Foundation of 2-Symbolic Plithogenic Maximum a Posteriori Estimation

Abstract

In this paper, we introduce and define for the first time the plithogenic loss function, plithogenic risk function, plithogenic maximum likelihood function, and plithogenic posterior risk function, which form a base to easily define the plithogenic maximum a posteriori estimator (Plithogenic MAP) and its conditions, algebraic isomorphism was used through equations, and finally, we worked on an example of a plithogenic random variables sample exponentially distributed with a gamma prior for the parameter distribution and used the quadratic loss function, we found the posterior distribution of the parameter which is also a plithogenic gamma distribution and taken the posterior mean as an estimate of the parameter, such results are similar to the classical case of MAP taking in consideration the plithogenic parts which represent generalized indeterminacy.

Keywords

• plithogenics
• loss function
• risk function
• plithogenic probability density function