Cdf.Hypergeometric Method

CdfHypergeometric Method

Evaluates the hypergeometric cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double Hypergeometric(
	int k,
	int sampleSize,
	int defectivesInLot,
	int lotSize
)

Public Shared Function Hypergeometric ( 
	k As Integer,
	sampleSize As Integer,
	defectivesInLot As Integer,
	lotSize As Integer
) As Double

public:
static double Hypergeometric(
	int k, 
	int sampleSize, 
	int defectivesInLot, 
	int lotSize
)

static member Hypergeometric : 
        k : int * 
        sampleSize : int * 
        defectivesInLot : int * 
        lotSize : int -> float

Parameters

k: Type: SystemInt32
An int, the argument at which the function is to be evaluated.
sampleSize: Type: SystemInt32
An int, the sample size, n.
defectivesInLot: Type: SystemInt32
An int, the number of defectives in the lot, m.
lotSize: Type: SystemInt32
An int, the lot size, l.

Return Value

Type: Double
A double, the probability that a hypergeometric random variable takes a value less than or equal to k.

Remarks

Method Cdf.Hypergeometric evaluates the distribution function of a hypergeometric random variable with parameters n, l, and m. The hypergeometric random variable X can be thought of as the number of items of a given type in a random sample of size n that is drawn without replacement from a population of size l containing m items of this type. The probability function is

$\Pr\left({X=j}\right)=\frac{{\left( {_j^m }\right)\left({_{n-j}^{l-m}}\right)}}{{\left({_n^l}\right)}} {\rm{for}}\,\,j=i,\;i+1,\,\,i+2,\;\ldots,\;\min\left({n,m}\right)$

where $i={\rm max}(0,n-l+m)$ .

If k is greater than or equal to i and less than or equal to $\min (n, m)$ , Cdf.Hypergeometric sums the terms in this expression for j going from i up to k. Otherwise, Cdf.Hypergeometric returns 0 or 1, as appropriate. So, as to avoid rounding in the accumulation, Cdf.Hypergeometric performs the summation differently depending on whether or not k is greater than the mode of the distribution, which is the greatest integer less than or equal to .

Reference

Cdf Class

Imsl.Stat Namespace

Other Resources

Example