = 0;
        double p = 0;
        double xsqk = 0;
        int j = 0;

        System.Diagnostics.Debug.Assert(k>0, "Domain error in StudentTDistribution");
        if( t==0 )
        {
            result = 0.5;
            return result;
        }
        if( t<-2.0 )
        {
            rk = k;
            z = rk/(rk+t*t);
            result = 0.5*ibetaf.incompletebeta(0.5*rk, 0.5, z);
            return result;
        }
        if( t<0 )
        {
            x = -t;
        }
        else
        {
            x = t;
        }
        rk = k;
        z = 1.0+x*x/rk;
        if( k%2!=0 )
        {
            xsqk = x/Math.Sqrt(rk);
            p = Math.Atan(xsqk);
            if( k>1 )
            {
                f = 1.0;
                tz = 1.0;
                j = 3;
                while( j<=k-2 & tz/f>AP.Math.MachineEpsilon )
                {
                    tz = tz*((j-1)/(z*j));
                    f = f+tz;
                    j = j+2;
                }
                p = p+f*xsqk/z;
            }
            p = p*2.0/Math.PI;
        }
        else
        {
            f = 1.0;
            tz = 1.0;
            j = 2;
            while( j<=k-2 & tz/f>AP.Math.MachineEpsilon )
            {
                tz = tz*((j-1)/(z*j));
                f = f+tz;
                j = j+2;
            }
            p = f*x/Math.Sqrt(z*rk);
        }
        if( t<0 )
        {
            p = -p;
        }
        result = 0.5+0.5*p;
        return result;
    }


    /*************************************************************************
    Functional inverse of Student's t distribution

    Given probability p, finds the argument t such that stdtr(k,t)
    is equal to p.

    ACCURACY:

    Tested at random 1 <= k <= 100.  The "domain" refers to p:
                         Relative error:
    arithmetic   domain     # trials      peak         rms
       IEEE    .001,.999     25000       5.7e-15     8.0e-16
       IEEE    10^-6,.001    25000       2.0e-12     2.9e-14

    Cephes Math Library Release 2.8:  June, 2000
    Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
    *************************************************************************/
    public static double invstudenttdistribution(int k,
        double p)
    {
        double result = 0;
        double t = 0;
        double rk = 0;
        double z = 0;
        int rflg = 0;

        System.Diagnostics.Debug.Assert(k>0 & p>0 & p<1, "Domain error in InvStudentTDistribution");
        rk = k;
        if( p>0.25 & p<0.75 )
        {
            if( p==0.5 )
            {
                result = 0;
                return result;
            }
            z = 1.0-2.0*p;
            z = ibetaf.invincompletebeta(0.5, 0.5*rk, Math.Abs(z));
            t = Math.Sqrt(rk*z/(1.0-z));
            if( p<0.5 )
            {
                t = -t;
            }
            result = t;
            return result;
        }
        rflg = -1;
        if( p>=0.5 )
        {
            p = 1.0-p;
            rflg = 1;
        }
        z = ibetaf.invincompletebeta(0.5*rk, 0.5, 2.0*p);
        if( AP.Math.MaxRealNumber*z<rk )
        {
            result = rflg*AP.Math.MaxRealNumber;
            return result;
        }
        t = Math.Sqrt(rk/z-rk);
        result = rflg*t;
        return result;
    }
}