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Modelling the effects of exposure to risk on junior faculty productivity incentives under the academic tenure system
Published in Nnamdi Nwulu, Mammo Muchie, Engineering Design and Mathematical Modelling, 2020
Now, letting µ = E(p) be the expected monetary value of publication, then p can be represented as p = + σe, where e is a random variable with zero mean, and introducing randomness in the monetary value of publication p. The random component e can exhibit any distribution for which both the mean and the variance exist. The standard deviation of the monetary value of publication, σ, can be interpreted as a mean-preserving spread parameter for the distribution of p. Therefore, in this analysis, the probability distribution of p will be characterized by the mean µ and the mean preserving spread parameter σ following the analysis of firm production under uncertainty by Sandmo (1971).
Coordinating supply chains with uncertain production cost by incomplete contracts
Published in International Journal of Production Research, 2022
Shouting Zhao, Juliang Zhang, T. C. E. Cheng
We next analyse the impact of the production cost uncertainty on the optimal capacity and profit. We use the mean preserving spread of the distribution to model the uncertainty. According to Rothschild and Stiglitz (1970), a mean-preserving spread is obtained by taking some probability masses from the centre of a distribution to the tails, in such a way to preserve the mean. The mean-preserving spread makes the distribution of a variable more dispersive, so increasing its variability. Thus, the mean preserving spread is often employed to compare the uncertainty of variables that have the same mean. It has been shown that the mean preserving spread of a distribution is better for measuring uncertainty than the variance (Rothschild and Stiglitz 1970; Van Mieghem 2007; Cui and Veeraraghavan 2016).