Balding–Nichols model

Balding-Nichols

Probability density function
Cumulative distribution function
Parameters	${\displaystyle 0<F<1}$(real) ${\displaystyle 0<p<1}$ (real) For ease of notation, let ${\displaystyle \alpha ={\tfrac {1-F}{F}}p}$, and ${\displaystyle \beta ={\tfrac {1-F}{F}}(1-p)}$
Support	${\displaystyle x\in (0;1)\!}$
PDF	${\displaystyle {\frac {x^{\alpha -1}(1-x)^{\beta -1}}{\mathrm {B} (\alpha ,\beta )}}\!}$
CDF	${\displaystyle I_{x}(\alpha ,\beta )\!}$
Mean	${\displaystyle p\!}$
Median	${\displaystyle I_{0.5}^{-1}(\alpha ,\beta )}$ no closed form
Mode	${\displaystyle {\frac {F-(1-F)p}{3F-1}}}$
Variance	${\displaystyle Fp(1-p)\!}$
Skewness	${\displaystyle {\frac {2F(1-2p)}{(1+F){\sqrt {F(1-p)p}}}}}$
MGF	${\displaystyle 1+\sum _{k=1}^{\infty }\left(\prod _{r=0}^{k-1}{\frac {\alpha +r}{{\frac {1-F}{F}}+r}}\right){\frac {t^{k}}{k!}}}$
CF	${\displaystyle {}_{1}F_{1}(\alpha ;\alpha +\beta ;i\,t)\!}$

In population genetics, the Balding–Nichols model is a statistical description of the allele frequencies in the components of a sub-divided population.^[1] 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

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

where B is the Beta distribution. This distribution has mean p and variance Fp(1 – p).^[2]

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.

References

This genetics article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e