eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2020-09-24 8 5 80 90 10.12691/tjant-8-5-1 TJANT2020851 article Aziz ATTA azizatta20@gmail.com 1 Mathematics and Structural Analysis, Atta Engineering Design Office, El Jadida, Morocco The theory of probability and statistics, thanks to its continuous modernization, has become more and more important in our life given its presence in several fields such as economics and prevision [8]. The binomial distribution is among the oldest probability distributions introduced by Bernoulli [1]. In the same context, we thought of generalizing this probability distribution under the name p-nomial distribution using p-nomial coefficients p-nomial theorem [7]. In this article, we are going to be interested in the introduction of this new probability distribution as well as an establishment of its various standard characteristics. the purpose of this article is therefore summarized in the tracing of the theoretical framework with some examples of application of the said p-nomial distribution. http://pubs.sciepub.com/tjant/8/5/1/tjant-8-5-1.pdf p-nomial coefficients p-nomial identity p-nomial distribution probability tree trinomial distribution