Neutrosophic moment exponential distribution: properties and modeling of child mortality rate data

Ghadah Alomani; R. Maya; M. R. Irshad; Amer I. Al-Omari; A. S. Aparna; Ghadah Alomani; R. Maya; M. R. Irshad; Amer I. Al-Omari; A. S. Aparna

doi:10.3934/math.20251222

AIMS Mathematics

2025, Volume 10, Issue 11: 27816-27836. doi: 10.3934/math.20251222

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Neutrosophic moment exponential distribution: properties and modeling of child mortality rate data

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India
3.
Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan

Received: 21 June 2025 Revised: 06 November 2025 Accepted: 18 November 2025 Published: 28 November 2025
MSC : 60E05, 62A86

This research extends traditional statistical distribution theory, which often neglects issues such as ambiguity, imprecision, or indeterminacy. The primary aim is to develop the neutrosophic moment exponential distribution as a refined version of the moment exponential distribution, specifically to tackle situations involving uncertainty. The study derives the proposed model's quantile function, Mills ratio, and elasticity, as well as its mean, variance, $ r^{\text{th}} $ moment, index of dispersion, and moment-generating function. It also establishes expressions for the survival function, hazard rate function, cumulative hazard function, and mean residual life function, which are visually explored through graphs. Furthermore, the research calculates information measures including extropy, weighted extropy, cumulative residual extropy, Shannon entropy, and Rényi entropy. The parameters of the proposed model are determined using maximum likelihood estimation, followed by a simulation study and an illustration of the distribution of the order statistics. Finally, the practical superiority of the proposed distribution over several existing models in the literature is demonstrated using a child mortality rate dataset.
- neutrosophic distribution,
- indeterminacy,
- survival function,
- hazard rate function,
- parameter estimation
Citation: Ghadah Alomani, R. Maya, M. R. Irshad, Amer I. Al-Omari, A. S. Aparna. Neutrosophic moment exponential distribution: properties and modeling of child mortality rate data[J]. AIMS Mathematics, 2025, 10(11): 27816-27836. doi: 10.3934/math.20251222

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Abstract

This research extends traditional statistical distribution theory, which often neglects issues such as ambiguity, imprecision, or indeterminacy. The primary aim is to develop the neutrosophic moment exponential distribution as a refined version of the moment exponential distribution, specifically to tackle situations involving uncertainty. The study derives the proposed model's quantile function, Mills ratio, and elasticity, as well as its mean, variance, $ r^{\text{th}} $ moment, index of dispersion, and moment-generating function. It also establishes expressions for the survival function, hazard rate function, cumulative hazard function, and mean residual life function, which are visually explored through graphs. Furthermore, the research calculates information measures including extropy, weighted extropy, cumulative residual extropy, Shannon entropy, and Rényi entropy. The parameters of the proposed model are determined using maximum likelihood estimation, followed by a simulation study and an illustration of the distribution of the order statistics. Finally, the practical superiority of the proposed distribution over several existing models in the literature is demonstrated using a child mortality rate dataset.

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