Chi-p distribution: characterization of the goodness of the fitting using L p norms

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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 languageEnglish (US)
Article number4
JournalJournal of Statistical Distributions and Applications
Issue number1
StatePublished - Dec 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computer Science Applications
  • Statistics, Probability and Uncertainty


  • Double Role
  • General Gaussian Distribution
  • Shape Parameter
  • Total Deviation
  • Unit Radius


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