Modified Skew Discrete Laplace Regression Models for Integer-Valued Data With Applications to Paired Samples.

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Statistical modeling traditionally focuses on count data.
• Discrete observations encompassing all integers (Z) are prevalent in various fields.
• Existing methods may not adequately address the nuances of integer-valued data beyond counts.

Purpose of the Study:

• To introduce a general parametric modeling framework for integer-valued data analysis.
• To develop a model applicable to paired discrete observations.
• To provide a method with interpretable regression coefficients and proper handling of discrete data.

Main Methods:

• Development of a novel regression model based on the modified skew discrete Laplace distribution.
• Application of a frequentist approach for statistical inference.
• Creation of diagnostic tools for assessing goodness-of-fit.
• Conducting simulation studies to evaluate estimator properties and residual distributions.

Main Results:

• The proposed model allows for straightforward interpretation of regression coefficients concerning mean and dispersion.
• Simulation studies confirm the asymptotic properties of estimators and test statistics.
• The model demonstrates effectiveness in analyzing diverse real-world datasets.

Conclusions:

• The modified skew discrete Laplace distribution provides a robust framework for integer-valued data.
• The developed methodology enhances the analysis of discrete observations in various scientific domains.
• The R package 'sdlrm' facilitates the implementation of these new estimation and inference procedures.