Novel two-parameter quadratic exponential distribution: Properties, simulation, and applications

Area of Science:

• Statistics
• Probability Distributions
• Mathematical Modeling

Background:

• Existing probability distributions may not adequately capture complex real-world data.
• There is a continuous need for flexible and robust statistical models.

Purpose of the Study:

• Introduce and analyze a novel two-parameter quadratic exponential distribution (NTPQED).
• Evaluate the statistical properties and practical applicability of the NTPQED.
• Compare the NTPQED's performance against established statistical models.

Main Methods:

• Derivation of key statistical properties: asymptotic behavior, moments, order statistics, and entropies.
• Inclusion of reliability measures: fuzzy reliability, value at risk, and excess functions.
• Simulation study assessing fifteen parameter estimation techniques.
• Application to three real-world datasets for empirical validation.

Main Results:

• The NTPQED exhibits desirable statistical characteristics.
• Parameter estimation methods were evaluated through simulation.
• Real-world data analysis confirmed the NTPQED's practical utility.
• The NTPQED consistently outperformed existing models based on goodness-of-fit tests.

Conclusions:

• The proposed NTPQED is a statistically sound and practically valuable distribution.
• The NTPQED demonstrates superior performance compared to existing models.
• This novel distribution holds potential for diverse applications in data analysis.