Pearson System

Generalizes the differential equation for the Gaussian Distribution

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(2)

0. , . E.g., Normal Distribution.

I. , . E.g., Beta Distribution.

II. , , where .

III. , , where . E.g., Gamma Distribution. This case isintermediate to cases I and VI.

IV. , .

V. , where . Intermediate to cases IV and VI.

VI. , where is the larger root. E.g., Beta Prime Distribution.

VII. , , . E.g., Student's t-Distribution.

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References

Craig, C. C. ``A New Exposition and Chart for the Pearson System of Frequency Curves.'' Ann. Math. Stat. 7, 16-28, 1936.

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, p. 107, 1951.

Pearson, K. ``Second Supplement to a Memoir on Skew Variation.'' Phil. Trans. A 216, 429-457, 1916.

• Dirichlet Beta Function
• Dirichlet Boundary Conditions
• Dirichlet Conditions
• Dirichlet Divisor Problem
• Dirichlet Energy
• Dirichlet Eta Function
• Dirichlet Fourier Series Conditions
• Dirichlet Function
• Dirichlet Integrals
• Dirichlet Kernel
• Dirichlet Lambda Function
• Dirichlet L-Series
• Dirichlet Region
• Dirichlet's Boxing-In Principle
• Dirichlet's Box Principle
• Dirichlet Series
• Dirichlet's Formula
• Dirichlet's Lemma
• Dirichlet's Principle
• Dirichlet's Test
• Dirichlet's Theorem
• Dirichlet Structure Constant
• Dirichlet Tessellation
• Dirty Beam
• Dirty Map