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The present paper shows that for certain algorithms such as sorting, the parameters of the input distribution must also be taken into account, apart from the input size, for a more precise evaluation of computational and time complexity (average case only) of the algorithm in question (the so-called “gold standard”). Some concrete results are presented to warrant a new and improved model for replacement sort (also called selection sort) aswhere the LHS gives the average case time complexity, n is the input size, p_i’s the parameters of the input distribution characterizing the sorting elements, i is the average number of interchanges which is a function of both the input size and the parameters, the rest of the terms arising due to linear regression and have usual meanings. The error term ϵ arises as we have fixed only the input size n in the model but varying the specific input elements and their relative positions in the …