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 /
*λ*^{2} - Skewness = 2
- Kurtosis = 6

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

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

how to analyse my time series data using spss

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

Charles