Non-Normal Distributions - Exponential Distribution

The exponential or negative exponential distribution has the probability density function:

f(x) = λ * e-λx
 0 <= x < ∞, λ > 0

where

λ (Lambda) is an exponential function parameter (an alternative parameterization is scale parameter b=1/λ)
e is the base of the natural logarithm, sometimes called Euler's e (2.71...)

Threshold (location) parameter

The range of this distribution is from 0 to infinity. Instead of 0 (zero), Statistica allows you to enter a different value for the lowest threshold (location) parameter; that value will be subtracted from the data values before the exponential distribution is fitted. Thus, the threshold value must be less than the smallest observed value.

Applications

The most common application of this distribution is to situations where one measures time-to-failure of a component, and where the failure rate is assumed to be constant over time.

Estimation

The unbiased maximum likelihood parameter estimate for b (=1/λ) is the overall mean.