Английская Википедия:Balding–Nichols model

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Шаблон:Short description Шаблон:Probability distribution {\mathrm{B}(\alpha,\beta)}\!</math> | cdf = <math>I_x(\alpha,\beta)\!</math> | mean = <math>p\!</math> | median = <math>I_{0.5}^{-1}(\alpha,\beta)</math> no closed form | mode = <math>\frac{F-(1-F)p}{3F-1}</math> | variance = <math>Fp(1-p)\!</math> | skewness = <math>\frac{2F(1-2p)}{(1+F)\sqrt{F(1-p)p}}</math> | kurtosis = | entropy = | mgf = <math>1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha+r}{\frac{1-F}{F}+r}\right) \frac{t^k}{k!}</math> | char = <math>{}_1F_1(\alpha; \alpha+\beta; i\,t)\!</math> }}

In population genetics, the Balding–Nichols model is a statistical description of the allele frequencies in the components of a sub-divided population. With background allele frequency p the allele frequencies, in sub-populations separated by Wright's F_ST F, are distributed according to independent draws from

<math>B\left(\frac{1-F}{F}p,\frac{1-F}{F}(1-p)\right)</math>

where B is the Beta distribution. This distribution has mean p and variance Fp(1 – p).

The model is due to David Balding and Richard Nichols and is widely used in the forensic analysis of DNA profiles and in population models for genetic epidemiology.