67 lines
3.5 KiB
C#
67 lines
3.5 KiB
C#
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using System.Text;
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using BotSharp.Algorithm.HiddenMarkovModel.MathUtils.Distribution;
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namespace BotSharp.Algorithm.HiddenMarkovModel.MathUtils.Statistics
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{
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/// <summary>
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/// This class represents the Central Limit Theorem.
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///
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/// The Central Limit Theorem (CLT) states that:
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/// The distribution of sample statistics (e.g., sample mean) is nearly normal, centered at the population mean, and with a standard deviation equal to the population standard deviation
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/// divided by square root of the sample size.
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/// </summary>
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public class CLT
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{
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/// <summary>
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/// Estimate the normal distribution of a sample mean (for a continuous variable)
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///
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/// The Central Limit Theorem (CLT) states that:
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/// The distribution of sample statistics (e.g., sample mean) is nearly normal, centered at the population mean, and with a standard deviation equal to the population standard deviation
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/// divided by square root of the sample size.
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///
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/// With CTL, we can estimate the the normal distribution of a sample, given its estimated mean and stddev as well as the sample size.
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///
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/// For the CTL to hold true for a sample, the following conditions must be met:
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/// 1. Independence: Sample observations must be independent.
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/// > random sample/assignment
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/// > if sampling without replacement, the sample size < 10% of the population
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/// 2. Sample size/skew: Either the population distribution is normal, or if the population distribution is skewed, the sample size is large (rule of thumb: sample size > 30)
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/// </summary>
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/// <param name="sampleMean">point estimate of sample mean</param>
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/// <param name="sampleStdDev">standard deviation of a random sample</param>
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/// <param name="sampleSize">the size of the random sample</param>
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/// <returns>The normal distribution of the sample means for a random sample drawn from the population</returns>
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public static Gaussian EstimateSampleMeanDistribution(double sampleMean, double sampleStdDev, int sampleSize)
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{
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double SE = StandardError.GetStandardError(sampleStdDev, sampleSize);
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return new Gaussian(sampleMean, SE);
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}
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/// <summary>
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/// Estimate the normal distribution of a sample proportion (for a categorical variable with two values { "SUCCESS", "FAILURE" })
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///
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/// The Centrl Limit Theorem (CLT) for proportions:
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/// The distribution of sample proportions is nearly normal, centered at the population proportion, and with a standard error inversely proportional to the sample size.
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///
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/// Conditions for the CLT for proportions:
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/// 1. Independence: Sampled observations must be independent.
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/// > random sample/assignment
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/// > if sampling without replacement, n < 10% population
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/// 2. Sample size / skew: There should be at least 10 successes and 10 failures in the sample: np >= 10 and n(1-p) >= 10
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/// </summary>
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/// <param name="p"></param>
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/// <param name="sampleSize"></param>
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/// <returns></returns>
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public static Gaussian EstimateSampleProportionDistribution(double p, int sampleSize)
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{
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double SE = StandardError.GetStandardErrorForProportion(p, sampleSize);
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return new Gaussian(p, SE);
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}
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}
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}
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