Normal approximation to the Student-t distribution | Vose Software

Normal approximation to the Student-t distribution

The Student-t distribution Student(n) is quite difficult to calculate, but when n is large it is well approximated by a Normal distribution, as follows:

Student(n) » Normal(0, 1)

A general rule for this approximation is that n > 30. The relationship between the Student-t and Normal distributions is not intuitively obvious, but is readily made apparent by doing a Taylor series expansion about x = 0 of the probability density function for the Student distribution.

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