Re: Installation of Rb-GSL setup config problems

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Dear Ara,
 
well thank you very much again.
Actually, I am trying to find parameter values for statistical  distributions 
from data, i.e.,
you have, say, a normal distribution, and some measured data that are  
distributed
according to it, but you don't know the mean and variance parameters.
Then, one can solve some equations called maximum likelihood equations for  
that.
I was writing a Ruby script to do that. I wanted it to be able to find  
parameters for
several well-known distributions. One of these is a lesser well-known one,  
the
Cauchy distribution, which is sometimes used to model random events  where
extremely high values have a higher probability than if the data were  
distributed
according to the normal distribution. Some people claim that, e.g., natural  
disasters
generate insurance claims that are distributed according to it or that the  
changes
in stock market values  are distributed like that ( when a crash  occurs, and 
your money is lost, you know the famous (normal distribution) random-walk  
pricing models are wrong).
This distribution has two parameters and I took a set of combined  likelihood
equations out of a book, which are solved numerically.
 
Now, thanks to you, I can solve them. Below is the code.
 
Best regards,
 
Axel
 
 
--------------------------------------------
 
require "gsl"
include Math
include MultiMin
 
class Hash
def  ml_fit
fitted_params
# fit distribution parameters  from data using maximum likelihood or method
#  of moments
# self is a hash with keys  'distribution', and values any of the  following:
#  'normal','bernoulli','binomial','uniform','gamma','exponential','cauchy'
# 'data' - an Array with the data measured.

nロァァンョ
  ョ゜ソィァァゥalse
raise 'No distribution specified'
else
if  self['distribution'].downcasenormal' or  
self['distribution'].downcasegaussian'
mu_val0
self['data'].each{|x|  mu_val_val+x}
mu_val_val/self['data'].length
fitted_params.store('mu_fitted',mu_val)
sigma_val0
self['data'].each{|x|  sigma_valgma_val+(x-mu_val)*(x-mu_val)}
sigma_valgma_val/self['data'].length
fitted_params.store('sigma_square_fitted',sigma_val)
end

if  self['distribution'].downcasebernoulli'
# p(x)x*(1-p)^(1-x), if x \in \{0,1\}, p(x) otherwise
p_fitted0
self['data'].each{|x|  p_fittedfitted+x}
p_fittedfitted/self['data'].length
fitted_params.store('p_fitted',p_fitted)
end
if  self['distribution'].downcasebinomial'
# needs parameter n  !
#  p(x)hoose{n,x} p^x (1-p)^(n-x), if x \in  \{0,..,n\}
if  self.has_key?('params')alse
raise('parameter n  missing')
end
p_fitted0
self['data'].each{|x|  p_fittedfitted+x}
p_fittedfitted/self['data'].length/self['params']['n']
fitted_params.store('p_fitted',p_fitted)
end
if  self['distribution'].downcasepoisson'
# p(x)rac{\lambada^x}{x!} exp(-\lambda), if x \in  \{0,1,..\}
lambda_fitted0
self['data'].each{|x|  lambda_fitted
mbda_fitted+x}
p_fittedfitted/self['data'].length
fitted_params.store('lambda_fitted',lambda_fitted)
end
if  self['distribution'].downcaseuniform'
# p(x)(b-a), if x \in  \[a,b\]
a_fittedロァァンョョ゜
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」  ゜ワャワィゥrac{\lambda^{\alpha}}{\Gamma_{\alpha}}  
x^{\alpha-1}exp(-\lambda*x), if x  >;
#  use method of moments to estimate  params
m_1_fitted0
self['data'].each{|x|  m_1_fitted1_fitted+x}
m_1_fitted1_fitted/self['data'].length

m_2_fitted0
self['data'].each{|x|  m_2_fitted2_fitted+x*x}
m_2_fitted1_fitted/self['data'].length
alpha_fitted_2_fitted*m_2_fitted)/(m_2_fitted-m_1_fitted*m_1_fitted)
lambda_fitted1_fitted/(m_2_fitted-m_1_fitted*m_1_fitted)
fitted_params.store('alpha_fitted',alpha_fitted)
fitted_params.store('lambda_fitted',lambda_fitted)
end
if  self['distribution'].downcaseexponential'
#  p(x)ambda*exp(-\lambda*x)
lambda_fitted0
self['data'].each{|x|  lambda_fitted
mbda_fitted+x}
lambda_fitted
mbda_fitted/self['data'].length
if  lambda_fitted
raise('error fitting exponential distribution parameter: lambda is  infinite')
else
lambda_fittedlambda_fitted
fitted_params.store('lambda_fitted',lambda_fitted)
end
end
if  self['distribution'].downcasecauchy'
#  p(x,\alpha,\beta)rac{\beta}{\pi*(\beta^2+(x-\alpha)^2))
# likelihood equations for parameters  are
#
#  \frac{\partial L}{\partial \alpha}<\sum_{i^{n}  
\frac{x_j-\alpha}{\beta^2+(x_j-\alpha)^2}#
#  \frac{\partial L}{\partial \beta}<\sum_{i^{n}  
\frac{\beta^2}{\beta^2+(x_j-\alpha)^2}2
# ( see Johnson, Kotz, and Balakrishnan, (1994), Continuous Univariate  
Distributions,  
# Volumes  I and II, 2nd. Ed., John Wiley and Sons, chapter 16 for details  )
# Solve  these equations using Nelder-Mead multidimensional  minimization
# do this several times to choose a good minimum from local  minima

alpha_v
beta_v

# now find the parameters, repeating the numerical  minimization
repetitions 00  # but stop after finding 5 parameter sets (in which the  
minimum search converged) to suitable values  (beta>0)
temp_min_val0000000.0
best_alpha伃se
best_beta伃se
repetitions.times  do
fmin_val,x,stョ゜
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