A new regression model for rates and proportions data with applications

Area of Science:

• Statistics
• Probability Theory
• Econometrics

Background:

• Continuous distributions are fundamental in statistical modeling.
• Existing regression models may not capture the full complexity of proportional data.
• The generalized odd log-logistic-G family offers a flexible framework for developing new distributions.

Purpose of the Study:

• To propose a new continuous distribution within the generalized odd log-logistic-G family.
• To develop an extended regression model based on this new distribution for analyzing proportional data.
• To evaluate the performance and efficiency of the proposed model and estimation methods.

Main Methods:

• Implementation of the new distribution and extended regression using the gamlss package in R.
• Frequentist and Bayesian analyses for parameter estimation.
• Non-parametric and parametric bootstrap methods for estimator efficiency.
• Simulation studies to assess the empirical distribution of maximum likelihood estimators.
• Comparison of quantile residuals with the standard normal distribution.

Main Results:

• The proposed distribution's density function can exhibit various shapes (symmetrical, asymmetrical, unimodal, bimodal).
• The extended regression model provides more realistic fits for proportional data compared to existing models.
• Simulation results verify the empirical distribution of maximum likelihood estimators.
• Bootstrap methods enhance the efficiency of parameter estimators.

Conclusions:

• The new continuous distribution and its associated extended regression model offer a valuable tool for analyzing proportional data.
• The flexibility of the proposed distribution allows for modeling diverse data patterns.
• The implemented estimation and validation techniques ensure reliable and efficient analysis.