/// <summary>
/// Tests that methods
/// of <see cref="RandomNumberGenerator"/>
/// returning an <see cref="Int32"/> sample point from a
/// statistical distribution
/// has been properly implemented.
/// </summary>
/// <typeparam name="TParameters">
/// The type of the distribution parameters.</typeparam>
/// <param name="distributionMean">The mean of the distribution
/// from which the sample has been drawn.</param>
/// <param name="distributionVariance">
/// The variance of the distribution
/// from which the sample has been drawn.</param>
/// <param name="sampleSize">The sample size.</param>
/// <param name="delta">The required accuracy.</param>
/// <param name="samplePointFunc">
/// A method returning a sample point from a
/// statistical distribution having the specified
/// parameters.</param>
/// <param name="distributionParameters">The parameters of the distribution
/// from which the sample is drawn.</param>
public static void Int32Succeed <TParameters>(
double distributionMean,
double distributionVariance,
int sampleSize,
double delta,
SamplePointFunc <int, TParameters> samplePointFunc,
params TParameters[] distributionParameters)
{
bool CanCheckChebyshevInequality =
!Double.IsInfinity(distributionMean)
&&
!Double.IsPositiveInfinity(distributionVariance);
// distribution.Sample()
{
var sample = DoubleMatrix.Dense(sampleSize, 1);
for (int i = 0; i < sampleSize; i++)
{
sample[i] = samplePointFunc(distributionParameters);
}
if (CanCheckChebyshevInequality)
{
RandomNumberGeneratorTest.CheckChebyshevInequality(
distributionMean: distributionMean,
distributionVariance: distributionVariance,
sampleMean: Stat.Mean(sample),
sampleSize: sampleSize,
delta: delta);
}
}
}
/// <summary>
/// Checks that the Chebyshev inequality holds true
/// for the mean of a sample draw from the specified
/// distribution.
/// </summary>
/// <param name="distribution">The distribution from which the
/// sample has been drawn.</param>
/// <param name="sampleMean">The observed sample mean.</param>
/// <param name="sampleSize">The sample size.</param>
/// <param name="delta">The delta: a positive, less than unity
/// quantity such that the probability of observing the sample
/// mean close to the population mean is at least
/// <c>1 - delta</c>.
/// </param>
/// <remarks>
/// <para>
/// It is assumed that the
/// <see cref="ProbabilityDistribution.Mean"/> and the
/// <see cref="ProbabilityDistribution.Variance"/> of
/// <paramref name="distribution"/> are finite, and
/// <paramref name="delta"/> is in the open interval
/// having extremes <c>0</c> and <c>1</c>.
/// Then the event
/// </para>
/// <para>
/// { | sampleMean - distribution.Mean() | < epsilon },
/// </para>
/// <para>
/// where epsilon = sampleStdDev / Math.Sqrt( sampleSize * delta ),
/// is expected to happen with probability
/// greater than or equal to 1 - delta.
/// Hence this method asserts that the event under study
/// holds true for the observed sample mean.
/// </para>
/// </remarks>
/// <exception cref="AssertFailedException">
/// <paramref name="distribution"/> has infinite mean.<br/>
/// -or-<br/>
/// <paramref name="distribution"/> has infinite variance.<br/>
/// -or-<br/>
/// <paramref name="delta"/> is not in the open interval
/// having extremes <c>0</c> and <c>1</c>.<br/>
/// -or-<br/>
/// The event did not happen for the mean of the observed
/// sample.
/// </exception>
/// <seealso href="https://en.wikipedia.org/wiki/Chebyshev%27s_inequality"/>
public static void CheckChebyshevInequality(
ProbabilityDistribution distribution,
double sampleMean,
int sampleSize,
double delta)
{
RandomNumberGeneratorTest.CheckChebyshevInequality(
distribution.Mean(),
distribution.Variance(),
sampleMean,
sampleSize,
delta);
}
/// <summary>
/// Tests that methods
/// of <see cref="RandomNumberGenerator"/>
/// returning a sample of integers to an array from a
/// statistical distribution
/// terminates successfully when expected.
