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stats_cdf_beta

(PECL stats >= 1.0.0)

stats_cdf_betaFonction CDF pour Distribution BETA. Calcule n'importe quel paramètre de distribution beta des valeurs données pour les autres

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 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.

Liste de paramètres

par1

par2

par3

which


Integer indicating which of the next four argument
values is to be calculated from the others.
Legal range: 1..4
which = 1 : Calculate P and Q from X,Y,A and B
which = 2 : Calculate X and Y from P,Q,A and B
which = 3 : Calculate A from P,Q,X,Y and B
which = 4 : Calculate B from P,Q,X,Y and A

Valeurs de retour


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

add a note add a note

User Contributed Notes 2 notes

up
0
n15m0_jk
2 months ago
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
up
0
Anonymous
6 years ago
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]
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