# Daudin [p-value] [iid] Calculates the exact p-value in the identically and independently distributed of a given local score, a sequence length that 'must not be too large' and for a given score distribution ```r daudin( local_score, sequence_length, score_probabilities, sequence_min = NULL, sequence_max = NULL, score_values = NULL ) ``` ## Arguments - `local_score`: the observed local score - `sequence_length`: length of the sequence - `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) ## Returns A double representing the probability of a local score as high as the one given as argument. ## Details Either `sequence_min` and `sequence_max` are specified as input, OR all possible score values in `score_values` vector ; one of this choice is required. 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 exponentiation which takes times. 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). ## Examples ```r p1 <- daudin(local_score = 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) p2 <- daudin(local_score = 4, sequence_length = 50, score_probabilities = c(0.2, 0.3, 0.1, 0.2, 0.1, 0.1), score_values = as.integer(-3:2)) p1 == p2 # TRUE 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) - 6 # keep only non null probability scores prob0 <- prob[prob != 0] # and associated probability p <- daudin(150, 10000, prob, sequence_min = -5, sequence_max = 5) p0 <- daudin(150, 10000, prob0, score_values = score_values) names(prob0) <- score_values p1 <- daudin(150, 10000, prob0) p == p0 # TRUE p == p1 # TRUE ```

daudin function