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Table 1 Probability density and mass functions of probability distributions used to define ISOpure.

From: Computational purification of individual tumor gene expression profiles leads to significant improvements in prognostic prediction

Probability density/mass functiona, b
Dirchlet x | a = Γ k = 1 K a k k = 1 K Γ a k k = 1 K x k a k - 1
Multinomial y | π = k = 1 K y k ! k = 1 K y k ! k = 1 K π k y k
  1. aThe parameters x, a, y, and π are all assumed to be vectors of length K. Note that the canonical parameter of the multinomial distribution that represents the number of trials is implicit here (that is, the number of trials here is defined as the sum of all elements of y).
  2. bΓ(a) is the gamma function of scalar a.