AN EXAMPLE OF AN ALTERNATIVE METHOD OF THE NORMAL DISTRIBUTION DENSITY DERIVATION VIA A CONCEPT OF A MULTI-OPTIONAL OPTIMALITY

Abstract

Considered a multi-optional method of finding a random value normal probability distribution density. Specific hybrid optional functions are taken into account at the optimization of an objective functional which includes an entropy uncertainty measure for those specific hybrid optional functions. Required mathematical models for obtaining the optimal multi-optional distributions suppose existence of a random value’s first and second moments of the distribution density. Normal distribution density is obtained in the way which does not deal with probability derivations but applies a multi-optional optimality concept instead. As a result, it is revealed that normal distribution density is the hybrid multi-optional effectiveness function delivering an extremal value to the objective functional. This is a new insight into the scientific substantiation of the well-known dependency derived in another way; also it is a new explanation of the widely spread in nature phenomenon.