Abstract
Recent statistical work has focused a lot on order k variations of discrete probability distributions and related generalizations. By referring to the generalized Yule distribution as the ‘‘doubly generalized Yule distribution’’ (DGYD), [19] obtained the distribution and described numerous uses for it. Through the development of an order k version of the DGYD and discussion of some of its key characteristics, including mean, variance, formulas for its probability generating function (p.g.f. ), recursion equations for its probabilities, raw moments, and factorial moments, we hope to advance the field. Additionally, we tried to estimate the parameters of this model using the maximum likelihood method. For the purpose of demonstrating the distribution’s applicability, it has been fitted to a few real-world data sets. A simulation study is done to assess the effectiveness of the maximum likelihood estimators, and the likelihood ratio test process is used to determine the relevance of the parameters.
