Probability plots based on Student's t-distribution

Area of Science:

• Statistics
• Data Analysis

Background:

• Normal distribution is a common error model.
• Probability plots, specifically half-normal plots, are used to test its validity.
• Real-world data frequently contain outliers that deviate from the normal distribution.

Purpose of the Study:

• To describe the application of t-distributions in probability plots for more realistic data modeling.
• To demonstrate a method for determining the optimal parameter (nu) for the t-distribution from data.
• To compare the modeling capabilities of t-distributions against normal distributions for data with potential outliers.

Main Methods:

• Utilizing probability plots with t-distributions instead of normal distributions.
• Developing and applying a data-driven method to estimate the parameter nu of the t-distribution.
• Analyzing datasets that appear to fit a normal distribution to assess the benefits of using a t-distribution.

Main Results:

• T-distributions provide a more realistic error model for data containing outliers.
• A method for determining the appropriate nu parameter for t-distributions from the data was successfully demonstrated.
• Even datasets that initially seem well-modeled by a normal distribution can exhibit improved representation using a t-distribution.

Conclusions:

• T-distributions are a valuable alternative to normal distributions for modeling real-world data, especially when outliers are present.
• The proposed method for parameter estimation enhances the practical application of t-distributions in statistical analysis.
• Employing t-distributions can lead to a more accurate understanding of data generating processes compared to relying solely on normal distributions.