nag_deviates_students_t_vector (g01tbc) returns a number of deviates associated with given probabilities of Student's -distribution with real degrees of freedom.
The deviate,
associated with the lower tail probability,
, of the Student's
-distribution with
degrees of freedom is defined as the solution to
For other values of
a transformation to the beta distribution is used and the result obtained from
nag_deviates_beta (g01fec).
For
an inverse asymptotic expansion of Cornish–Fisher type is used. The algorithm is described by
Hill (1970).
The input arrays to this function are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See
Section 2.6 in the g01 Chapter Introduction for further information.
- 1:
ltail – IntegerInput
On entry: the length of the array
tail.
Constraint:
.
- 2:
tail[ltail] – const Nag_TailProbabilityInput
On entry: indicates which tail the supplied probabilities represent. For
, for
:
- The lower tail probability, i.e., .
- The upper tail probability, i.e., .
- The two tail (confidence interval) probability,
i.e., .
- The two tail (significance level) probability,
i.e., .
Constraint:
, , or , for .
- 3:
lp – IntegerInput
On entry: the length of the array
p.
Constraint:
.
- 4:
p[lp] – const doubleInput
On entry:
, the probability of the required Student's
-distribution as defined by
tail with
,
.
Constraint:
, for .
- 5:
ldf – IntegerInput
On entry: the length of the array
df.
Constraint:
.
- 6:
df[ldf] – const doubleInput
On entry: , the degrees of freedom of the Student's -distribution with , .
Constraint:
, for .
- 7:
t[] – doubleOutput
-
Note: the dimension,
dim, of the array
t
must be at least
.
On exit: , the deviates for the Student's -distribution.
- 8:
ivalid[] – IntegerOutput
-
Note: the dimension,
dim, of the array
ivalid
must be at least
.
On exit:
indicates any errors with the input arguments, with
- No error.
-
On entry, | invalid value supplied in tail when calculating . |
-
On entry, | , |
or | . |
-
- The solution has failed to converge. The result returned should represent an approximation to the solution.
- 9:
fail – NagError *Input/Output
-
The NAG error argument (see
Section 3.6 in the Essential Introduction).
The results should be accurate to five significant digits, for most argument values. The error behaviour for various argument values is discussed in
Hill (1970).
Not applicable.
The value
may be calculated by using a transformation to the beta distribution and calling
nag_deviates_beta_vector (g01tec). This function allows you to set the required accuracy.
This example reads the probability, the tail that probability represents and the degrees of freedom for a number of Student's -distributions and computes the corresponding deviates.