Inverse unit compound Rayleigh distribution: statistical properties with applications in different fields

Area of Science:

• Statistics
• Probability Distributions
• Mathematical Modeling

Background:

• The need for flexible probability distributions in statistical modeling is ongoing.
• Existing distributions may not adequately capture the complexities of all real-world data.
• The unit compound Rayleigh distribution (UCRD) serves as a basis for developing new distributions.

Purpose of the Study:

• To introduce and characterize a novel two-parameter distribution: the inverse unit compound Rayleigh distribution (IUCRD).
• To explore the mathematical properties of the IUCRD, including its quantile function, mode, moments, and heavy-tailedness.
• To evaluate the performance of the IUCRD against existing distributions using real-world datasets.

Main Methods:

• The IUCRD is derived via the inverse transformation of the UCRD.
• Key statistical properties of the IUCRD are mathematically derived and analyzed.
• Parameter estimation methods, including KE and ML, are compared using Monte Carlo simulations.
• Goodness of fit statistics are employed to compare the IUCRD with other distributions on real-world data.

Main Results:

• The IUCRD exhibits flexible properties, including unimodal or non-increasing PDF, and adjustable skewness.
• The hazard rate function of the IUCRD can be upside-down bathtub-shaped or non-decreasing.
• The KE method is identified as the best estimation methodology, with ML as the second best.
• The IUCRD demonstrates superior fit to five real-world datasets compared to seven other distributions.

Conclusions:

• The inverse unit compound Rayleigh distribution (IUCRD) is a valuable addition to the family of continuous probability distributions.
• The IUCRD's flexibility and demonstrated superior fit make it a preferable choice for various data analysis scenarios.
• The study validates the utility of the IUCRD in practical applications, outperforming established distributions like UCRD and inverse exponential variants.