negative hypergeometric random variable

fX(x)=(x+b-1x)(W+B-b-xW-x)(W+BW), x={0,1,,W}


  • W{1,2,}

  • B{1,2,}

  • b{1,2,,B}




  1. 1.

    X represents the number of “special” items (from the W special items) present before the bth object from a population with B items.

  2. 2.

    The expected valueMathworldPlanetmath of X is noted as E[X]=WbB+1

  3. 3.

    The varianceMathworldPlanetmath of X is noted as Var[X]=Wb(B-b+1)(W+B+1)(B+2)(B+1)2

Approximation techniques:

If (x2)W and (b2)B then X can be approximated as a negative binomial random variable with parameters r=b and p=WW+B. This approximation simplifies the distributionPlanetmathPlanetmath by looking at a system with replacement for large values of W and B.

Title negative hypergeometric random variable
Canonical name NegativeHypergeometricRandomVariable
Date of creation 2013-03-22 12:25:05
Last modified on 2013-03-22 12:25:05
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 16
Author alozano (2414)
Entry type Definition
Classification msc 62E15
Synonym negative hypergeometric distribution