/// <summary>
/// Gets the inverse of the cumulative distribution function (icdf) for
/// this distribution evaluated at probability <c>p</c>. This function
/// is also known as the Quantile function.
/// </summary>
///
/// <param name="p">A probability value between 0 and 1.</param>
///
/// <returns>
/// A sample which could original the given probability
/// value when applied in the <see cref="DistributionFunction"/>.
/// </returns>
///
public override double InverseDistributionFunction(double p)
{
if (this.exact)
{
return(base.InverseDistributionFunction(p));
}
return(approximation.InverseDistributionFunction(p));
}
/// <summary>
/// Gets the inverse of the cumulative distribution function (icdf) for
/// this distribution evaluated at probability <c>p</c>. This function
/// is also known as the Quantile function.
/// </summary>
///
/// <param name="p">A probability value between 0 and 1.</param>
///
/// <returns>
/// A sample which could original the given probability
/// value when applied in the <see cref="UnivariateContinuousDistribution.DistributionFunction(double)"/>.
/// </returns>
///
protected internal override double InnerInverseDistributionFunction(double p)
{
if (this.exact)
{
return(base.InnerInverseDistributionFunction(p));
}
return(approximation.InverseDistributionFunction(p));
}
/// <summary>
/// Gets the inverse of the cumulative distribution function (icdf) for
/// this distribution evaluated at probability <c>p</c>. This function
/// is also known as the Quantile function.
/// </summary>
///
/// <param name="p">A probability value between 0 and 1.</param>
///
/// <returns>
/// A sample which could original the given probability
/// value when applied in the <see cref="UnivariateContinuousDistribution.DistributionFunction(double)"/>.
/// </returns>
///
protected internal override double InnerInverseDistributionFunction(double p)
{
if (this.exact)
{
if (n1 > n2)
{
Trace.TraceWarning("Warning: Using a MannWhitneyDistribution where the first sample is larger than the second.");
double lower = 0;
double upper = 0;
double f = DistributionFunction(0);
if (f > p)
{
while (f > p && !double.IsInfinity(lower))
{
lower = upper;
upper = 2 * upper + 1;
f = DistributionFunction(upper);
}
}
else if (f < p)
{
while (f < p && !double.IsInfinity(upper))
{
upper = lower;
lower = 2 * lower - 1;
f = DistributionFunction(lower);
}
}
else
{
return(0);
}
if (double.IsNegativeInfinity(lower))
{
lower = double.MinValue;
}
if (double.IsPositiveInfinity(upper))
{
upper = double.MaxValue;
}
double value = BrentSearch.Find(DistributionFunction, p, lower, upper);
return(value);
}
return(base.InnerInverseDistributionFunction(p));
}
return(approximation.InverseDistributionFunction(p));
}
public void InverseDistributionFunctionTest()
{
double[] expected =
{
Double.NegativeInfinity, -4.38252, -2.53481, -1.20248,
-0.0640578, 1.0, 2.06406, 3.20248, 4.53481, 6.38252,
Double.PositiveInfinity
};
NormalDistribution target = new NormalDistribution(1.0, 4.2);
for (int i = 0; i < expected.Length; i++)
{
double x = i / 10.0;
double actual = target.InverseDistributionFunction(x);
Assert.AreEqual(expected[i], actual, 1e-5);
Assert.IsFalse(Double.IsNaN(actual));
}
}
