A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application

Area of Science:

• Statistics
• Probability Theory

Background:

• Real-world data often exhibits skewness, high kurtosis, and outliers.
• Existing bounded distributions may not adequately model such complex data characteristics.

Purpose of the Study:

• Introduce a novel heavy-tailed slash-type distribution on a bounded interval.
• Develop methods for parameter estimation and assess its performance for modeling skewed, high-kurtosis data with outliers.

Main Methods:

• Defined a new bounded distribution using a slash random variable and the logistic function.
• Derived maximum likelihood, least-square, and weighted least-square estimators.
• Conducted a simulation study to evaluate estimator performance.

Main Results:

• The proposed distribution effectively models skewed and high-kurtosis data with outliers.
• Parameter estimation methods (MLE, LS, WLS) were derived and assessed via simulation.
• The new distribution demonstrated superior fit compared to existing models on real data.

Conclusions:

• The novel bounded slash-type distribution is a valuable tool for analyzing complex real-world data.
• The proposed estimation methods are reliable for parameter estimation.
• This distribution offers an improved modeling alternative for datasets with extreme values.