Generating Random Numbers Until Some Condition Is Met in R

R Language is mainly used for machine learning, statistics, and data analysis. Objects, functions, and R packages can easily be created by R. However we can use this language for other purposes like generating random numbers until a number greater than 0.9 is generated. We can do that using loops as R supports three kinds of loops.

Loops

To solve this problem first we need to understand the Concepts of Loops in R– R is very good at performing repetitive tasks. If we want a set of operations to be repeated several times we use what’s known as a loop. When you create a loop, R will execute the instructions in the loop a specified number of times or until a specified condition is met.

There are three main types of loops in R

For Loop: With the for loop we can execute a set of statements, once for each item in a vector, array, list, etc.
While Loop: While Loop can execute a block of code as long as a specified condition is reached.
Repeat Loop: This loop can execute a block of code multiple times, however the repeat loop does not have any condition to terminate the loop. You need to put an exit condition implicitly with a break statement inside the loop.

Uniform Distribution

A uniform distribution is a probability distribution where each value in the range from a to b has an equal chance of being selected. The ‘runif()’ function is used to generate sequence of random numbers in 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)

Generate random numbers using For Loop

# initialize a variable to store the random number
x <- 0
 
# use a for loop to generate random numbers from a uniform distribution

for (i in 1:100) {

  # generate a random number between 0 and 1

  x <- runif(1)

  # print the random number

  print(x)

  # check if the random number is greater than 0.9

  if (x > 0.9) {

    # break the loop

    break

  }
}

Output

[1] 0.5482922
[1] 0.81156
[1] 0.3938314
[1] 0.9569094

1. First, it initializes a variable called x and assigns it the value of 0. This variable will store the random number that will be generated in each iteration of the loop.
2. Next, it uses a for loop to repeat a block of code 100 times. The for loop has a variable called i that takes values from 1 to 100 in each iteration. The for loop is enclosed by curly braces {} that indicate the start and end of the loop body.
3. Inside the loop body, the code does the following:
It generates a random number between 0 and 1 using the runif function, which takes one argument: the number of random numbers to generate. In this case, it is 1. The random number is assigned to the variable x.
It prints the value of x using the print function, which displays the output on the console.
It checks if the value of x is greater than 0.9 using the if statement, which evaluates a logical condition and executes a block of code if it is true. The if statement is also enclosed by curly braces {} that indicate the start and end of the conditional block.
Inside the conditional block, the code uses the break statement, which terminates the execution of the loop and jumps out of it.
After the loop ends, the code stops running.

Generate random numbers using While Loop

1. First, it initializes a variable called `x` and assigns it the value of 0. This variable will store the random number that will be generated in each iteration of the loop.

2. Next, it uses a `while` loop to repeat a block of code as long as a condition is true. The `while` loop has a condition that checks if the value of `x` is less than or equal to 0.9. The `while` loop is enclosed by curly braces `{}` that indicate the start and end of the loop body.

3. Inside the loop body, the code does the following:

a. It generates a random number between 0 and 1 using the `runif` function, which takes one argument: the number of random numbers to generate. In this case, it is 1. The random number is assigned to the variable `x`.

b. It prints the value of `x` using the `print` function, which displays the output on the console.

4. After the loop ends, the code stops running.

# initialize a variable to store the random number
x <- 0
 
# use a while loop to generate random numbers from a uniform distribution

while (x <= 0.9) {

  # generate a random number between 0 and 1

  x <- runif(1)

  # print the random number

  print(x)
}

Output

[1] 0.1120839
[1] 0.4356025
[1] 0.02041804
[1] 0.5944996
[1] 0.7476459
[1] 0.3314883
[1] 0.4432616
[1] 0.8747775
[1] 0.2771189
[1] 0.4299433
[1] 0.2105656
[1] 0.2088417
[1] 0.7823486
[1] 0.3891303
[1]...

Assign the value while (x <= 0.9).
This is a while loop that continues executing as long as the value of x is less than or equal to 0.9.
x <- runif(1):
In each iteration of the loop, a random number between 0 and 1 is generated using the runif() function.
The 1 argument specifies that a single random number should be generated.
print(x):
After generating the random number, the value of x is printed to the console using the print() function.

Generate random numbers using Repeat Loop

1. First, it initializes a variable called `x` and assigns it the value of 0. This variable will store the random number that will be generated in each iteration of the loop.

2. Next, it uses a `repeat` loop to repeat a block of code indefinitely. The `repeat` loop is enclosed by curly braces `{}` that indicate the start and end of the loop body.

3. Inside the loop body, the code does the following:

b. It prints the value of `x` using the `print` function, which displays the output on the console.

c. It checks if the value of `x` is greater than 0.9 using the `if` statement, which evaluates a logical condition and executes a block of code if it is true. The `if` statement is also enclosed by curly braces `{}` that indicate the start and end of the conditional block.

d. Inside the conditional block, the code uses the `break` statement, which terminates the execution of the loop and jumps out of it.

4. After the loop ends, the code stops running.

# initialize a variable to store the random number
x <- 0
 
# use a repeat loop to generate random numbers from a uniform distribution

repeat {

  # generate a random number between 0 and 1

  x <- runif(1)

  # print the random number

  print(x)

  # check if the random number is greater than 0.9

  if (x > 0.9) {

    # break the loop

    break

  }
}

Output
[1] 0.288129
[1] 0.5386403
[1] 0.1097055
[1] 0.6238026
[1] 0.9355597

x <- 0: Initialize the variable x with a value of 0.
repeat: This initiates an infinite loop using the repeat keyword. The loop will keep running until the break statement is encountered.
Inside the loop:
x <- runif(1): Generate a random number between 0 and 1 using the runif() function. This function returns a random number from a uniform distribution.
print(x): Print the generated random number to the console.
if (x > 0.9) : Check if the generated random number is greater than 0.9.
If the condition is true, the break statement is executed, which terminates the repeat loop.
If the condition is false, the loop continues to generate and print random numbers.

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