The exponentiated-log-logistic geometric distribution: Dual activation

Bayesian and Classical Inference for the Generalized Log-Logistic Distribution with Applications to Survival Data

The generalized log-logistic distribution is especially useful for modelling survival data with variable hazard rate shapes because it extends the log-logistic distribution by adding an extra parameter to the classical distribution, resulting in greater flexibility in analyzing and modelling various data types. We derive the fundamental mathematical and statistical properties of the proposed distribution in this paper. Many well-known lifetime special submodels are included in the proposed distribution, including the Weibull, log-logistic, exponential, and Burr XII distributions. The maximum likelihood method was used to estimate the unknown parameters of the proposed distribution, and a Monte Carlo simulation study was run to assess the estimators' performance. This distribution is significant because it can model both monotone and nonmonotone hazard rate functions, which are quite common in survival and reliability data analysis. Furthermore, the proposed distribution's flexibility and usefulness are demonstrated in a real-world data set and compared to its submodels, the Weibull, log-logistic, and Burr XII distributions, as well as other three-parameter parametric survival distributions, such as the exponentiated Weibull distribution, the three-parameter log-normal distribution, the three-parameter (or the shifted) log-logistic distribution, the three-parameter gamma distribution, and an exponentiated Weibull distribution. The proposed distribution is plausible, according to the goodness-of-fit, log-likelihood, and information criterion values. Finally, for the data set, Bayesian inference and Gibb's sampling performance are used to compute the approximate Bayes estimates as well as the highest posterior density credible intervals, and the convergence diagnostic techniques based on Markov chain Monte Carlo techniques were used.

Comparison between Highly Complex Location Models and GAMLSS

This paper presents a discussion regarding regression models, especially those belonging to the location class. Our main motivation is that, with simple distributions having simple interpretations, in some cases, one gets better results than the ones obtained with overly complex distributions. For instance, with the reverse Gumbel (RG) distribution, it is possible to explain response variables by making use of the generalized additive models for location, scale, and shape (GAMLSS) framework, which allows the fitting of several parameters (characteristics) of the probabilistic distributions, like mean, mode, variance, and others. Three real data applications are used to compare several location models against the RG under the GAMLSS framework. The intention is to show that the use of a simple distribution (e.g., RG) based on a more sophisticated regression structure may be preferable than using a more complex location model.