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The t distribution is often used as an alternative to the normal distribution as a model for data, which often has heavier tails than the normal distribution allows for; see e.g. Lange et al. [14] The classical approach was to identify outliers (e.g., using Grubbs's test) and exclude or downweight them in some way.
Demonstration of density estimation using Kernel density estimation: The true density is a mixture of two Gaussians centered around 0 and 3, shown with a solid blue curve. In each frame, 100 samples are generated from the distribution, shown in red. Centered on each sample, a Gaussian kernel is drawn in gray.
As the sample size n grows sufficiently large, the distribution of ^ will be closely approximated by a normal distribution. [1] Using this and the Wald method for the binomial distribution , yields a confidence interval, with Z representing the standard Z-score for the desired confidence level (e.g., 1.96 for a 95% confidence interval), in the ...
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
For n independent and identically distributed discrete random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability mass function g(x) the range of the X i is the range of a sample of size n from a population with distribution function G(x).
For example, Tukey's range test and Duncan's new multiple range test (MRT), in which the sample x 1, ..., x n is a sample of means and q is the basic test-statistic, can be used as post-hoc analysis to test between which two groups means there is a significant difference (pairwise comparisons) after rejecting the null hypothesis that all groups ...
The action (the integration ) of this distribution on a test function can be interpreted as a weighted average of the distribution on the support of the test function, even if the values of the distribution at a single point are not well-defined.
Student's t-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis.