Applications of single valued trapezoidal neutrosophic maximum a posteriori estimation in real-life problems

In this paper, we introduce Single-Valued Trapezoidal Neutrosophic Maximum a Posteriori (SVTN-MAP) estimation to deal with uncertainty in prior distribution parameters, where prior parameters are assumed to be Single-Valued Trapezoidal Neutrosophic Numbers (SVTN), allowing the estimate of the unknown parameter to be flexible when considering uncertainty, such a method tackles the lack of prior information or vagueness in prior parameters to reach a more informative and reliable estimate, which will be an SVTN-number also. Four applications in several fields were made to study the benefits and limitations of the proposed method. In the first application, the sample was Bernoulli distributed, with an unknown parameter following a Beta distribution with parameters α ̃ and β ̃, in the second application; observations were drawn from an exponential distribution, prior distribution was Gamma with parameters r ̃ and (λ_۰ ) ̃, in the third application; the data was normally distributed with an unknown parameter μ~N((μ_۰ ) ̃,σ_۰^۲ ), and finally, in the fourth application; a Poisson sample was drawn with a Gamma prior λ~Gamma(α ̃,β ̃ ). Results were discussed in detail throughout the paper with illustrations and simulations to compare the traditional and the new model. The simulations have shown that the proposed method performs better than the traditional method due to its adaptability when dealing with ambiguity in prior information and its ability to view the full picture.

کلیدواژه ها:

Estimation Theory ، Maximum a Posteriori ، Neutrosophy ، Single-Valued Trapezoidal Number ، Vagueness in Information ، Real-Life Applications ، probability distribution