PHP 7.2.0 Beta 3 Released


(PECL stats >= 1.0.0)

stats_cdf_binomialCalculates any one parameter of the binomial distribution given values for the others.


float stats_cdf_binomial ( float $par1 , float $par2 , float $par3 , int $which )

Returns the cumulative distribution function, its inverse, or one of its parameters, of the binomial 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, n, and p denotes cumurative distribution function, the number of successes, the number of trials, and the success rate for each trial, respectively.

Return value and parameters
which Return value par1 par2 par3
1 CDF x n p
2 x CDF n p
3 n x CDF p
4 p x CDF n



The first parameter


The second parameter


The third parameter


The flag to determine what to be calculated

Return Values

Returns CDF, x, n, or p, determined by which.

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User Contributed Notes 1 note

2 years ago
Calculates any one parameter of the binomial
     distribution given values for the others.


     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 S,XN,PR and OMPR
               iwhich = 2 : Calculate S from P,Q,XN,PR and OMPR
               iwhich = 3 : Calculate XN from P,Q,S,PR and OMPR
               iwhich = 4 : Calculate PR and OMPR from P,Q,S and XN

     P <--> The cumulation from 0 to S of the binomial distribution.
            (Probablility of S or fewer successes in XN trials each
            with probability of success PR.)
            Input range: [0,1].

     Q <--> 1-P.
            Input range: [0, 1].
            P + Q = 1.0.

     S <--> The number of successes observed.
            Input range: [0, XN]
            Search range: [0, XN]

     XN  <--> The number of binomial trials.
              Input range: (0, +infinity).
              Search range: [1E-100, 1E100]

     PR  <--> The probability of success in each binomial trial.
              Input range: [0,1].
              Search range: [0,1]

     OMPR  <--> 1-PR
              Input range: [0,1].
              Search range: [0,1]
              PR + OMPR = 1.0

     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 PR + OMPR .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.
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