# Continuous Uniform Distribution in R

The continuous uniform distribution is also referred to as the probability distribution of any random number selection from the continuous interval defined between intervals a and b. A uniform distribution holds the same probability for the entire interval. Thus, its plot is a rectangle, and therefore it is often referred to as Rectangular distribution. Here we will discuss various functions and cases in which these functions should be used to get a required probability.

For uniform distribution, we first need a randomly created sequence ranging between two numbers. The runif() function in R programming language is used to generate a sequence of random following the uniform distribution.

Syntax:runif(n, min = 0, max = 1)

Parameter:

- n= number of random samples
- min=minimum value(by default 0)
- max=maximum value(by default 1)

**Example:**

## R

`print` `(` `"Random 15 numbers between 1 and 3"` `)` `runif` `(15, min=1, max=3) ` |

**Output**

[1] “Random 15 numbers between 1 and 3”

[1] 1.534 1.772 1.027 1.765 2.739 1.681 1.964 2.199 1.987 1.372 2.655 2.337 2.588 1.216 2.447

### Quantile for a probability

By a quantile, we mean the fraction (or percent) of points below the given value. qunif() method is used to calculate the corresponding quantile for any probability (p) for a given uniform distribution. To use this simply the function had to be called with the required parameters.

Syntax:qunif(p, min = 0, max = 1)

Parameter :

- p – The vector of probabilities
- min , max – The limits for calculation of quantile function

**Example 1:**

## R

`min <- 0` `max <- 40` ` ` `print ` `(` `"Quantile Function Value"` `)` ` ` `# calculating the quantile function value` `qunif` `(0.2, min = min, max = max)` |

**Output**

[1] “Quantile Function Value”

[1] 8

The x values can be specified in the form of a sequence of vectors using the seq() method in R. The corresponding y positions can be calculated.

**Example 2:**

## R

`min <- 0` `max <- 1` ` ` `# Specify x-values for qunif function` `xpos <- ` `seq` `(min, max , by = 0.02) ` ` ` `# supplying corresponding y coordinations` `ypos <- ` `qunif` `(xpos, min = 10, max = 100) ` ` ` `# plotting the graph ` `plot` `(ypos) ` |

**Output**

### Probability Density Function

dunif() method in R programming language is used to generate density function. It calculates the uniform density function in R language in the specified interval (a, b).

Syntax:dunif(x, min = 0, max = 1, log = FALSE)

Parameter:

- x: input sequence
- min, max= range of values
- log: indicator, of whether to display the output values as probabilities.

The result produced will be for each value of the interval. Hence, a sequence will be generated.

**Example 1:**

## R

`# generating a sequence of values` `x <- 5:10` `print ` `(` `"dunif value"` `)` ` ` `# calculating density function` `dunif` `(x, min = 1, max = 20)` |

**Output**

[1] “dunif value”

[1] 0.05263158 0.05263158 0.05263158 0.05263158 0.05263158 0.05263158

All values are equal and this is the reason why it is called uniform distribution. Let us plot it for a better picture.

**Example 2: **

## R

`min <- 0` `max <- 100` ` ` `# Specify x-values for qunif function` `xpos <- ` `seq` `(min, max , by = 0.5) ` ` ` `# supplying corresponding y coordinations` `ypos <- ` `dunif` `(xpos, min = 10, max = 80) ` ` ` `# plotting the graph ` `plot` `(ypos , type=` `"o"` `) ` |

**Output**

### Cumulative probability distribution

The punif() method in R is used to calculate the uniform cumulative distribution function, this is, the probability of a variable X taking a value lower than x (that is, x <= X). If we need to compute a value x > X, we can calculate 1 – punif(x).

**Syntax:**

punif(q, min = 0, max = 1, lower.tail = TRUE)

All the independent probabilities that satisfy the comparison condition will be added.

**Example:**

## R

`min <- 0 ` `max <- 60` ` ` `# calculating punif value` `punif ` `(15 , min =min , max = max)` |

**Output**

[1] 0.25

**Example:**

## R

`min <- 0 ` `max <- 60` ` ` `# calculating punif value` `punif ` `(15 , min =min , max = max, lower.tail=` `FALSE` `)` |

**Output**

[1] 0.75