Abstract
This paper derives (1) the Chi-p distribution, i.e., the analog of Chi-square distribution but for datasets that follow the General Gaussian distribution of shape p, and (2) develops the statistical test for characterizing the goodness of the fitting with L p norms. It is shown that the statistical test has double role when the fitting method is induced by the L p norms: For given the shape parameter p, the test is rated based on the estimated p-value. Then, a convenient characterization of the fitting rate is developed. In addition, for an unknown shape parameter and if the fitting is expected to be good, then those L p norms that correspond to unlikely p-values are rejected with a preference to the norms that maximized the p-value. The statistical test methodology is followed by an illuminating application.
Original language | English (US) |
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Article number | 4 |
Journal | Journal of Statistical Distributions and Applications |
Volume | 1 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1 2014 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Computer Science Applications
- Statistics, Probability and Uncertainty
Keywords
- Double Role
- General Gaussian Distribution
- Shape Parameter
- Total Deviation
- Unit Radius