  The topic of the article is the parametric study of the complexity of
algorithms on arrays of pairwise distinct integers. We introduce a model that
takes into account the non-uniformness of data, which we call the Ewens-like
distribution of parameter $\theta$ for records on permutations: the weight
$\theta^r$ of a permutation depends on its number $r$ of records. We show that
this model is meaningful for the notion of presortedness, while still being
mathematically tractable. Our results describe the expected value of several
classical permutation statistics in this model, and give the expected running
time of three algorithms: the Insertion Sort, and two variants of the Min-Max
search.
