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Pearson defined the fourth standardized moment of a symmetric distribution as its kurtosis. There has been much discussion in the literature concerning both the meaning of kurtosis, as well as the effectiveness of the classical sample kurtosis as a reliable measure of peakedness and tail weight. In this paper, we consider an alternative measure, developed by Crow and Siddiqui [1], used to describe kurtosis. Its value is calculated for a number of common distributions, and a derivation of its asymptotic distribution is given. Simulations follow, which reveal an interesting connection to the literature on the ratio of normal random variables.

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Placement and support of students in first-year mathematics courses at institutions of higher education has long been a consequential issue. In a bid to address it, many systems and institutions of higher learning have elected to implement a co-remediation framework in place of pre-remediation, due in large part to the prohibitive cost of the latter, both in terms of financial resource, as well as student academic progress. Accompanying this evolution has been the expansion of the introductory mathematics curriculum beyond algebra to include statistics and quantitative reasoning. The present study discusses three distinct introductory mathematics courses at a large urban public M.S. granting institution in the U.S., with the goal of identifying the characteristics that correlate with success in each. Conditional probability and non-completion rate analyses were implemented to compare student performance in each course. Predictive models were then trained and validated, building insight concerning the differential relationships of demographic and academic covariates with course completion.