Journal of Statistical Theory and Applications, Vol. 16, No. 2 (June 2017) 269–283 ___________________________________________________________________________________________________________ An Alternative Approach of Binomial and Multinomial Distributions Mian Arif Shams Adnan Department of Mathematical Science, Ball State University, Muncie, IN 47304, USA
[email protected] Md. Tareq Ferdous Khan Department of Statistics, Jahangirnagar University, Dhaka-1342, Bangladesh Md. Forhad Hossain Department of Statistics, Jahangirnagar University, Dhaka-1342, Bangladesh Abdullah Albalawi Department of Mathematical Science, Ball State University, Muncie, IN 47304, USA Received 4 April 2015 Accepted 18 September 2016 Abstract In this paper we have tried to present an alternative approach for two discrete distributions such as Binomial and Multinomial with a new concept of sampling having a more general form apart from the traditional methods of sampling. The existing distributions may be obtained as a special case of our newly suggested technique. The basic distributional properties of the proposed distributions are also been examined including the limiting form of the proposed Binomial distribution to normal distribution. Keywords: Generalized Binomial Distribution, Generalized Multinomial Distribution, Sampling Methods, Distributional Properties, Arithmetic Progression, Limiting Form. Mathematics Subject Classification: 60E05, 62E10, 62E15, 62E20. 1. Introduction The discrete distributions are widely used in the diversified field and among them