RT_weibest

(rtools/RT_weibest.m)

Function Synopsis

[a,mu] = RT_weibest(x,fast)

Help text

function [a,mu] = RT_weibest(x, fast)

 Estimates the shape parameters A and mean MU of a Weibull distribution 
 that best fits the data in X.

 Note that this is not the `usual' form for the Weibull, which uses a
 non-linear scale parameter (b). For simulation, explicit definition
 in terms of the mean MU is more meaningful. For theoretical
 manipulation of equations, you're better off using b though.
 The conversion from b is MU = a^(-b) * gamma(1 + b) which is performed in
 RT_weibest.m

 A Weibull distribution in Amplitude, is also a Weibull distribution
 in Intensity. This `power law invariance' is useful for simulation, but
 it causes confusion over whether the `usual' shape parameter (c) refers
 to Amplitude _or_ Intensity in radar texts. It most often refers to Amplitude,
 but this toolbox uses Intensity as the natural measure, so check your
 conventions.

 The form used is such that the mean value is MU and larger
 A is closer to a Gaussian distribution. A = 1
 is equivalent to an exponential distribution.

 The method uses an initial least squares fit to Weibull paper.
 It is not the Maximum Likelihood Solution, but A is reasonably
 accurate (MU is quite poor). To return this estimate, set the
 FAST flag.

 With FAST unset or 0, a numerical MLE solution is generated (slow)
 but this can fail when a is too small (a ~< 0.1).

 Source: Direct evaluation of linear approximation, improvement
         via a call to RT_weibLL.m

 Part of the Matlab Radar Toolbox v0.11 by Glen Davidson at www.radarworks.com
 Please acknowledge use of this toolbox in any publication or software.
 This header must be retained in any derivative work

Cross-Reference Information

RT_weibLL                     rtools/RT_weibLL.m

weibull_demo                  rtools/weibull_demo.m