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The fundamental problem of similarity studies, in the frame of data-mining,is to examine and detect similar items in articles, papers, books, with hugesizes. In this paper, we are interested in the probabilistic, and thestatistical and the algorithmic aspects in studies of texts. We will be usingthe approach of $k$\textit{-shinglings}, a $k$\textit{-shingling} being definedas 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 quickalgorithms to compute the similarity in short times. This will be achieved inusing approximation methods. The first approximation method is statistical and,is based on the theorem of Glivenko-Cantelli. The second is the bandingtechnique. And the third concerns a modification of the algorithm proposed byRajaraman and al (% \cite{AnandJeffrey}), denoted here as (RUM). The Jaccardindex is the one used in this paper. We finally illustrate these results of thepaper on the four Gospels. The results are very conclusive.

Probabilistic, statistical and algorithmic aspects of the similarity of texts and application to Gospels comparison