Distributions generated by the hypergeometric function \(_{p+1}F_p(\alpha_1,\dots,\alpha_{p+1};\gamma_1,\dots,\gamma_p;\lambda)\) (Q2783483)
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scientific article; zbMATH DE number 1730458
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distributions generated by the hypergeometric function \(_{p+1}F_p(\alpha_1,\dots,\alpha_{p+1};\gamma_1,\dots,\gamma_p;\lambda)\) |
scientific article; zbMATH DE number 1730458 |
Statements
21 April 2002
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discrete distributions
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Pearson's family
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Gaussian hypergeometric functions
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Distributions generated by the hypergeometric function \(_{p+1}F_p(\alpha_1,\dots,\alpha_{p+1};\gamma_1,\dots,\gamma_p;\lambda)\) (English)
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Using the hypergeometric distribution \(_{p+1}F_{p}(\alpha_{1},\dots,\alpha_{p+1}; \gamma_{1},\dots,\gamma_{p},\lambda)\) a family of discrete Pearson distributions is determined. The authors uses the corresponding moment generating functions and obtain an expression of the needed hypergeometric series. The estimation of the parameters is analyzed. Some distributions are generated and plotted for \(p=2,3,5\) and 6.
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