On stuttering generalized Yule distribution: properties and applications

Kumar and Harisankar ( Commun.Statist.-Theor.Meth. , 2020) obtain a generalized version of Yule distribution through the name ‘doubly generalized Yule distribution(DGYD)’ and indicated several applications of the distribution. Through the present article we attempt to develop an order k version of the DGYD and discuss some of its important properties such as mean, variance, expressions for its probability generating function (p.g.f) and recursion formulae for its probabilities, raw moments and factorial moments. Further we attempted the estimation of the parameters of this model by the method of maximum likelihood. The distribution has been fitted to some real life data sets for illustrating its practical relevance. The likelihood ratio test procedure is applied for examining the significance of the parameters and a simulation study is conducted for evaluating the performances of the maximum likelihood estimators of the parameters of the DGYD. Classification code: Classification code:60E05;62E15