On parameter estimation of the standard omega distribution

Area of Science:

• Statistics
• Probability Theory
• Statistical Distributions

Background:

• The standard omega distribution is a probabilistic model for data on the unit interval.
• It is a unit form of the exponentiated half logistic distribution.
• Existing beta-like distributions may lack a clear distribution function.

Purpose of the Study:

• To perform a detailed shape analysis of the omega distribution.
• To investigate the existence and uniqueness of its parameter estimators (MLE and Bayesian).
• To demonstrate the practical utility of the omega distribution.

Main Methods:

• Detailed shape analysis of the omega distribution.
• Theoretical discussion on the existence and uniqueness of maximum likelihood estimators (MLEs) and Bayesian estimates.
• Simulation study for comparing estimators.
• Real data fitting demonstrations.

Main Results:

• The omega distribution exhibits flexibility, capable of J-shaped, reverse J-shaped, U-shaped, and unimodal forms with varying skewness.
• It possesses a clear distribution function, unlike the ordinary beta distribution.
• The existence and uniqueness of MLEs are established, preventing spurious solutions.
• Simulation studies and data fitting confirm its usefulness compared to other beta-like distributions.

Conclusions:

• The omega distribution is a versatile and practical alternative to other beta-like distributions for modeling rates and percentages.
• Its well-defined properties, including unique estimators, enhance its applicability in statistical modeling.
• The distribution's flexibility in shape makes it suitable for a wide range of data patterns.