Extension of Generalized Bernoulli Learning Models

B. S. El-Desouky, F. A. Shiha, A. M. Magar

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.

DOI: 10.4236/ojmsi.2015.31003                

Abstract

In this article, we study the generalized Bernoulli learning model based on the probability of success p_i = a_i /n where i = 1,2,...n 0<a₁<a₂<...<a_n<n and n is positive integer. This gives the previous results given by Abdulnasser and Khidr [1], Rashad [2] and EL-Desouky and Mahfouz [3] as special cases, where p_i = i/n p_i = i²/n² and p_i = i^p/n^p respectively. The probability function P(W_n = k) of this model is derived, some properties of the model are obtained and the limiting distribution of the model is given.

Keywords

Stirling Numbers, Bernoulli Learning Models, Comtet Numbers, Inclusion-Exclusion Principle

Conflicts of Interest

The authors declare no conflicts of interest.

References

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