Difference between revisions of "Student's t-distribution"
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| − | + | == StudentT(dof) == | |
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| − | = StudentT(dof) = | ||
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The Student-T distribution describes the deviation of a sample mean from the true mean when the samples are generated by a normally distributed process. The statistic | The Student-T distribution describes the deviation of a sample mean from the true mean when the samples are generated by a normally distributed process. The statistic | ||
| − | + | :<code>t = (m - u)/(s*Sqrt(n))</code> | |
| − | where m is the sample mean, u the actual mean, s the sample standard deviation, and n the sample size, is distributed according to the Student-T distribution with n-1 degrees of freedom. The parameter, «dof», is the degrees of freedom. | + | where m is the sample mean, u the actual mean, s the sample standard deviation, and n the sample size, is distributed according to the Student-T distribution with ''n - 1'' degrees of freedom. The parameter, «dof», is the degrees of freedom. Student-T distributions are bell-shaped, much like a [[Normal|normal distribution]], but with heavier tails, especially for smaller degrees of freedom. When ''n = 1'', it is known as the Cauchy distribution. For efficiency reasons, when a latin-hypercube sampling method is selected, psuedo-latin-hypercube method is used to sample the Student-T, which samples from the T-distribution, but does not guarantee a perfect latin spread of the samples. |
| − | = Parameter Estimation = | + | == Parameter Estimation == |
| + | If you want to estimate the parameter from sample data ''X'' indexed by ''I'', you can use the following estimation formula provided that <code>Variance(X, I) > 1</code>: | ||
| + | :<code>«dof» := 2*Variance(X, I)/(Variance(X, I) - 1)</code> | ||
| − | + | ==Example== | |
| − | + | [[Image:Student-T.jpg]] | |
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| + | == See Also == | ||
| + | * [[Variance]] | ||
| + | * [[Normal]] | ||
* [[Dens_StudentT]] | * [[Dens_StudentT]] | ||
* [[CumStudentT]] | * [[CumStudentT]] | ||
Revision as of 19:58, 18 January 2016
StudentT(dof)
The Student-T distribution describes the deviation of a sample mean from the true mean when the samples are generated by a normally distributed process. The statistic
t = (m - u)/(s*Sqrt(n))
where m is the sample mean, u the actual mean, s the sample standard deviation, and n the sample size, is distributed according to the Student-T distribution with n - 1 degrees of freedom. The parameter, «dof», is the degrees of freedom. Student-T distributions are bell-shaped, much like a normal distribution, but with heavier tails, especially for smaller degrees of freedom. When n = 1, it is known as the Cauchy distribution. For efficiency reasons, when a latin-hypercube sampling method is selected, psuedo-latin-hypercube method is used to sample the Student-T, which samples from the T-distribution, but does not guarantee a perfect latin spread of the samples.
Parameter Estimation
If you want to estimate the parameter from sample data X indexed by I, you can use the following estimation formula provided that Variance(X, I) > 1:
«dof» := 2*Variance(X, I)/(Variance(X, I) - 1)
Example
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