The SMp(x or y;PXmin,Xmax,ML,p1,p2,Max) a Probabilistic Distribution, or a Probability Density Function of a Random Variable X

Abstract

In this study, the statistical models project (SMp) proposes a six-parameter probabilistic function of two steps that can generate probabilistic functions (PFs) for a random continuous/discrete variable X, SMp(x); showed the actual widely used binomial (BD), Poisson and normal distributions, their deficiencies and limitations and the little or non-probabilistic importance of the former; and developed the first version of the computer tool associated with the proposed function, which is a MATLAB application of two modules. One of these modules models stochastic data (x;y), such as those that follow the identical or similar behaviors of the normal, Poisson, BD and others, and those associated with stochastic processes/effects (SP/Es), such as, normal tissue complication, percentage depth dose, and pharmacokinetic. The second module calculates the probabilities for a random continuous variable X using SMp(x).

The proposed function can be used in the role of some probabilistic distributions (PDs) or probability density functions (PDFs), and overcome their deficiencies and limitations. SMp(x) generates three SMp types of the SP/Es if variable x is replaced for y. For its probabilistic conditions, at least one SMp(x) parameter depends on the others. One of the main objectives of this study is showing that the BD is actually a mathematic exercise and creation, and the advantages of the SMp in its role SMp-normal over the Gaussian distribution.