Motivated by the paper of Dandekar (1955), a one-urn model with Polya-Eggenberger sampling scheme is developed, which yields a large number of discrete distributions, including the Dandekar's modified binomial distribution, as particular cases. The model is further modified to some new generalized distributions of order k. Some probable applications of these models were discussed in Dandekar (1955) and Feller (1968) in fields of fertility study and radioactivity. It also has applications in premium determination in insurance sector. Copyright © Taylor & Francis Group, LLC.

Sen K.

Agarwal M.L.

Bhattacharya S.

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Shiv Nadar University

Geiger Counter-Type Pólya–Eggenberger Distributions

Communications in Statistics - Theory and Methods

Journal of Applied Probability

Run Statistics Defined on the Multicolor URN Model

Advances in Applied Probability

Success run statistics defined on an urn model

Polya, Inverse Polya, and Circular Polya Distributions of Orderkforl-Overlapping Success Runs