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

In: Neutrosophic Operational Research

Author

Listed:
  • Rehan Ahmad Khan Sherwani

    (College of Statistical and Actuarial Sciences, University of the Punjab, New Campus Lahore)

  • Muhammad Aslam

    (Faculty of Science, King Abdulaziz University)

  • Muhammad Ali Raza

    (Government College University Faisalabad)

  • Muhammad Farooq

    (King Abdulaziz University)

  • Muhammad Abid

    (Government College University Faisalabad)

  • Muhammad Tahir

    (King Abdulaziz University)

Abstract

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.

Suggested Citation

  • Rehan Ahmad Khan Sherwani & Muhammad Aslam & Muhammad Ali Raza & Muhammad Farooq & Muhammad Abid & Muhammad Tahir, 2021. "Neutrosophic Normal Probability Distribution—A Spine of Parametric Neutrosophic Statistical Tests: Properties and Applications," Springer Books, in: Florentin Smarandache & Mohamed Abdel-Basset (ed.), Neutrosophic Operational Research, pages 153-169, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-57197-9_8
    DOI: 10.1007/978-3-030-57197-9_8
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