What Is EXPON.DIST in Google Sheets?
EXPON.DIST in Google Sheets is used to calculate the value of the exponential distribution function. It is helpful in determining the probability of a given event occurring within a certain period. The function has three parameters: x, lambda, and cumulative. By adjusting these parameters, you can model and analyze different types of exponential distributions to suit your data and analysis needs. It is usually used in scenarios where the time between events is randomly distributed.
For example, let us calculate the Probability Density Function (PDF) and Cumulative exponential distribution function for x = 0.6 and lambda = 8. Here, if the cumulative parameter is TRUE, the function returns the cumulative distribution function (CDF); if FALSE, it returns the probability density function (PDF). Let us see the results below. Thus, the EXPON.DIST in Google sheets is used to give the probabilities of times between the events. It is often used in reliability analysis and queuing theory.
Table of Contents
Key Takeaways
- The EXPON.DIST function calculates the exponential distribution which is useful for modeling time between events in a Poisson process.
- The syntax of the EXPON.DIST function is as follows =EXPON.DIST(x, lambda, cumulative)
- Here, x is the random variable, lambda, the rate parameter, and cumulative, is a logical value (we enter TRUE for CDF and FALSE for PDF).
- Some of the practical uses of the EXPON.DIST function in Google sheets include finding time between customer arrivals, finding a product’s lifetime, calculating the time of occurrence of an event, and so on.
Syntax
Here is the syntax for the EXPON.DIST function:
EXPON.DIST(x, lambda, cumulative)
- x: The value of the random variable. It represents the time or space for which you calculate the exponential distribution.
- lambda: The rate parameter of the distribution. It is a positive number.
- cumulative: A logical value that determines the type of the function. If TRUE, the function returns the cumulative distribution function (CDF); if FALSE, it returns the probability density function (PDF).
How To Use EXPON.DIST in Google Sheets?
As seen, we use EXPON.DIST in Google Sheets to calculate the exponential distribution, which can be used in many real-life scenarios. Let us look at how we can use this function with a simple example.
Step 1: Click on the cell where you want the result of the EXPON.DIST function to appear.
Step 2: Start typing the function directly into the cell B4. Suppose you want to calculate the probability density at x = 4 for an exponential distribution with a rate parameter (lambda) of 0.7. Start by typing =EXPON.DIST(.
=EXPON.DIST(
Step 3: Enter the x value (e.g., 2), followed by a comma. Enter the lambda value (e.g., 0.7), and enter TRUE for the cumulative distribution function (CDF) or FALSE for the probability density function (PDF). Close the parentheses.
=EXPON.DIST(B1, B2, B3)
Step 4: Press Enter: This will calculate the PDF value and display it in the selected cell.
From the Google Sheets Menu
Let us look at how to insert the function from the Google Sheets menu.
Step 1: First, go to the “Insert” option. Go to “Functions” and choose “Statistical.”
Step 2: Choose the EXPON.DIST function and enter the required arguments.
Difference Between PDF and CDF
Whenever we use the EXPON.DIST in Google sheets, we mention the cumulative parameter as TRUE or FALSE. Here, TRUE means the cumulative distribution function (CDF), and FALSE means the probability density function (PDF).
The probability density function assumes that the events occur at a constant rate on average over time. It shows the probability that a random variable will have a particular value.
The CDF shows the likelihood that a particular value will be less than or equal to a random variable. It is not a smooth curve, unlike the PDF.
Examples
You can effectively use the EXPON.DIST function in Google Sheets for various statistical and probability analyses. Let us look at some examples of how to calculate the exponential distribution under different everyday scenarios.
Example #1
The number of minutes between the time a defective product will appear in an assembly line can be modeled by exponential distribution.
In this Expon Dist Google Sheets example, let us suppose the number of hours between defective products appearing in an assembly line is every 50 minutes. If a product has just arrived, what is the probability that we will get another one within the next 30 minutes?
Step 1: Find the value of lambda and enter the value of x in the Google sheet.
Here λ = 1/50 = 0.02
Step 2: Now, as we are finding the probability density function, the value of the third argument is FALSE, entered in cell B3. Now, enter the following formula in B4
=EXPON.DIST(B1,B2,B3)
Step 3: Press Enter. You get the PDF value of 0.0109 or 1%.
Example #2 – Calculating the Probability Density Function
Let us look at some interesting practical examples for EXPON.DIST. We are looking at the customers entering a store on an average of every 6 minutes. Once a customer arrives, find the probability that another customer will arrive within the next four minutes.
Step 1: Here, we calculate the value of lambda as 1/ɥ, 1/6. Hence, we get the lambda value of 0.1667 when entered in cell B1.
Step 2: We must find the probability of a customer entering within 4 minutes. Hence, x = 4. Enter this value in cell B2.
Step 3: Now, to calculate the exponential distribution, enter the following formula in cell B4.
=EXPON.DIST(B2,B1,B3)
Here, FALSE represents calculating the PDF.
Step 4: Now, the probability that a customer will enter within 4 minutes is 0.08556 or 8.55%.
Thus, it is used to find the exponential distribution to model the time between independent events.
Example #3 – Calculating the Cumulative Distribution Function
An area is located in a flood-prone region and gets flooded from time to time. Suppose a flood occurs every 300 days on average. Immediately after a flood occurs, find the probability that the next flood will occur only after 400 days.
To solve this, we first find the value of lambda λ.
Here lambda = 1/300 = 0.00333
We are finding the occurrence of a flood after 400 days. So, x = 400.
Step 1: Here, we apply the formula with TRUE as we are finding the cumulative distribution function. So, enter the following formula in cell B4.
=EXPON.DIST(B2,B1,B3)
Step 2: Press Enter. You get the value of the CDF as 0.7364028619. It shows that the probability of the occurrence of a flood after 400 days is 73.6% approx.
Important Things To Note
- If the value of x or lambda is nonnumeric, EXPON.DIST returns the #VALUE! Error value. For non-integer values, it rounds them to the nearest integer.
- It is usually used in scenarios where the time between events is randomly distributed—some practical applications of EXPON.DIST in Google Sheets includes reliability analysis, where we can estimate the time of failure of a machine and predict the time until an event occurs, such as earthquakes, and so on.
Frequently Asked Questions (FAQs)
When the argument cumulative is set to TRUE, EXPON.DIST calculates the cumulative distribution function (CDF). It gives the probability that a random variable is less than or equal to x.
When the cumulative argument is set to FALSE, EXPON.DIST returns the probability density function (PDF). This value gives the probability that a variable takes on a specific value x.
• The #NUM! error occurs if lambda is less than or equal to 0.
• The #VALUE! error occurs if x or lambda is non-numeric, or if the cumulative is not a BOOLEAN value TRUE or FALSE.
BINOM.DIST is used to model the number of successes in a fixed number of independent Bernoulli trials, while EXPON.DIST is used to model the time between events in a Poisson process.
The BINOM.DIST is used in scenarios where you have a fixed number of trials with a binary outcome (success/failure), and you want to find the probability of certain number of successes. E.g., flipping a coin.
EXPON.DIST is used where events occur independently at a constant average rate. Examples include the time until a machine part fails It is a continuous probability distribution.
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