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 :