The Zero-Adjusted Log-Symmetric Distributions: Point and Intervalar Estimation.

Area of Science:

• Statistics
• Probability Theory
• Data Analysis

Background:

• Semi-continuous data, common in fields like biostatistics and econometrics, often requires specialized modeling approaches.
• Existing distributions may not adequately capture the characteristics of data with a high proportion of zero values and a continuous positive component.

Purpose of the Study:

• To introduce and investigate a novel class of semi-continuous probability distributions: the zero-adjusted log-symmetric (ZALS) distributions.
• To derive key properties and parameter estimation methods for the ZALS family.
• To assess the performance of the proposed estimators through simulation and demonstrate practical utility with real data.

Main Methods:

• Theoretical derivation of ZALS distribution properties.
• Application of the maximum likelihood estimation (MLE) method for parameter estimation.
• Development of confidence intervals (CIs) for the estimated parameters.
• Conducting a simulation study to evaluate MLE performance across different tail behaviors (lighter/heavier).
• Illustrative application using a real-world dataset.

Main Results:

• The ZALS distribution is formally defined and its fundamental properties are established.
• Maximum likelihood estimators and confidence intervals for ZALS parameters are derived.
• Simulation results indicate that the MLEs perform adequately in both lighter and heavier-tailed scenarios.
• The real data application demonstrates the practical applicability and flexibility of the ZALS distribution.

Conclusions:

• The proposed zero-adjusted log-symmetric distribution offers a flexible and effective tool for modeling semi-continuous data.
• The maximum likelihood method provides reliable parameter estimation for this new class of distributions.
• The ZALS family is a valuable addition to the statistical toolkit for analyzing complex datasets with zero-inflated and continuous components.