Neutrosophic Normal Probability Distribution—A Spine of Parametric Neutrosophic Statistical Tests: Properties and Applications

The importance of normal probability distribution can’t be denied in inferential statistics due to its wide applicability. In classical statistics, the parameters of the normal probability distribution are assumed to be certain and complete, but in real-life problems, these can be imprecise, vague, unclear, or indeterminate. In such situations, neutrosophic normal probability distribution proposed by Smarandache (Introduction to neutrosophic statistics, Infinite Study; 2014) is potentially useful which incorporates the indeterminacy of the parameters in solving the problems. The idea proposed by Smarandache (Introduction to neutrosophic statistics, Infinite Study; 2014) was limited and needs extensions. In this paper, we extended the concept of neutrosophic normal distribution by defining it in various forms with examples. Important properties like mean, variance, moment generating function, characteristics function, cumulants, quartile deviation, and mean deviation under neutrosophic normal probability distribution are derived. Besides, neutrosophic quantile function and neutrosophic Q-Q plot of the distribution are proposed and computed under different success probabilities. In the last, maximum likelihood estimates, entropy, and Fisher information matrix are also provided for the neutrosophic normal probability distribution.