Neutrosophic Formulation of the Quadratic Transmuted  Generalized Exponential Distribution: Properties and  Applications

Kumarapandiyan Gnanasegaran; Benitta Susan Aniyan; Abdul Kani Jabarali

Authors

Kumarapandiyan Gnanasegaran Assistant Professor, Department of Statistics, University of Madras, Madras Christian College, Chennai, Tamilnadu 600059, India;
Benitta Susan Aniyan Research Scholar, Department of Statistics, University of Madras, Madras Christian College, Chennai, Tamilnadu 600059, India;
Abdul Kani Jabarali Assistant Professor, Department of Statistics, University of Madras, Madras Christian College, Chennai, Tamilnadu 600059, India;

Keywords:

Neutrosophic; indeterminacy; transmutation; generalized exponential distribution; maximum like lihood estimator; Monte Carlo simulation.

Abstract

The Quadratic Transmuted Generalized Exponential Distribution (QTGED) enhances the general
ized exponential distribution, making it a significant development for handling complex decision-making con
texts. Traditional statistical distributions often focus on representing degrees of truth or membership in fuzzy
sets, yet they struggle to capture situations involving incomplete, vague, or contradictory data accurately. This
study introduces the Neutrosophic Quadratic Transmuted Generalized Exponential Distribution (NQTGED),
specifically designed to address indeterminacy and transmuted data. Neutrosophic theory is essential here, as
it overcomes the limitations of classical and fuzzy set theories by effectively managing uncertainty, indetermi
nacy, and inconsistency in data. By simultaneously representing truth, indeterminacy, and falsity, neutrosophic
sets offer a comprehensive framework for modeling uncertainty. Traditional distributions lack the adaptability
needed for evolving data complexities, often falling short when faced with non-standard data distributions or
outliers. Addressing these challenges requires innovative approaches that incorporate advanced mathematical
models for uncertainty. This is especially valuable in real-world situations, where data is frequently incomplete,
imprecise, or contradictory, and sometimes transmuted. The study derives various mathematical properties of
the model, assesses parameter estimation using maximum likelihood and simulation, and demonstrates practical
applications with cancer remission data. Simulation results reveal that Neutrosophic Average Biases (NABs)
and Neutrosophic Mean Square Errors (NMSEs) decrease as sample sizes increase, indicating strong and ac
curate parameter estimation. NQTGED provides superior fit and performance, offering significant insights for
applications in reliability engineering and biomedical sciences.