  The efficient modeling for disorder in a phenomena depends on the chosen
score and objective functions. The main parameters in modeling are location,
scale and shape. The exponential power distribution known as generalized
Gaussian is extensively used in modeling. In real world, the observations are
member of different parametric models or disorder in a data set exists. In this
study, estimating equations for the parameters of exponential power
distribution are derived to have robust and also efficient M-estimators when
the data set includes disorder or contamination. The robustness property of
M-estimators for the parameters is examined. Fisher information matrices based
on the derivative of score functions from $\log$, $\log_q$ and distorted
log-likelihoods are proposed by use of Tsallis $q$-entropy in order to have
variances of M-estimators. It is shown that matrices derived by score functions
are positive semidefinite if conditions are satisfied. Information criteria
inspired by Akaike and Bayesian are arranged by taking the absolute value of
score functions. Fitting performances of score functions from estimating
equations and objective functions are tested by applying volume, information
criteria and mean absolute error which are essential tools in modeling to
assess the fitting competence of the proposed functions. Applications from
simulation and real data sets are carried out to compare the performance of
estimating equations and objective functions. It is generally observed that the
distorted log-likelihood for the estimations of parameters of exponential power
distribution has superior performance than other score and objective functions
for the contaminated data sets.
