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Student's t-distribution (or simply the t-distribution) is a probability
distribution that arises in the problem of estimating the mean of a
normally distributed population when the sample size is small.
Student's t-distribution arises when (as in nearly all practical statistical
work) the population standard deviation is unknown and has to be estimated
from the data. It is
the basis of the popular Student's t-tests for the statistical significance
of the difference between two sample means, and for confidence intervals
for the difference between two population means. The Student's
t-distribution is a special case of the generalised hyperbolic distribution.