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

A modified Bagdonavicius-Nikulin chi-square goodness-of-fit is defined and studied. The lymphoma data is analyzed using the modified goodness-of-fit test statistic. Different 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.

Automated summary

A modified Bagdonavicius-Nikulin chi-square goodness-of-fit is defined and studied in this paper. The modified goodness-of-fit test statistic is applied to analyze the lymphoma data. Different non-Bayesian estimation methods under complete samples schemes, including maximum likelihood least square estimation method, Cramer-von Mises estimation method, weighted least square estimation method, left tail-Anderson Darling estimation method, and right tail Anderson Darling estimation method, are considered, discussed, and compared. Numerical simulation studies are conducted to compare these estimation methods. The potential of the new model is illustrated through the analysis of three real data sets and its comparison with other well-known generalizations.