Should a questionnaire generate only a finite number of scores, the data will then be considered polytomous and suitable statistical techniques will be used to analyse any such data.
Each matrix entry, w ia, was set to log((f ia + δ)/(P a + δ)), where f ia is the frequency with which base a appears in the ith position in the known sites, P a is the frequency with which base a appears in the promoters of genes and δ is a small number added to ensure that the weight matrix score is finite even when f ia = 0.
This is always a potential problem when using a finite scale aiming to simultaneously measure absolute and change in score.
Let us first prove that all moments of user scores are finite, even if no cut-offs are used.
As a result, all innocent and guilty user score moments are finite, and so for large c from the Central Limit Theorem, it follows that the distributions of user scores will converge to Gaussians.
While the aim of this paper is to derive score pdf for finite-size samples, it appears that infinite-size samples were assumed in eqs (7 - 9) and elsewhere.
By projecting the functional curves onto set of eigenfunctions, we can reduce the dimension to finite number, functional principal component scores.
If you use real alignment scores using an amino acid weight matrix such as BLOSUM [ 7], the number of possible scores is still finite although much greater than with k-tuple distances.
Although the discretization of individual risk scores into a finite (and often small) set of risk groups may introduce bias (Gerds and Schumacher, 2001), this approach is very intuitive and conforms to the daily doctors' decision making process, e.g. the attribution of either low or high risk to patients.
Taking into account the finite sample effect and the skewness of peak intensity distribution, the form of asymptotic score statistics (P-values) of RAId_DbS [ 13] is derived theoretically.
