(PECL stats >= 1.0.0)
stats_cdf_beta — Calculates any one parameter of the beta distribution given values for the others
$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 cumurative distribution function, the value of the random
variable, and shape parameters of the beta distribution, respectively.
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 |
par1The first parameter
par2The second parameter
par3The third parameter
whichThe flag to determine what to be calculated
Returns CDF, x, alpha, or beta, determined by which.
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
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]