New bounded probability model: Properties, estimation, and applications.

Area of Science:

• Statistics and Probability Theory
• Mathematical Modeling

Background:

• Existing probability distributions may not adequately capture complex data patterns.
• The Tiessier distribution offers a foundation for developing more versatile statistical models.

Purpose of the Study:

• To introduce a novel unit distribution with a versatile hazard function capable of various shapes (e.g., bathtub, N-shaped).
• To explore the fundamental properties of this new distribution.
• To evaluate parameter estimation techniques and compare the new distribution's performance against established models.

Main Methods:

• Development of a new unit distribution extending the Tiessier distribution.
• Implementation of maximum likelihood estimation and eleven alternative parameter approximation methods.
• Conducting simulation studies to assess parameter estimation accuracy, especially with small sample sizes.
• Applying the novel distribution to two real-world datasets and evaluating its performance using model selection criteria and goodness-of-fit tests.

Main Results:

• The study demonstrates the precision of parameter estimation methods, even for small sample sizes.
• The novel distribution's performance was evaluated against established models on two datasets.
• The new distribution exhibited superior performance in capturing data patterns compared to existing models.

Conclusions:

• The new unit distribution offers a versatile and effective tool for statistical modeling.
• The developed parameter estimation methods are robust and accurate.
• The distribution has potential for cross-disciplinary applications and advances probability theory and statistical inference.