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A Look at the Primary Order Preserving Properties of Stochastic Orders: Theorems, Counterexamples and Applications in Cognitive Psychology

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  • Mohsen Soltanifar

    (Biostatistics Division, Dalla Lana School of Public Health, University of Toronto, 620-155 College Street, Toronto, ON M5T 3M7, Canada
    Analytics Division, College of Professional Studies, Northeastern University, 1400-410 West Georgia Street, Vancouver, BC V6B 1Z3, Canada
    Continuing Studies Division, Population Data BC, University of Victoria, B364-3800 Finnerty Road, Victoria, BC V8P 5C2, Canada
    This paper is an extended version of our paper published in “ Soltanifar, M. Some Results on the Additivity and Multiplication Order Preserving Properties of Stochastic Orders. In JSM Proceedings ; SSC Section; American Statistical Association: Alexandria, VA, USA, 2020; pp. 476–483”.)

Abstract

In this paper, we prove that for a set of ten univariate stochastic orders including the usual order, a univariate stochastic order preserves either both, one or none of additivity and multiplication properties over the vector space of real-valued random variables. Then, classifying participant’s quickness in a mental chronometry trial to “weakly faster” and “strongly faster”, we use the above results for the usual stochastic order to establish necessary and sufficient conditions for a participant to be strongly faster than the other in terms of the fitted Wald, Exponentially modified Wald(ExW), and Exponentially modified Gaussian(ExG) distributional parameters. This research field remains uncultivated for other univariate stochastic orders and in several directions.

Suggested Citation

  • Mohsen Soltanifar, 2022. "A Look at the Primary Order Preserving Properties of Stochastic Orders: Theorems, Counterexamples and Applications in Cognitive Psychology," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4362-:d:978511
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    Cited by:

    1. Mohsen Soltanifar & Chel Hee Lee, 2023. "SimSST: An R Statistical Software Package to Simulate Stop Signal Task Data," Mathematics, MDPI, vol. 11(3), pages 1-15, January.

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