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

Exponential distribution pdf

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

Exponential distribution function

Other key statistical properties are:

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

4 Responses to Exponential Distribution

  1. umar says:

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

  2. 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

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