The central limit theorem asserts that means of independent, identically distributed variables will converge to a normal distribution provided they are light tailed enough. ...

MaxMixtureKernels is an option for SmoothKernelDistribution and related functions that specifies the maximum number and location of kernel functions to use in the estimation.

JarqueBeraALMTest[data] tests whether data is normally distributed using the Jarque\[Dash]Bera ALM test.JarqueBeraALMTest[data, " property"] returns the value of " property".

LocationEquivalenceTest[{data_1, data_2, ...}] tests whether the means or medians of the data_i are equal. LocationEquivalenceTest[{data_1, ...}, " property"] returns the ...

TransformedDistribution[expr, x \[Distributed] dist] represents the transformed distribution of expr where the random variable x follows the distribution ...

AlternativeHypothesis is an option for hypothesis testing functions like LocationTest that specifies the alternative hypothesis.

SkewNormalDistribution[\[Mu], \[Sigma], \[Alpha]] represents a skew-normal distribution with shape parameter \[Alpha], location parameter \[Mu], and scale parameter \[Sigma].

SmoothKernelDistribution[{x_1, x_2, ...}] represents a smooth kernel distribution based on the data values x_i.SmoothKernelDistribution[{{x_1, y_1, ...}, {x_2, y_2, ...}, ...

ProbabilityScalePlot[{x_1, x_2, ...}] generates a normal probability plot of the samples x_i. ProbabilityScalePlot[{x_1, x_2, ...}, " dist"] generates a probability plot ...

PairedHistogram[{x_1, x_2, ...}, {y_1, y_2, ...}] plots a paired histogram of the values x_i and y_i.PairedHistogram[{x_1, x_2, ...}, {y_1, y_2, ...}, bspec] plots a paired ...