The students' t distribution has a symmetric PDF (with no skew), and thus you assume that the sample and/or population also have such a PDF (Probability Distribution Function).
>> the Kolmogorov-Smirnov two-sample test, which essentially compares the empirical distribution functions of the two samples without implicitly assuming normality. http://en.wikipedia.org/wiki/Kolmogorov–Smirnov_test
> The generalized matrix t-distribution is the compound distribution that results from an infinite mixture of a matrix normal distribution with an inverse multivariate gamma distribution placed over either of its covariance matrices.
But does a matrix t-distribution describe nonlinear variance in complex wave functions?
> In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system.
A Q12 question:
How frequently are quantum density operators described by a parametric t distribution?
t statistic > History: https://en.wikipedia.org/wiki/T-statistic#History
Students' t distribution: https://en.wikipedia.org/wiki/Student%27s_t-distribution
"What are some alternatives to sample mean and t-test when comparing highly skewed distributions" https://www.quora.com/What-are-some-alternatives-to-sample-m... :
>> the Kolmogorov-Smirnov two-sample test, which essentially compares the empirical distribution functions of the two samples without implicitly assuming normality. http://en.wikipedia.org/wiki/Kolmogorov–Smirnov_test
> You may also be interested in the Wald-Wolfowitz runs test (http://en.wikipedia.org/wiki/Wald–Wolfowitz_runs_test ) and the Mann-Whitney test (http://en.wikipedia.org/wiki/Mann–Whitney_U ).
Statistical Significance > Limitations, Challenges: https://en.wikipedia.org/wiki/Statistical_significance#Limit...
Statistical hypothesis test > Criticism, Alternatives: https://en.wikipedia.org/wiki/Statistical_hypothesis_test#Cr...
There are Multivariate Students' t distributions: https://en.wikipedia.org/wiki/Multivariate_t-distribution
Matrix t distribution: https://en.wikipedia.org/wiki/Matrix_t-distribution :
> The generalized matrix t-distribution is the compound distribution that results from an infinite mixture of a matrix normal distribution with an inverse multivariate gamma distribution placed over either of its covariance matrices.
But does a matrix t-distribution describe nonlinear variance in complex wave functions?
Quantum statistical mechanics: https://en.wikipedia.org/wiki/Quantum_statistical_mechanics :
> In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system.
A Q12 question: How frequently are quantum density operators described by a parametric t distribution?