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.

Mathematical search technique for detecting moving novel coronavirus disease (COVID-19) based on minimizing the weight function.

The study of search plans has found considerable interest between searchers due to its interesting applications in our real life like searching for located and moving targets. This paper develops a method for detecting moving targets. We propose a novel strategy based on weight function W ( Z ) , W ( Z ) = λ H ( Z ) + ( 1 - λ ) L ( Z ) , where H ( Z ) , L ( Z ) are the total probabilities of un-detecting, and total effort respectively, is searching for moving novel coronavirus disease (COVID-19) cells among finite set of different states. The total search effort will be presented in a more flexible way, so it will be presented as a random variable with a given distribution. The objective is searching for COVID-19 which hidden in one of n cells in each fixed number of time intervals m and the detection functions are supposed to be known to the searcher or robot. We look in depth for the optimal distribution of the total effort which minimizes the probability of undetected the target over the set of possible different states. The effectiveness of this model is illustrated by presenting a numerical example.