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α: calibrated so average coauthorship-adjusted count equals average raw count
Based on time series of crude oil prices (daily spot), this paper analyses price fluctuation with two significant parameters [tau] (speculators' time scales of investment) and [epsilon] (speculators' expectations of return) by using Zipf analysis technique, specifically, by mapping [tau]-returns of prices into 3-alphabeted sequences (absolute frequencies) and 2-alphabeted sequences (relative frequencies), containing the fundamental information of price fluctuations. This paper empirically explores parameters and identifies various types of speculators' cognition patterns of price behavior. In order to quantify the degree of distortion, a feasible reference is proposed: an ideal speculator. Finally, this paper discusses the similarities and differences between those cognition patterns of speculators' and those of an ideal speculator. The resultant analyses identify the possible distortion of price behaviors by their patterns.