daudin {localScore}

Daudin [p-value] [iid]

Description

Calculates the exact p-value in the identically and independantly distributed of a given local score, a sequence length that 'must not be too large' and for a given score distribution

Usage

daudin(
  localScore,
  sequence_length,
  score_probabilities,
  sequence_min,
  sequence_max
)

Arguments

localScore

the observed local score

sequence_length

length of the sequence

score_probabilities

the probabilities for each score from lowest to greatest

sequence_min

minimum score

sequence_max

maximum score

Details

Small in this context depends heavily on your machine. On a 3,7GHZ machine this means for daudin(1000, 5000, c(0.2, 0.2, 0.2, 0.1, 0.2, 0.1), -2, 3) an execution time of ~2 seconds. This is due to the calculation method using matrix exponentation which becomes very fast very slow. The size of the matrix of the exponentiation is equal to a+1 with a the local score value. The matrix must be put at the power n, with n the sequence length. Moreover, it is known that the local score value is expected to be in mean of order log(n).

Value

A double representing the probability of a local score as high as the one given as argument

Examples

daudin(localScore = 4, sequence_length = 50, 
score_probabilities = c(0.2, 0.3, 0.1, 0.2, 0.1, 0.1), sequence_min = -3, sequence_max = 2)