### On a Modified Yule Distribution

#### Abstract

A modified version of Yule distribution is introduced here and discuss some of its properties by deriving expressions for its probability generating function, raw moments, factorial moments etc. Certain recursion formulae for its probabilities, raw moments and factorial moments are also developed. Various methods of estimation are employed for estimating the parameters of the distribution and certain test procedures are suggested for testing the significance of the additional parameters of the distribution. The distribution has been fitted to certain real-life data sets for illustrating its usefulness, compared with certain existing models available in the literature. Further, a simulation study is conducted for assessing the performance of the maximum likelihood estimators.

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DOI: 10.6092/issn.1973-2201/7990