From M yaffe Notes cont Lecture #2 Probability values for the extreme value distribution(A)and the normal distribution(B). The area under each curve is I The random sequence alignment scores would give rise to an"extreme value distribution -like a skewed gaussian Called Gumbel extreme value distribution or a normal distribution with a mean m and a variance o, the height of the curve is described by Y1/ov2) exp[-(x-m)2/2021 For an extreme value distribution, the height of the curve is described by Y=exp[-x-e-x].and P(S>x)=1-exp[-e-xx-ul)l where u=(In Kmn)/n Can show that mean extreme score is-log2 (nm), and the probability of getting a score that exceeds some number of standard deviations"X is P(S>X)- Kmne-x ***K and n are tabulated for different matrices *** For the less statistically inclined E- Kmne-usFrom M. Yaffe Notes (cont) Lecture #2 • The random sequence alignment scores would give rise to an “extreme value” distribution – like a skewed gaussian. • Called Gumbel extreme value distribution For a normal distribution with a mean m and a variance σ, the height of the curve is described by Y=1/(σ√2π) exp[-(x-m)2/2σ2] For an extreme value distribution, the height of the curve is described by Y=exp[-x-e-x] …and P(S>x) = 1-exp[-e-λ(x-u)] where u=(ln Kmn)/λ Can show that mean extreme score is ~ log2(nm), and the probability of getting a score that exceeds some number of “standard deviations” x is: P(S>x)~ Kmne-λx. ***K and λ are tabulated for different matrices **** For the less statistically inclined: E~ Kmne -λS -2 -1 0.2 Yev 0.4 -4 4 0.4 B. Yn Probability values for the extreme value distribution (A) and the normal distribution (B). The area under each curve is 1. 0 1 2 X X A. 3 4 5