In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models are introduced and studied. We show that the GLL density is rewritten as a two-member linear combination of the exponentiated G-densities and that, consequently, many of its mathematical properties arise directly, such as moment-based expressions. A maximum likelihood estimation procedure for the GLL parameters is provided and the behavior of the resulting estimates is evaluated by Monte Carlo experiments. An application to repairable data is made. The results argue for the use of the exponential law as the basis for the GLL-G family.
We propose a new autoregressive moving average (ARMA) process with generalized gamma (G) marginal law, called G‐ARMA. We derive some of its mathematical properties: moment‐based closed‐form expressions, score function, and Fisher information matrix. We provide a procedure for obtaining maximum likelihood estimates for the G‐ARMA parameters. Its performance is quantified and discussed using Monte Carlo experiments, considering (among others) various link functions. Finally, our proposal is applied to solve remote sensing problems using synthetic aperture radar (SAR) imagery. In particular, the G‐ARMA process is applied to real data from images taken in the Munich and San Francisco regions. The results show that G‐ARMA describes the neighborhoods of SAR features better than the gamma‐ARMA process (a reference for asymmetric positive data). For pixel ray modeling, our proposal outperforms and gamma‐ARMA.
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