[Help-gsl] Problem with gsl_multifit_fdfsolver

[johann.zoffmann]

Hi,

i want use the gsl-solver  lmsder for the follwing model:

fi = Yi - yi
Yi = log(gsl_cdf_gamma_Q(t,a,b)

i use a numerical approximation for the derivatives of a and b: 
da = a*0,01
db = b*0,01
dfi/da = log(((gsl_cdf_gamma_Q(t,a+da,b)-gsl_cdf_gamma_Q(t,a-da,b))/2*da) 
dfi/db = log(((gsl_cdf_gamma_Q(t,a,b+db)-gsl_cdf_gamma_Q(t,a,b-db))/2*db) 

my problemes are:
1. solver calculate negative a and b values - negativ values are not allowed in 
the gamma-distribution function
2. good starting values lead to good results but how can I determine good 
starting values at runtime ? 

    for example - fitting for a particular dataset (have dertermined a, b with 
common statistic software)
    start values for a = 0.1 b = 3.0 result: a = 0.17874; b = 3.11659  -> 
chisq/dof = 0.29  = perfect result
    
    start for the same dataset with a = 0.1 b = 3.5 => a = -0.00151 b = 3.56884 
- the iteration has not convergend yet

I tried the following solutions:
1. if a or b is negativ set value for fi to 0.0 in gamma_f - otherwise i have 
to stop the iteration with a function 
    error-code
2. if a or b is negativ set value for Jacobian matrix J(i,j) to 0.0 in gamma_df

Can anybody help me ?

Thanks
johann