The lower tail probability of the noncentral
-distribution with
degrees of freedom and noncentrality parameter
,
, is defined by
where
is a central
-distribution with
degrees of freedom.
The value of
at which the Poisson weight,
, is greatest is determined and the summation
(1) is made forward and backward from that value of
.
The recursive relationship:
is used during the summation in
(1).
The summations described in
Section 3 are made until an upper bound on the truncation error relative to the current summation value is less than
tol.
Background information to multithreading can be found in the
Multithreading documentation.
The number of terms in
(1) required for a given accuracy will depend on the following factors:
-
(i)The rate at which the Poisson weights tend to zero. This will be slower for larger values of .
-
(ii)The rate at which the central probabilities tend to zero. This will be slower for larger values of and .