/// <summary>
/// 少数のベルヌーイ試行をベータ分布により信頼区間を計算します
/// </summary>
/// <param name="successNum">成功数</param>
/// <param name="sampleNum">サンプル数</param>
/// <param name="condidenceValue">信頼区間（デフォルトでは0.95）</param>
/// <returns>信頼区間の推定値</returns>
public static CInterval ExactConfidenceIntervalBinomial(int successNum, int sampleNum, double condidenceValue = 0.95)
{
//参考：http://ynomura.dip.jp/archives/2010/01/18.html
if (sampleNum == 0)
{
throw new DivideByZeroException("sampleNumが0です");
}
//信頼度のパラメーター
var alpha = 1 - condidenceValue;
var result = new CInterval();
result.Upper = 1 - BetaDistribution.QBeta(alpha / 2, sampleNum - successNum, successNum + 1);
result.Median = (double)successNum / (double)sampleNum;
result.Lower = 1 - BetaDistribution.QBeta(1 - alpha / 2, sampleNum - successNum + 1, successNum);
result.SampleNum = sampleNum;
if (result.Upper == 0.0 && result.Lower == 0.0)
{
result.Upper = result.Median;
result.Lower = result.Median;//近似しきれない場合対策
}
return(result);
}
/// <summary>
/// ベルヌーイ試行を正規分布近似した信頼区間を計算します
/// </summary>
/// <param name="probSuccess">成功率の推定値</param>
/// <param name="sampleNum">標本数</param>
/// <param name="trimExcess">信頼区間を0以下または1以上で打ち切るオプション。デフォルトではオン</param>
/// <param name="zValue">z値。デフォルトでは95%信頼区間になります</param>
/// <returns>信頼区間の推定値</returns>
public static CInterval ConfidenceIntervalBinomial(double probSuccess, int sampleNum, bool trimExcess = true, double zValue = 1.959964)
{
if (sampleNum == 0)
{
throw new DivideByZeroException("sampleNumが0です");
}
//標準誤差
var sdError = Math.Sqrt(probSuccess * (1 - probSuccess) / (double)sampleNum);
var upper = probSuccess + sdError * zValue;
var lower = probSuccess - sdError * zValue;
var median = probSuccess;
if (trimExcess)
{
upper = Math.Max(Math.Min(upper, 1.0), 0.0);
lower = Math.Max(Math.Min(lower, 1.0), 0.0);
median = Math.Max(Math.Min(median, 1.0), 0.0);
}
var result = new CInterval()
{
Lower = lower,
Median = median,
Upper = upper,
SampleNum = sampleNum,
};
return(result);
}
/// <summary> /// Projects this onto the vector provided with the interval on the line returned. /// </summary> public abstract void Project(C2DVector Vector, CInterval Interval);
/// <summary> /// Projects this onto the line provided with the interval on the line returned. /// </summary> public abstract void Project(C2DLine Line, CInterval Interval);
