Distribution Fitting Articles |
Software
Exponential Distribution
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.
Parameters
- inverse scale parameter
(
)
Domain
Probability Density Function (PDF)
Exponential Distribution Fitting
EasyFit allows to automatically or manually fit the Exponential distribution and 40 additional distributions to your data, compare the results, and select the best fitting model using the goodness of fit tests and interactive graphs.
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:
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 |
Applications
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).