Abstract:
e 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. 'e 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. 'is
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. 'e 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
