Distribution Fitting Software & Articles

Exponential Distribution

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The Exponential distribution is used to model Poisson processes, which are situations in which an object initially in state A can change to state B with constant probability per unit time lambda. The time at which the state actually changes is described by an exponential random variable with parameter lambda.


- inverse scale parameter ()


Probability Density Function (PDF)

Exponential distribution PDF

Exponential Distribution Fitting

EasyFit allows to automatically or manually fit the Exponential distribution and 55 additional distributions to your data, compare the results, and select the best fitting model using the goodness of fit tests and interactive graphs. Watch the short video about EasyFit and get your free trial.

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Exponential Distribution Graphs and Properties

EasyFit displays all graphs and properties of the Exponential distribution, presenting the results in an easy to read & understand manner. EasyFit calculates statistical moments (mean, variance etc.), quantiles, tail probabilities depending on the distribution parameters you specify.

Random Numbers from the Exponential Distribution

You can easily generate random numbers from the Exponential distribution in a variety of ways:

  • directly from EasyFit
  • in Excel sheets using the worksheet functions provided by EasyFitXL
  • in your VBA applications using the EasyFitXL library

Excel Worksheet and VBA Functions

EasyFitXL enables you to use the following functions in your Excel sheets and VBA applications:

Function Name
ExpPdf Probability Density Function
ExpCdf Cumulative Distribution Function
ExpHaz Hazard Function
ExpInv Inverse CDF (Quantile Function)
ExpRand Random Numbers
ExpMean Mean
ExpVar Variance
ExpStdev Standard Deviation

Learn more: EasyFit Help on the Exponential distribution


The Exponential distribution is extensively used in reliability engineering to describe units that have a constant failure rate. It is also used to model:

  • the time between events that happen at a constant average rate (e.g. the time until the next phone call arrives);
  • the time until a radioactive particle decays, or the time between beeps of a geiger counter;
  • the distance between mutations on a DNA strand;
  • the distance between roadkill on a given street;
  • the interarrival times (i.e. the times between customers entering the system).