Abstract
Some new type of modifications of binomial and Poisson distributions, are discussed. First, we consider Bernoulli trials of lengthn with success ratep up to time whenm times of successes occur, and then, changing the success rate to γp, we continue the remaining trial. The distribution of number of successes is called the modified binomial distribution. The Poisson limit (n tends to infinity andp tends to 0, keepingnp=λ) of the modified binomial is called the modified Poisson distribution. The probability functions of modified binomial and Poisson distributions are given (Section 1).
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