Modified New [0, 1] - Right Truncated Exponential Rayleigh Distribution Structure and Application.

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Truncated distributions offer realistic and accurate representations of constrained data.
• They are fundamental in modern statistical modeling and the analysis of constrained data.

Purpose of the Study:

• Introduce the novel [0,1] truncated exponential Rayleigh distribution ([0,1]-RTERD).
• Present its statistical functions (CDF, PDF, survival, hazard) and mathematical properties.
• Evaluate its performance in modeling lifespan and reliability data.

Main Methods:

• Developed a two-parameter [0,1]-RTERD (scale and shape).
• Derived mathematical and statistical properties including median, moments, skewness, kurtosis, order statistics, MGF, Rényi entropy, and quantile function.
• Employed maximum likelihood estimation for parameter estimation.

Main Results:

• The [0,1]-RTERD demonstrated superior fit and precision compared to traditional models for lifespan and reliability data.
• Model validation was performed using actual datasets.
• Statistical information criteria were used for comparison with other continuous distributions.

Conclusions:

• The [0,1]-RTERD provides a robust framework for data constrained to the [0,1] interval.
• It offers flexibility in shape, center, and width due to normalization.
• The distribution's properties are reflected in key statistical measures like expected value and standard deviation.