help mata mm_cebinomial()
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Title

    mm_cebinomial() -- Conditional expectation of a binomial distributed
                       random variable


Syntax

        real matrix mm_cebinomial(n, k, p)

    where

        n:  real matrix n
        k:  real matrix k
        p:  real matrix p


Description

    mm_cebinomial() returns the expected value of a binomial distributed
    random variable conditional on the variable being equal to k or larger.
    That is, mm_cebinomial() returns

        E(X|X>=k)

    where

        X ~ B(n, p)

    and n is the number of trials and p is the success probability.

    When n, k, and p are not scalar, mm_cebinomial() returns
    element-by-element results. n, k, and p are required to be r-conformable
    (see help [M-6] glossary).

Remarks

    The expectation of X ~ B(n, p) conditional on X>=k may be written as

        E(X|X>=k) = k + [ P(X>=k+1) + ... + P(X=n) ] / P(X>=k)

    where P(X>=k) is the probability of k or more successes, which is
    computed as Binomial(n, k, p) (see [M-5] normal()).


Conformability

    mm_cebinomial(n,k,p) requires n, k, and p be r-conformable (see help
    [M-6] glossary). Returned is a matrix of max(argument rows) rows and
    max(argument columns) columns containing element-by-element calculated
    results.


Diagnostics

    mm_cebinomial() returns missing if any of the arguments are missing.

    mm_cebinomial() returns missing if arguments are out of range (p>1, p<0,
    n<=0, k<0, or k>n) or if n or k are non-integer.


Source code

    mm_cebinomial.mata


Author

    Ben Jann, ETH Zurich, jann@soz.gess.ethz.ch


Also see