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The efficient modeling for disorder in a phenomena depends on the chosenscore and objective functions. The main parameters in modeling are location,scale and shape. The exponential power distribution known as generalizedGaussian is extensively used in modeling. In real world, the observations aremember of different parametric models or disorder in a data set exists. In thisstudy, estimating equations for the parameters of exponential powerdistribution are derived to have robust and also efficient M-estimators whenthe data set includes disorder or contamination. The robustness property ofM-estimators for the parameters is examined. Fisher information matrices basedon the derivative of score functions from $\log$, $\log_q$ and distortedlog-likelihoods are proposed by use of Tsallis $q$-entropy in order to havevariances of M-estimators. It is shown that matrices derived by score functionsare positive semidefinite if conditions are satisfied. Information criteriainspired by Akaike and Bayesian are arranged by taking the absolute value ofscore functions. Fitting performances of score functions from estimatingequations and objective functions are tested by applying volume, informationcriteria and mean absolute error which are essential tools in modeling toassess the fitting competence of the proposed functions. Applications fromsimulation and real data sets are carried out to compare the performance ofestimating equations and objective functions. It is generally observed that thedistorted log-likelihood for the estimations of parameters of exponential powerdistribution has superior performance than other score and objective functionsfor the contaminated data sets.

On the estimating equations and objective functions for parameters of exponential power distribution: Application for disorder