The runif() function

The runif() function generates random numbers from a uniform distribution. A uniform distribution is a distribution in which all values are equally likely. The runif() function takes three arguments:

• n: the number of random numbers to generate
• min: the lower bound of the distribution
• max: the upper bound of the distribution

The default values for min and max are 0 and 1, respectively.

Here is an example of how to use the runif() function to generate 10 random numbers from a uniform distribution between 0 and 1:

set.seed(123)
r <- runif(10)

Output:

print(r)

 [1] 0.2875775 0.7883051 0.4089769 0.8830174 0.9404673 0.0455565 0.5281055
 [8] 0.8924190 0.5514350 0.4566147

The runif() function can also be used to generate random numbers from other distributions, such as the normal distribution, the Poisson distribution, and the binomial distribution.

The punif() function

The punif() function calculates the cumulative probability density function (CDF) of the uniform distribution. The CDF is the probability that a random variable will be less than or equal to a certain value.

The punif() function takes three arguments:

• x: the value at which to calculate the CDF
• min: the lower bound of the distribution
• max: the upper bound of the distribution

Here is an example of how to use the punif() function to calculate the CDF of a uniform distribution between 0 and 1 at the value 0.5:

set.seed(123)
p <- punif(0.5, min = 0, max = 1)

Output:

print(p)

[1] 0.5

This means that there is a 50% chance that a random variable from this distribution will be less than or equal to 0.5.

The dunif() function

The dunif() function calculates the probability density function (PDF) of the uniform distribution. The PDF is the probability that a random variable will be equal to a certain value.

The dunif() function takes three arguments:

• x: the value at which to calculate the PDF
• min: the lower bound of the distribution
• max: the upper bound of the distribution

Here is an example of how to use the dunif() function to calculate the PDF of a uniform distribution between 0 and 1 at the value 0.5:

set.seed(123)
d <- dunif(0.5, min = 0, max = 1)

Output:

print(d)

This means that the probability of a random variable from this distribution being equal to 0.5 is 1.

The quinf() function

The quinf() function calculates the quantile function of the uniform distribution. The quantile function is the inverse of the CDF. It takes a probability as an input and returns the value that has that probability.

The quinf() function takes two arguments:

• p: the probability
• min: the lower bound of the distribution
• max: the upper bound of the distribution

Here is an example of how to use the quinf() function to calculate the quantile of a uniform distribution between 0 and 1 at the probability 0.5:

set.seed(123)
q <- qunif(0.5, min = 0, max = 1)

Output:

print(q)

[1] 0.5

This means that there is a 50% chance that a random variable

If you want to easily see different versions of the uniform distribution then you can either code them out or use the TidyDensity package. Let’s take a quick look.

pacman::p_load(TidyDensity)

n <- 5000

tidy_uniform(.n = n) |>
  tidy_autoplot()

With TidyDensity

Now different variations can be visualized with the following workflow:

tidy_multi_single_dist(
  .tidy_dist = "tidy_uniform",
  .param_list = list(
    .n = n,
    .min = 0,
    .max = c(1,5,10),
    .num_sims = 5
  )
) |>
  tidy_multi_dist_autoplot()

Voila!