Non-Normal Distributions - Rayleigh Distribution
The Rayleigh distribution has the probability density function:
f(x) = x/b2 * e^[-(x2/2b2)]
0 <= x < ∞b > 0
where
| b | is the scale parameter |
| e | is the base of the natural logarithm, sometimes called Euler's e (2.71...) |
Threshold (location) parameter
The valid range for the Rayleigh 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 Rayleigh distribution is fitted. Thus, the threshold value must be less than the smallest observed value.
Applications
If two independent variables y1 and y2 are independent from each other and normally distributed with equal variance, then the variable x=Ö(y12+ y22) will follow the Rayleigh distribution. Thus, an example (and appropriate metaphor) for such a variable would be the distance of darts from the target in a dart-throwing game, where the errors in the two dimensions of the target plane are independent and normally distributed.
Estimation
Maximum likelihood parameter estimates for the Rayleigh distribution are computed as described in Evans, Hastings, and Peacock (1993).