Evaluates the noncentral Student's t cumulative probability distribution function.
double
scalar value representing the argument at which the function is to be evaluated. int
scalar value representing the number of degrees of freedom. This must be positive. double
scalar value representing the noncentrality parameter. A double
scalar value representing the probability that a noncentral Student's t random variable takes a value less than or equal to t
.
Method NoncentralstudentsT
evaluates the distribution function F
of a noncentral t random variable with idf
degrees of freedom and noncentrality parameter delta
; that is, with , , and ,
where is the gamma function. The value of the distribution function at the point is the probability that the random variable takes a value less than or equal to .
The noncentral t random variable can be defined by the distribution function above, or alternatively and equivalently, as the ratio of a normal random variable and an independent chi-squared random variable. If w has a normal distribution with mean and variance equal to one, has an independent chi-squared distribution with degrees of freedom, and
then has a noncentral distribution with degrees of freedom and noncentrality parameter .
The distribution function of the noncentral can also be expressed as a double integral involving a normal density function (see, for example, Owen 1962, page 108). The method NoncentralstudentsT
uses the method of Owen (1962, 1965), which uses repeated integration by parts on that alternate expression for the distribution function.
Cdf Class | Imsl.Stat Namespace | Example