Authors:Kanwar Sen, Manju Agarwal, and Sonali Bhattacharya
Pólya-Eggenberger F-S Models of order (k1, k2) are proposed and their probability functions obtained. The results are extended to obtain probability functions of Inverse Pólya-Eggenberger F-S models of order (k1, k2). The Binomial Distribution of order (k1, k2) (see) and some new discrete distributions of order (k1, k2) are obtained as particular cases of these models.
For fixed integers n(= 0) and μ, the number of ways in which a moving particle taking a horizontal step with probability p and a vertical step with probability q, touches the line Y = n+μX for the first time, have been counted. The concept has been applied to obtain various probability distributions in independent and Markov dependent trials.