stats_cdf_beta

Method

Cumulative distribution function (P) is calculated directly by
code associated with the following reference.

DiDinato, A. R. and Morris, A. H. Algorithm 708: Significant
Digit Computation of the Incomplete Beta Function Ratios. ACM
Trans. Math. Softw. 18 (1993), 360-373.

Computation of other parameters involve a seach for a value that
produces the desired value of P. The search relies on the
monotinicity of P with the other parameter.

Note

The beta density is proportional to
t^(A-1) * (1-t)^(B-1)

Arguments


P -- The integral from 0 to X of the chi-square
distribution.
Input range: [0, 1].

Q -- 1-P.
Input range: [0, 1].
P + Q = 1.0.

X -- Upper limit of integration of beta density.
Input range: [0,1].
Search range: [0,1]

Y -- 1-X.
Input range: [0,1].
Search range: [0,1]
X + Y = 1.0.

A -- The first parameter of the beta density.
Input range: (0, +infinity).
Search range: [1D-100,1D100]

B -- The second parameter of the beta density.
Input range: (0, +infinity).
Search range: [1D-100,1D100]

STATUS -- 0 if calculation completed correctly
-I if input parameter number I is out of range
1 if answer appears to be lower than lowest
search bound
2 if answer appears to be higher than greatest
search bound
3 if P + Q .ne. 1
4 if X + Y .ne. 1

BOUND -- Undefined if STATUS is 0

Bound exceeded by parameter number I if STATUS
is negative.

Lower search bound if STATUS is 1.

Upper search bound if STATUS is 2.