/// <summary>
/// Returns the integral from <tt>x</tt> to infinity of the gamma
/// probability density function:
/// <pre>
/// inf.
/// b -
/// a | | b-1 -at
/// y = ----- | t e dt
/// - | |
/// | (b) -
/// x
/// </pre>
/// The incomplete gamma integral is used, according to the
/// relation
/// <para>
/// y = Gamma.incompleteGammaComplement( b, a*x ).
///
/// </para>
/// </summary>
/// <param name="a"> the paramater a (alpha) of the gamma distribution. </param>
/// <param name="b"> the paramater b (beta, lambda) of the gamma distribution. </param>
/// <param name="x"> integration end point. </param>
/// <returns> result </returns>
public static double gammaComplemented(double a, double b, double x)
{
if (x < 0.0)
{
return(0.0);
}
return(GammaFunctions.incompleteGammaComplement(b, a * x));
}
/// <summary>
/// Returns the area under the right hand tail (from <tt>x</tt> to
/// infinity) of the Chi square probability density function
/// with <tt>v</tt> degrees of freedom.
/// <pre>
/// inf.
/// -
/// 1 | | v/2-1 -t/2
/// P( x | v ) = ----------- | t e dt
/// v/2 - | |
/// 2 | (v/2) -
/// x
/// </pre>
/// where <tt>x</tt> is the Chi-square variable.
///
/// The incomplete gamma integral is used, according to the
/// formula
///
/// <tt>y = chiSquareComplemented( v, x ) = incompleteGammaComplement( v/2.0, x/2.0 )</tt>.
///
///
/// The arguments must both be positive.
/// </summary>
/// <param name="v"> degrees of freedom. </param>
/// <param name="x"> x </param>
/// <returns> result </returns>
/// <exception cref="ArithmeticException"> error </exception>
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: public static double chiSquareComplemented(double v, double x) throws ArithmeticException
public static double chiSquareComplemented(double v, double x)
{
if (x < 0.0 || v < 1.0)
{
return(0.0);
}
return(GammaFunctions.incompleteGammaComplement(v / 2.0, x / 2.0));
}
/// <summary>
/// Returns the sum of the first <tt>k</tt> terms of the Poisson distribution.
/// <pre>
/// k j
/// -- -m m
/// > e --
/// -- j!
/// j=0
/// </pre>
/// The terms are not summed directly; instead the incomplete
/// gamma integral is employed, according to the relation
/// <para>
/// <tt>y = poisson( k, m ) = Gamma.incompleteGammaComplement( k+1, m )</tt>.
///
/// The arguments must both be positive.
///
/// </para>
/// </summary>
/// <param name="k"> number of terms. </param>
/// <param name="mean"> the mean of the poisson distribution. </param>
/// <returns> result </returns>
/// <exception cref="ArithmeticException"> error </exception>
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: public static double poisson(int k, double mean) throws ArithmeticException
public static double poisson(int k, double mean)
{
if (mean < 0)
{
throw new System.ArgumentException();
}
if (k < 0)
{
return(0.0);
}
return(GammaFunctions.incompleteGammaComplement((double)(k + 1), mean));
}