Log-epsilon-skew normal: A generalization of the log-normal distribution

Area of Science:

• Statistics
• Probability Theory
• Data Modeling

Background:

• The log-normal distribution is a common choice for modeling non-negative data.
• Existing models may lack the flexibility needed for certain complex datasets.
• There is a need for extended distributions to better capture data characteristics.

Purpose of the Study:

• Introduce and analyze the novel log-epsilon-skew normal (LESN) distribution.
• Establish the LESN distribution as a generalization of the log-normal distribution.
• Provide a flexible statistical tool for analyzing non-negative real-world data.

Main Methods:

• Mathematical derivation of the LESN distribution properties.
• Analysis of the hazard function, moments, skewness, and kurtosis.
• Development and application of maximum likelihood estimation (MLE) for LESN parameters.
• Simulation studies to evaluate MLE performance.
• Application to two real-world datasets.

Main Results:

• The LESN distribution is formally defined and its key properties are derived.
• The relationship between LESN and log-normal distributions is established.
• Maximum likelihood estimation procedures for LESN parameters are discussed.
• Simulation results demonstrate the behavior of MLEs.
• Successful application of LESN to real-world data illustrates its practical utility.

Conclusions:

• The log-epsilon-skew normal (LESN) distribution offers a valuable extension to the log-normal distribution.
• The LESN distribution provides a flexible framework for modeling various types of non-negative data.
• Maximum likelihood estimation is a viable method for parameter estimation of the LESN distribution.