Probability density function of Student's t-distribution

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stats::tPDF(a) returns a procedure representing the probability density function

of Student's t-distribution with shape parameter ('degrees of freedom') a > 0.

The procedure f := stats::tPDF(a) can be called in the form f(x) with an arithmetical expression x. The return value of f(x) is either a floating-point number or a symbolic expression:

If x is a floating-point number and a can be converted to a floating-point number, then f(x) returns a floating-point number.

f(infinity) and f(-infinity) produce the result 0.0.

In all other cases, the expression is returned.

If floating-point results are desired, call f(x) with a floating-point value x.

Numerical values for a are only accepted if they are real and positive.


Example 1

We evaluate the probability density function with a = at various points:

f := stats::tPDF(3/4):
f(-infinity), f(-PI), f(1/2), f(0.5), f(3), f(infinity)

delete f:

Example 2

We use symbolic arguments:

f := stats::tPDF(a): f(x), f(0.3)

When numerical values are assigned to a, the function f starts to produce floating-point values for floating-point arguments:

a := PI: f(0.3)

delete f, a:



The shape parameter: an arithmetical expression representing a positive real value

Return Values


See Also

MuPAD Functions