Evaluates the Student's t cumulative probability distribution function.

Parameters

t

A double specifying the argument at which the function is to be evaluated.

df

A double specifying the number of degrees of freedom. This must be at least one.

Return Value

A double specifying the probability that a Student's t random variable takes a value less than or equal to t.

Remarks

Method StudentsT evaluates the distribution function of a Student's t random variable with df degrees of freedom. If the square of t is greater than or equal to df, the relationship of a t to an f random variable (and subsequently, to a beta random variable) is exploited, and routine Beta is used. Otherwise, the method described by Hill (1970) is used. If df is not an integer, if df is greater than 19, or if df is greater than 200, a Cornish-Fisher expansion is used to evaluate the distribution function. If df is less than 20 and is less than 2.0, a trigonometric series (see Abramowitz and Stegun 1964, equations 26.7.3 and 26.7.4, with some rearrangement) is used. For the remaining cases, a series given by Hill (1970) that converges well for large values of t is used.

For greater right tail accuracy, Cdf.ComplementaryStudentsT.

See Also

Cdf Class | Imsl.Stat Namespace | Example

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