(PECL stats >= 1.0.0)

stats_cdf_betaCalculates any one parameter of the beta distribution given values for the others


    float $par1,
    float $par2,
    float $par3,
    int $which
): float

Returns the cumulative distribution function, its inverse, or one of its parameters, of the beta distribution. The kind of the return value and parameters (par1, par2, and par3) are determined by which.

The following table lists the return value and parameters by which. CDF, x, alpha, and beta denotes cumulative distribution function, the value of the random variable, and shape parameters of the beta distribution, respectively.

Return value and parameters
which Return value par1 par2 par3
1 CDF x alpha beta
2 x CDF alpha beta
3 alpha x CDF beta
4 beta x CDF alpha



The first parameter


The second parameter


The third parameter


The flag to determine what to be calculated

Return Values

Returns CDF, x, alpha, or beta, determined by which.

add a note

User Contributed Notes 2 notes

14 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
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]
7 years ago
Decided to dive into the source code and provide a simple explanation:

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
To Top