  The fundamental problem of similarity studies, in the frame of data-mining,
is to examine and detect similar items in articles, papers, books, with huge
sizes. In this paper, we are interested in the probabilistic, and the
statistical and the algorithmic aspects in studies of texts. We will be using
the approach of $k$\textit{-shinglings}, a $k$\textit{-shingling} being defined
as a sequence of $k$ consecutive characters that are extracted from a text
($k\geq 1$ ). The main stake in this field is to find accurate and quick
algorithms to compute the similarity in short times. This will be achieved in
using approximation methods. The first approximation method is statistical and,
is based on the theorem of Glivenko-Cantelli. The second is the banding
technique. And the third concerns a modification of the algorithm proposed by
Rajaraman and al (% \cite{AnandJeffrey}), denoted here as (RUM). The Jaccard
index is the one used in this paper. We finally illustrate these results of the
paper on the four Gospels. The results are very conclusive.