/// </summary>
/// <typeparam name="TParameters">
/// The type of the distribution parameters.</typeparam>
/// <param name="distributionMean">The mean of the distribution
/// from which the sample has been drawn.</param>
/// <param name="distributionVariance">
/// The variance of the distribution
/// from which the sample has been drawn.</param>
/// <param name="sampleSize">The sample size.</param>
/// <param name="delta">The required accuracy.</param>
/// <param name="sampleArrayFunc">
/// A method returning a sample from a
/// statistical distribution having the specified
/// parameters.</param>
/// <param name="distributionParameters">The parameters of the distribution
/// from which the sample is drawn.</param>
public static void Int32Succeed <TParameters>(
double distributionMean,
double distributionVariance,
int sampleSize,
double delta,
SampleArrayFunc <int, TParameters> sampleArrayFunc,
params TParameters[] distributionParameters)
{
bool CanCheckChebyshevInequality =
!Double.IsInfinity(distributionMean)
&&
!Double.IsPositiveInfinity(distributionVariance);
// distribution.Sample(sampleSize, destinationArray, destinationIndex)
{
int destinationSize = sampleSize * 10;
int partialSize = sampleSize;
var sample = new int[destinationSize];
int[] destinationArray = sample;
IndexCollection destinationIndexes =
IndexCollection.Sequence(0, partialSize, destinationSize - 1);
foreach (var destinationIndex in destinationIndexes)
{
sampleArrayFunc(
partialSize,
destinationArray,
destinationIndex,
distributionParameters);
}
if (CanCheckChebyshevInequality)
{
RandomNumberGeneratorTest.CheckChebyshevInequality(
distributionMean: distributionMean,
distributionVariance: distributionVariance,
sampleMean: sample.Average(),
sampleSize: sampleSize,
delta: delta);
}
}
}
/// <summary>
/// Tests that methods
/// of <see cref="RandomNumberGenerator"/>
/// returning a sample of doubles to an array from a
/// statistical distribution
/// terminates successfully when expected.
/// </summary>
/// <typeparam name="TParameters">
/// The type of the distribution parameters.</typeparam>
/// <param name="distributionMean">The mean of the distribution
/// from which the sample has been drawn.</param>
/// <param name="distributionVariance">
/// The variance of the distribution
/// from which the sample has been drawn.</param>
/// <param name="sampleSize">The sample size.</param>
/// <param name="delta">The required accuracy.</param>
/// <param name="sampleArrayFunc">
/// A method returning a sample from a
/// statistical distribution having the specified
/// parameters.</param>
/// <param name="distributionParameters">The parameters of the distribution
/// from which the sample is drawn.</param>
public static void DoubleSucceed <TParameters>(
double distributionMean,
double distributionVariance,
int sampleSize,
double delta,
SampleArrayFunc <double, TParameters> sampleArrayFunc,
params TParameters[] distributionParameters)
{
bool canCheckChebyshevInequality =
!Double.IsInfinity(distributionMean)
&&
!Double.IsPositiveInfinity(distributionVariance);
// distribution.Sample(sampleSize, destinationArray, destinationIndex)
{
int destinationSize = sampleSize * 10;
int partialSize = sampleSize;
var sample = DoubleMatrix.Dense(destinationSize, 1);
double[] destinationArray = sample.GetStorage();
IndexCollection destinationIndexes =
IndexCollection.Sequence(0, partialSize, destinationSize - 1);
foreach (var destinationIndex in destinationIndexes)
{
sampleArrayFunc(
partialSize,
destinationArray,
destinationIndex,
distributionParameters);
}
if (canCheckChebyshevInequality)
{
RandomNumberGeneratorTest.CheckChebyshevInequality(
distributionMean: distributionMean,
distributionVariance: distributionVariance,
sampleMean: Stat.Mean(sample),
sampleSize: sampleSize,
delta: delta);
}
}
}