beta distribution

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11: 29.3 Definitions and Basic Properties

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§29.3(ii) Distribution

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29.3.10 $${\beta }_p-H-\frac{{\alpha }_{p-1}{\gamma }_p}{{\beta }_{p-1}-H-}\frac{{\alpha }_{p-2}{\gamma }_{p-1}}{{\beta }_{p-2}-H-}\mathrm{\cdots }=\frac{{\alpha }_p{\gamma }_{p+1}}{{\beta }_{p+1}-H-}\frac{{\alpha }_{p+1}{\gamma }_{p+2}}{{\beta }_{p+2}-H-}\mathrm{\cdots },$$

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Symbols:

$p$: nonnegative integer, $H$ , ${\alpha }_p$ , ${\beta }_p$ and ${\gamma }_p$

Referenced by:

§29.20(i), §29.3(iii), §29.3(iii), §29.3(iii), §29.3(iii)

Permalink:

http://dlmf.nist.gov/29.3.E10

Encodings:

pMML, png, TeX

See also:

Annotations for §29.3(iii), §29.3 and Ch.29

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$${\beta }_p=4p^2(2-k^2),$$

… ►The continued fraction following the second negative sign on the left-hand side of (29.3.10) is finite: it equals 0 if $p=0$, and if $p>0$, then the last denominator is ${\beta }_0-H$. … ►

$${\beta }_p={(2p+2)}^2(2-k^2),$$

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12: Bibliography G

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Quasirandom distributed bases for bound problems. J. Chem. Phys. 114 (9), pp. 3929–3939.

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Referenced by:

§18.39(iii).

Encodings:

BibTeX

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Algorithm 222: Incomplete beta function ratios. Comm. ACM 7 (3), pp. 143–144.

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Notes:

Variable-precision Algol program. For a Certification see same journal 7 (1964), p. 244.

External Links:

ISSN 0001-0782, Document, Certification

Referenced by:

§8.28(iv).

Encodings:

BibTeX

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