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Continuous Uniform Distribution in R

  • Last Updated : 06 Jun, 2021

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




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