Exponential Distribution

The exponential distribution can be used to determine the probability that it will take a given number of trials to arrive at the first success in a Poisson distribution; i.e. it describes the inter-arrival times in a Poisson process. It is the continuous counterpart to the geometric distribution, and it too is memoryless.

Definition 1: The exponential distribution has probability density function (pdf) given by

Excel Function: Excel provides the following function for the exponential distribution:

EXPONDIST(x, λ, cum) where λ is the parameter in Definition 1 and cum = TRUE or FALSE

EXPONDIST(x, λ, FALSE) =  f(x) where f is the pdf value at x as defined above

EXPONDIST(x, λ, TRUE) = F(x) where F is the cumulative distribution function value at x corresponding to f above

In Excel 2010, 2013 and 2016 there is the additional function EXPON.DIST which is equivalent to EXPONDIST.

Observation: The exponential distribution is equivalent to the gamma distribution with α = 1 and β = 1/λ. Thus, EXPONDIST(x, λ, cum) = GAMMADIST(x, 1, 1/λ, cum).

There is no EXPON.INV(p, λ) function in Excel, but GAMMA.INV(p, 1, 1/λ) can be used instead.

The cumulative distribution function is

Other key statistical properties are:

• Mean = 1 / λ
• Median = ln 2/λ
• Mode = 0
• Range = [0, ∞)
• Variance = 1 / λ2
• Skewness = 2
• Kurtosis = 6

10 Responses to Exponential Distribution

1. nwabunor says:

how to analyse my time series data using spss

• Charles says:

Sorry, but I don’t use SPSS and so can’t advise you about that. The website is oriented towards statistics using Excel.
Charles

2. umar says:

how do I generate an expected values for Chi square goodness of fit using negative exponential distribution in excel

• Charles says:

If you are using the Chi-square goodness of fit test to check whether your data is a good fit for a negative exponential distribution, you can follow the approach shown in Example 4 of the webpage http://www.real-statistics.com/chi-square-and-f-distributions/goodness-of-fit/.
This Example tests the fit for a Poisson distribution. Use the EXPON.DIST formula instead of the POISSON formula.
Charles

3. aghaee says:

Dear frinds
Give me help
I need a real data set in any field that have exponential distribution.
size of data should be at least 300

• Charles says:

Sorry, but I don’t have such real data.
Charles

if I have bivariate case of exponential distribution How compute skeness & kurtosis
in Matlab or Rpackage

thank you

• Charles says:

Sorry, but I don’t use Matlab or R. This website focuses on Excel.
Charles