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// Accord Statistics Library
// The Accord.NET Framework
// http://accord-framework.net
//
// Copyright © César Souza, 2009-2017
// cesarsouza at gmail.com
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
//
namespace Accord.Statistics.Testing
{
using System;
using Accord.Compat;
/// <summary>
/// Wald's Test using the Normal distribution.
/// </summary>
///
/// <remarks>
/// <para>
/// The Wald test is a parametric statistical test named after Abraham Wald
/// with a great variety of uses. Whenever a relationship within or between
/// data items can be expressed as a statistical model with parameters to be
/// estimated from a sample, the Wald test can be used to test the true value
/// of the parameter based on the sample estimate.</para>
///
/// <para>
/// Under the Wald statistical test, the maximum likelihood estimate of the
/// parameter(s) of interest θ is compared with the proposed value θ', with
/// the assumption that the difference between the two will be approximately
/// normal.</para>
///
/// <para>
/// References:
/// <list type="bullet">
/// <item><description><a href="http://en.wikipedia.org/wiki/Wald_test">
/// Wikipedia, The Free Encyclopedia. Wald Test. Available on:
/// http://en.wikipedia.org/wiki/Wald_test </a></description></item>
/// </list></para>
/// </remarks>
///
/// <seealso cref="ZTest"/>
///
/// <seealso cref="Accord.Statistics.Distributions.Univariate.NormalDistribution"/>
///
[Serializable]
public class WaldTest : ZTest
{
/// <summary>
/// Constructs a Wald's test.
/// </summary>
///
/// <param name="statistic">The test statistic, as given by (θ-θ')/SE.</param>
///
public WaldTest(double statistic)
: base(statistic, OneSampleHypothesis.ValueIsDifferentFromHypothesis)
{
}
/// <summary>
/// Constructs a Wald's test.
/// </summary>
///
/// <param name="estimatedValue">The estimated value (θ).</param>
/// <param name="hypothesizedValue">The hypothesized value (θ').</param>
/// <param name="standardError">The standard error of the estimation (SE).</param>
///
public WaldTest(double estimatedValue, double hypothesizedValue, double standardError)
: base(sampleMean: estimatedValue, hypothesizedMean: hypothesizedValue, standardError: standardError, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis)
{
}
}
}