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 independently distributed model

Usage

maxPartialSumd(
  k,
  score_probabilities,
  sequence_min = NULL,
  sequence_max = NULL,
  score_values = NULL
)

Arguments

k	value at which calculates the probability
score_probabilities	the probabilities for each score from lowest to greatest (Optionnaly with scores as names)
sequence_min	minimum score (optional if score_values OR names(score_probabilities) is defined)
sequence_max	maximum score (optional if score_values OR names(score_probabilities) is defined)
score_values	vector of integer score values, associated to score_probabilities (optional if sequence_min and sequence_max OR names(score_probabilities) are defined)

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)
prob <- c(0.08, 0.32, 0.08, 0.00, 0.08, 0.00, 0.00, 0.08, 0.02, 0.32, 0.02)
score_values <- which(prob != 0) - 7 # keep only non null probability scores
prob0 <- prob[prob != 0]             # and associated probability
p <- maxPartialSumd(10, prob, sequence_min = -6, sequence_max =  4)
p0 <- maxPartialSumd(10,prob0, score_values = score_values)
p == p0 # TRUE

localScore documentation built on June 8, 2025, 10:34 a.m.