Truncated Power-Normal Distribution with Application to Non-Negative Measurements

Area of Science:

• Statistics
• Probability Theory
• Mathematical Statistics

Background:

• The power-normal (PN) distribution is a flexible model for continuous data.
• Existing models may not adequately capture the characteristics of positive-valued data.
• Truncated distributions offer a way to adapt existing models for specific data ranges.

Purpose of the Study:

• To introduce and study a truncated positive version of the power-normal distribution.
• To extend the half-normal distribution by using a zero truncation point.
• To evaluate the proposed model's performance for positive data.

Main Methods:

• Derivation of probabilistic properties for the new distribution.
• Estimation of model parameters using maximum likelihood and moments methods.
• Fitting the proposed model to two real-world positive datasets.

Main Results:

• The proposed truncated power-normal model demonstrates good performance.
• The model serves as a viable extension of the half-normal distribution.
• Comparative analysis indicates favorable results against alternative models for positive data.

Conclusions:

• The truncated positive power-normal distribution is a promising model for analyzing positive data.
• The estimation methods (maximum likelihood and moments) are effective for the proposed model.
• The model's flexibility and performance make it suitable for practical applications in statistics.