stats_cdf_beta
(PECL stats:1.0.0-1.0.2)
stats_cdf_beta — CDF function for BETA Distribution. Calculates any one parameter of the beta distribution given values for the others.
Описание
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.
Список параметров
- par1
-
- par2
-
- par3
-
- 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
Возвращаемые значения
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
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Коментарии
Additional Notes, taken from source.
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
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]
Decided to dive into the source code and provide a simple explanation:
Parameters:
int $which - Select which parameter to use in the CDF Binomial calculation, based on what the prior 3 parameters are.
where $which is 4:
$arg1 = p
$arg2 = sn
$arg3 = xn
returns pr
$which = 3
$arg1 = p
$arg2 = sn
$arg3 = pr
returns xn
$which = 2
$arg1 = p
$arg2 = xn
$arg3 = pr
returns sn
$which = 1
$arg1 = sn
$arg2 = xn
$arg3 = pr
returns p