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