The exponential generalized log-logistic model: Bagdonavičius-Nikulin test for validation and non-Bayesian estimation methods

Abstract

A modified Bagdonaviˇcius-Nikulin chi-square goodness-of-fit is defined and studied. The lymphoma data is analyzed using the modified goodness-of-fit test statistic. Di ff erent non-Bayesian estimation methods under complete samples schemes are considered, discussed and compared such as the maximum likelihood least square estimation method, the Cramer-von Mises estimation method, the weighted least square estimation method, the left tail-Anderson Darling estimation method and the right tail Anderson Darling estimation method. Numerical simulation studies are performed for comparing these estimation methods. The potentiality of the new model is illustrated using three real data sets and compared with many other well-known generalizations. Cram´er-von-Mises estimation, the weighted least square estimation, the left tail-Anderson Darling estimation, and the right tail Anderson Darling estimation methods. Numerical simulation studies were performed for comparing these estimation methods using di ff erent sample sizes and three di ff erent combinations of parameters. The potentiality of the EG-LL model is illustrated using three real data sets and the model is compared with many other well-known generalizations. The new model was proven worthy in modeling breaking stress, survival times and medical data sets. The Barzilai-Borwein algorithm is employed via a simulation study for assessing the performance of the estimators with di ff erent sample sizes as sample size tends to ∞ . Using the Bagdonaviˇcius-Nikulin goodness-of-fit test for validation, we propose a modified chi-square GOF tests for the EG-LL model. We have analyzed a lymphoma data set consisting of times (in months) from diagnosis to death for 31 individuals with advanced non Hodgkin’s lymphoma clinical symptoms by using our model under the modified Bagdonaviˇcius-Nikulin goodness-of-fit test statistic. Based on the MLEs, the modified Bagdon-aviˇcius-Nikulin goodness-of-fit test recovered the loss of information for the grouping data and fol-24