stats_cdf_beta -- CDF function for BETA Distribution. Calculates any one parameter of the beta distribution given values for the others.
Description
float stats_cdf_beta ( float par1, float par2, float par3, int which )
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 search 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.
Parameters
par1
Its description
par2
Its description
par3
Its description
which
Integer indicating which of the next four argument
values is to be calculated from the others.
Legal range: 1..4
iwhich = 1 : Calculate P and Q from X,Y,A and B
iwhich = 2 : Calculate X and Y from P,Q,A and B
iwhich = 3 : Calculate A from P,Q,X,Y and B
iwhich = 4 : Calculate B from P,Q,X,Y and A
Return Values
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
