# Hypergeometric Distribution in R Programming

Hypergeometric Distribution in R Language is defined as a method that is used to calculate probabilities when sampling without replacement is to be done in order to get the density value.

In R, there are 4 built-in functions to generate Hypergeometric Distribution:

• dhyper()
`dhyper(x, m, n, k)`
• phyper()
`phyper(x, m, n, k)`
• qhyper()
`qhyper(x, m, n, k)`
• rhyper()
`rhyper(N, m, n, k)`

where,

x: represents the data set of values
m: size of the population
n: number of samples drawn
k: number of items in the population
N: hypergeometrically distributed values

#### Functions To Generate Hypergeometric Distribution

##### dhyper() Function

It is defined as Hypergeometric Density Distribution used in order to get the density value.

Syntax:

```dhyper(x_dhyper, m, n, k)
```

Example 1:

 `  `  `# Specify x-values for dhyper function ` `x_dhyper <- ``seq``(0, 22, by = 1.2) ` ` `  `# Apply dhyper function ` `y_dhyper <- ``dhyper``(x_dhyper, m = 45, n = 30, k = 20)    ` `  `  `# Plot dhyper values ` `plot``(y_dhyper)  `

Output:

##### phyper() Function

Hypergeometric Cumulative Distribution Function used estimating the number of faults initially resident in a program at the beginning of the test or debugging process based on the hypergeometric distribution and calculate each value in x using the corresponding values.

Syntax:

`phyper(x, m, n, k)`

Example 1:

 `# Specify x-values for phyper function ` `x_phyper <- ``seq``(0, 22, by = 1)     ` `   `  `# Apply phyper function ` `y_phyper <- ``phyper``(x_phyper, m = 40, n = 20, k = 31)   ` ` `  `# Plot phyper values ` `plot``(y_phyper)   `

Output:

##### qhyper() Function

It is basically Hypergeometric Quantile Function used to specify a sequence of probabilities between 0 and 1.

Syntax:

`qhyper(x, m, n, k)`

Example 1:

 `# Specify x-values for qhyper function ` `x_qhyper <- ``seq``(0, 1, by = 0.02)         ` ` `  `# Apply qhyper function ` `y_qhyper <- ``qhyper``(x_qhyper, m = 49, n = 18, k = 30)     ` ` `  `# Plot qhyper values ` `plot``(y_qhyper) `

Output:

##### rhyper() Function

It generally refers to generating random numbers function by specifying a seed and sample size.

Syntax:

`rhyper(x, m, n, k)`

Example 1:

 `# Set seed for reproducibility ` `# Specify sample size ` `set.seed``(400)                                  ` `N <- 10000                                       ` ` `  `# Draw N hypergeometrically distributed values ` `y_rhyper <- ``rhyper``(N, m = 50, n = 20, k = 30)  ` `y_rhyper          ` ` `  `# Plot of randomly drawn hyper density ` `hist``(y_rhyper,                                           ` `     ``breaks = 50, ` `     ``main = ``""``) `

Output :

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