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The distribution of this sum is given by P X ; N dX = 2 - N 2 Γ N 2 e - 1 2 X X N 2 - 1 dX, with X ≡ χ 2. (5).
We then compared the permutation distribution of this sum to the observed sum.
We then compared the permutation distribution of this sum to the observed sum, the p value is defined as the proportion of times the sum of these squared log2 ratios (post/pre) was greater than the observed sum of the log2 ratios (post/pre) of genes associated with age.
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Under the background model, the distribution function of this sum of n independent and identically distributed (i.i.d).i.d
The distribution of the sum of independent identically distributed gamma random variables is well known.
However, within the scientific field, it is necessary to know the distribution of the sum of independent non-identically distributed (i.n.i.d).n.i.d
Assuming independence between base calls, this probability can be computed using the distribution of the sum of n independent Bernoulli random variables with success probabilities p1, p2,…, p n where p i = 10−0.1× Q i.
In this study, we describe the use of approximation methods to calculate the distribution of the sum of i.n.i.d.n.i.d
The second one is related to the asymptotic representation of the distribution of the sum of independent random variables.
To calculate the exact probability distribution of the sum of i.n.i.d.n.i.d
Additionally, Moschopoulos [13] calculated the distribution of the sum of i.n.i.d.n.i.d
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com