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math/
ml_distfit.pro
Routines
result = ML_NNL(P)hessian, name, param, correlresult = derivee2xy(name, xparam, nx, ny)ML_DISTFIT, X, Parm, Function_Name [, ConfRegion], FITA=FITA, LIKELIHOOD=LIKELIHOOD, LIKERANGE=LIKERANGE, CONSTRAINT=CONSTRAINTPerforms maximum likelihood fitting of a distribution.
Routine details
top source ML_DISTFIT
Math
ML_DISTFIT, X, Parm, Function_Name [, ConfRegion], FITA=FITA, LIKELIHOOD=LIKELIHOOD, LIKERANGE=LIKERANGE, CONSTRAINT=CONSTRAINT
Performs maximum likelihood fitting of a distribution.
Parameters
- X in
Array of input data values. This is passed straight to the user-supplied function, so complicated data structures that encompass multi-dimensional information for each data point can be used.
- Parm in
Variable containing initial guesses for parameters on input and best fit values on output.
- Function_Name in
Name of user-supplied function defining the distribution. The function must accept 2 arguments, X and Parm, and return a vector containing the likelihood values for each data point in X for the point in parameter space given by Parm. The likelihood must be normalized so that its total integral over all possible values of X is a constant, regardless of Parm (it makes the most sense to normalize this integral to unity, but that is not strictly required).
- ConfRegion optional
Lower and upper error estimates of each parameter, marginalized over the other parameters. I.e. ConfRegion[*,0] returns [low0,high0] where low0 <= parm[0] <= high0
Keywords
- FITA in
Vector of which parameters should be fit (1 for each parameter to be fit, 0 for each parameter to be held constant). THERE IS A BUG IN THE IMPLEMENTATION. DO NOT USE.
- LIKELIHOOD in
Outputs an M-dimensional array with the likelihood values over the range of parameter space probed. M is the number of parameters that are fitted, which can be less than the length of Parm if FITA is used.
- LIKERANGE in
2xM dimensional array containing the bounds of the LIKELIHOOD array.
- CONSTRAINT in
Name of a user-supplied function that takes a parameter vector as input and returns 1 if the point in parameter space is permitted and 0 if it is not permitted.
Examples
Fit the width and offset of a zero-centered Gaussian plus constant
distribution.
First, define the distribution function:
FUNCTION gauss_plus_const, X, Parm
; Parm[0]=constant offset, Parm[1]=width sigma
vmax = 2000.
normalization = Parm[1]*SQRT(!pi/2.)*ERF(vmax/(SQRT(2.)*Parm[1])) $
+ vmax*Parm[0]
distribution = EXP(-X^2/(2.*Parm[1]^2)) + Parm[0]
RETURN, distribution/normalization
END
Then generate some data that should adhere to this distribution,
with a width of 250 and a constant term containing 10% of the points.
IDL> data = [250*RANDOMN(seed, 900), 4000*(RANDOMU(seed, 100) - 0.5)]
And finally fit the distribution:
IDL> parm = [0., 100.]
IDL> ML_DISTFIT, data, parm, 'gauss_plus_const', parmconf
IDL> PRINT, parm
0.0625345 223.94577
IDL> PRINT, parmconf
0.057511609 0.0973332
207.087 243.841
Author information
- History:
Written by: Jeremy Bailin. Thanks to the writers of MLEfit.pro, which furnished the Hessian routines, Peder Norberg for useful discussions, and Nicolas Petitclerc for additional testing. 27 Nov 2008 Release in JBIU.
File attributes
| Modification date: | Tue Sep 14 14:25:11 2010 |
| Lines: | 299 |