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Extending and modifying entropy and divergence measures, deriving their properties, and using them to characterize random variables. and to construct beta sufficient partitions w.r.t. those measures. Moreover, using them to obtain optimal censoring schemes in case of progressive type II schemes.
  
Generating new classes of probability distributions, studying their properties, and applying them in some inferential statistical problems.
  
Bayesian and non-Bayesian statistical estimation, testing, and prediction
  
Resampling methods, simulation, Bootstrap, and jackknife.
  
Approximating distributions, asymptotic normality, asymptotic distribution of posterior distribution.
  
Goodness of fit tests using EDF, MGF, Chracterization properties, Transformations, Dynamic entropy measures, Divergence measures. Moreover, Model selection using AIC type procedures.