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#Statistical

EXPON.DIST

Excel Functions

Get the PDF or CDF of the exponential distribution.

Syntax

EXCEL 
=EXPON.DIST(x, lambda, cumulative)

Arguments

Parameter Description
x The value at which to evaluate the distribution (must be ≥ 0).
lambda The rate parameter of the distribution (must be > 0).
cumulative A logical value that determines the form of the function. If TRUE, returns the cumulative distribution function; if FALSE, returns the probability density function.

Return Value

A number representing the probability density or cumulative probability value.

Details

The EXPON.DIST function calculates values for the exponential distribution, which is a continuous probability distribution used to model the time between events in a Poisson process. The exponential distribution is characterized by its "memoryless" property, meaning the probability of an event occurring in the next time interval is independent of how much time has already elapsed. This makes it ideal for modeling systems with constant event rates, such as radioactive decay, customer arrivals, and equipment failures with no aging effects. Suppose we are analyzing customer arrivals at a coffee shop. Historical data suggests that customers arrive following a Poisson process with an average rate of 12 customers per hour. This scenario is a good example of the exponential distribution because i

Examples

Example #1 - Customer arrival analysis

To calculate the probability that the next customer will arrive within 10 minutes, we can use the cumulative distribution function (CDF):

EXCEL 
=EXPON.DIST(10/60, 12, TRUE) // returns 0.865
Example #1 - Customer arrival analysis

To find the probability that the next customer arrives after 10 minutes, subtract the CDF from 1:

EXCEL 
=1-EXPON.DIST(10/60, 12, TRUE) // returns 0.135
Example #2 - Effect of rate parameter (lambda)

For example, consider different coffee shops with varying customer traffic levels. All follow an exponential distribution, but they have different rat

EXCEL 
=EXPON.DIST(5/60,  6, TRUE)  // returns 0.393
=EXPON.DIST(5/60, 12, TRUE)  // returns 0.632
=EXPON.DIST(5/60, 24, TRUE)  // returns 0.865
Example #3 - Cumulative vs. probability density
EXCEL 
=EXPON.DIST(1.5, 2.0, FALSE) // returns 0.100 (PDF)
Example #3 - Cumulative vs. probability density
EXCEL 
=EXPON.DIST(1.5, 2.0, TRUE)  // returns 0.950 (CDF)
Example #3 - Cumulative vs. probability density

Using the CDF, you can easily calculate probabilities for different scenarios. To calculate the probability of an event occurring below a threshold:

EXCEL 
=EXPON.DIST(threshold, lambda, TRUE)

See Also

WEIBULL.DIST GAMMA.DIST NORM.DIST