Syntax. EXPON.DIST(x,lambda,cumulative)
Definition. This function returns the probabilities of an exponential distributed random variable. Use EXPON.DIST() to model the time between events. For example, you can calculate the probability that a call center will receive a call after three minutes, although the hourly average for incoming calls is three minutes.
Arguments
x (required). The value of the function.
lambda (required). The value that is passed.
cumulative (required). The logical value. If cumulative is TRUE, the cumulative distribution is returned; otherwise, the probability density function is returned.
Note
If x or lambda isn’t a numeric value, the EXPON.DIST() function returns the #VALUE! error.
If x is less than 0, the function returns the #NUM! error.
If lambda is less than or equal to 0, the function returns the #NUM! error.
Background. These functions have a special characteristic: Over equal intervals, the function value changes by the same factor. These functions are useful for describing growth and decaying processes for which the value changes by the same factor in equal time intervals. The inverse functions are called logarithms. The exponential function x = ex with Euler’s number e is the basis (see Figure 12-38).
As mentioned previously, the EXPON.DIST() function returns the probabilities of independent events, such as the time it takes an ATM machine to disperse money or other waiting times.
Here is another example: If a support call center receives a call every three minutes, you can use this function to calculate the probability that the phone will ring after only one minute. This is called an exponential random variable, because the ringing of the phone and the time are independent from each other. The EXPON.DIST() function calculates the probability that this will happen.
The equation for the probability density is:
f(x; λ) = λe–λx
The equation for the distribution function is:
F(x; λ) = 1 – e–λx
Example. Let’s use with the example of the call center. Assume that you operate a call center for a printer manufacturer. The call center is open 24 hours a day, seven days a week. You want to analyze the call pattern and count the incoming calls every hour over one day. This means that the time interval is 60 minutes.
The recorded calls result in the statistics shown in Figure 12-39.
After you have calculated the average of all incoming calls, you can make the following statements:
Every hour, an average of 21 calls come in.
This means that, on average, every three minutes a customer calls.
Now you want to know the probability that a customer will call after two minutes. To find out, you use the EXPON.DIST() function. What information do you have to enter for the arguments?
x = 2, because we want to calculate the probability for a call after 2 minutes.
Lambda = 3, because this is the mean value of events per interval and therefore the passed value.
cumulative = TRUE, because in our example the cumulative distribution should be returned.
Figure 12-40 shows the result from the calculation of the probability with the EXPON.DIST() function.
The probability for a call coming in after two minutes is 99 percent.
As you can see in Figure 12-40, the probability decreases as the time interval decreases. This means that the probability for a call to come in after 0.2 minutes (12 seconds) is only 45 percent.