### 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.*

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