# Balding–Nichols model

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Parameters Probability density function Cumulative distribution function $0 (real)$0 (real) For ease of notation, let$\alpha ={\tfrac {1-F}{F}}p$ , and $\beta ={\tfrac {1-F}{F}}(1-p)$ $x\in (0;1)\!$ ${\frac {x^{\alpha -1}(1-x)^{\beta -1}}{\mathrm {B} (\alpha ,\beta )}}\!$ $I_{x}(\alpha ,\beta )\!$ $p\!$ $I_{0.5}^{-1}(\alpha ,\beta )$ no closed form ${\frac {F-(1-F)p}{3F-1}}$ $Fp(1-p)\!$ ${\frac {2F(1-2p)}{(1+F){\sqrt {F(1-p)p}}}}$ $1+\sum _{k=1}^{\infty }\left(\prod _{r=0}^{k-1}{\frac {\alpha +r}{{\frac {1-F}{F}}+r}}\right){\frac {t^{k}}{k!}}$ ${}_{1}F_{1}(\alpha ;\alpha +\beta ;i\,t)\!$ 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 FST F, are distributed according to independent draws from

$B\left({\frac {1-F}{F}}p,{\frac {1-F}{F}}(1-p)\right)$ 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.