maxPartialSumd: Maximum of the partial sum [probability] [iid]

In localScore: Package for Sequence Analysis by Local Score

Maximum of the partial sum [probability] [iid]

Description

Calculates the distribution of the maximum of the partial sum process for a given value in the identically and independantly distributed model

Usage

maxPartialSumd(k, score_probabilities, sequence_min, sequence_max)

Arguments

k	value at which calculates the probability
score_probabilities	the probabilities for each unique score from lowest to greatest
sequence_min	minimum score
sequence_max	maximum score

Details

Implement the formula (4) of the article Mercier, S., Cellier, D., & Charlot, D. (2003). An improved approximation for assessing the statistical significance of molecular sequence features. Journal of Applied Probability, 40(2), 427-441. doi:10.1239/jap/1053003554
Important note : the calculus of the parameter of the distribution uses the resolution of a polynome which is a function of the score distribution, of order max(score)-min(score). There exists only empirical methods to solve a polynome of order greater that 5 with no warranty of reliable solution. The found roots are checked internally to the function and an error message is throw in case of inconsistency.

Value

A double representing the probability of the maximum of the partial sum process equal to k

Examples

maxPartialSumd(10, c(0.08, 0.32, 0.08, 0.00, 0.08, 0.00, 0.00, 0.08, 0.02, 0.32, 0.02), -6, 4)

localScore documentation built on Nov. 3, 2023, 1:08 a.m.