Non-Normal Distributions - Gamma Distribution
The Gamma distribution has the probability density function:
f(x) = (x/b)c-1 * e(-x/b) * [1/b Γ(c)] 0 <= x, b > 0, c > 0
where
| Γ | (Gamma) is the Gamma function |
| b | is the scale parameter |
| a | is the so-called shape parameter |
| 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 (inclusive) 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 Gamma distribution is fitted. Thus, the threshold value must be less than the smallest observed value.
Applications
The Gamma distribution is appropriate for the distribution of a quality characteristic that is the result of c independent events, which occur at a constant rate of Lambda=1/b. For example, if the failure of a component is the result of c independent failures of subcomponents (occurring at a constant rate of 1/b), then the time to failure will follow a Gamma distribution. Hahn and Shapiro (1967) point out that this distribution also often yields a good empirical fit, when no explicit theoretical model exists. For example, the time-to-failure for capacitors or the distribution of family income follows this distribution.