/// <summary>
/// Returns the integral from zero to <tt>x</tt> of the gamma probability
/// density function.
/// <pre>
/// x
/// b -
/// a | | b-1 -at
/// y = ----- | t e dt
/// - | |
/// | (b) -
/// 0
/// </pre>
/// The incomplete gamma integral is used, according to the
/// relation
///
/// <tt>y = Gamma.incompleteGamma( b, a*x )</tt>.
/// </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 gamma(double a, double b, double x)
{
if (x < 0.0)
{
return(0.0);
}
return(GammaFunctions.incompleteGamma(b, a * x));
}
/// <summary>
/// Returns the area under the left hand tail (from 0 to <tt>x</tt>)
/// 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.
/// <para>
/// The incomplete gamma integral is used, according to the
/// formula
/// </para>
/// <para>
/// <tt>y = chiSquare( v, x ) = incompleteGamma( v/2.0, x/2.0 )</tt>.
/// </para>
/// <para>
/// The arguments must both be positive.
///
/// </para>
/// </summary>
/// <param name="v"> degrees of freedom. </param>
/// <param name="x"> integration end point. </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 chiSquare(double v, double x) throws ArithmeticException
public static double chiSquare(double v, double x)
{
if (x < 0.0 || v < 1.0)
{
return(0.0);
}
return(GammaFunctions.incompleteGamma(v / 2.0, x / 2.0));
}
/// <summary>
/// Returns the sum of the terms <tt>k+1</tt> to <tt>Infinity</tt> of the Poisson distribution.
/// <pre>
/// inf. j
/// -- -m m
/// > e --
/// -- j!
/// j=k+1
/// </pre>
/// The terms are not summed directly; instead the incomplete
/// gamma integral is employed, according to the formula
/// <para>
/// <tt>y = poissonComplemented( k, m ) = Gamma.incompleteGamma( k+1, m )</tt>.
///
/// The arguments must both be positive.
///
/// </para>
/// </summary>
/// <param name="k"> start term. </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 poissonComplemented(int k, double mean) throws ArithmeticException
public static double poissonComplemented(int k, double mean)
{
if (mean < 0)
{
throw new System.ArgumentException();
}
if (k < -1)
{
return(0.0);
}
return(GammaFunctions.incompleteGamma((double)(k + 1), mean));
}
