Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum $\log_q$ Likelihood Estimation for Parameters of Weibull
  Distribution and Properties: Monte Carlo Simulation   The maximum ${\log}_q$ likelihood estimation method is a generalization of
the known maximum $\log$ likelihood method to overcome the problem for modeling
non-identical observations (inliers and outliers). The parameter $q$ is a
tuning constant to manage the modeling capability. Weibull is a flexible and
popular distribution for problems in engineering. In this study, this method is
used to estimate the parameters of Weibull distribution when non-identical
observations exist. Since the main idea is based on modeling capability of
objective function
$\rho(x;\boldsymbol{\theta})=\log_q\big[f(x;\boldsymbol{\theta})\big]$, we
observe that the finiteness of score functions cannot play a role in the robust
estimation for inliers. The properties of Weibull distribution are examined. In
the numerical experiment, the parameters of Weibull distribution are estimated
by $\log_q$ and its special form, $\log$, likelihood methods if the different
designs of contamination into underlying Weibull distribution are applied. The
optimization is performed via genetic algorithm. The modeling competence of
$\rho(x;\boldsymbol{\theta})$ and insensitiveness to non-identical observations
are observed by Monte Carlo simulation. The value of $q$ can be chosen by use
of the mean squared error in simulation and the $p$-value of Kolmogorov-Smirnov
test statistic used for evaluation of fitting competence. Thus, we can overcome
the problem about determining of the value of $q$ for real data sets.

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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con