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Quantile cumulative distribution function and its applications

Abstract

In this article, we consider functions having the properties of both the cumulative distribution function and the quantile function. Due to these characteristics, we term such functions quantile cumulative distribution functions. The comparison distribution function defined by Parzen (1982) for comparing the probability distributions of two populations is an example of such a function. We discuss some properties of the quantile cumulative distribution function and its usefulness in generating new continuous probability distributions on the unit interval. An overview of some of their applications is also presented to emphasize the importance of the quantile cumulative distribution function.

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date_range 2024

language English

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Mathew Angel

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Cumulative distribution function

quantile function

quantile density function

comparison distribution

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Effect of corrosion on flexural strength of reinforced concrete beams with polypropylene fibers

Abstract

An experimental study was performed to investigate the effects of polypropylene fibers on uncorroded and corroded reinforced concrete beams. Three different volume fractions of polypropylene fibers having 0, 0.5, and 1.5%, were tested at four corrosion levels of 0% and approximately 5, 7, and 9%. A full scale of an accelerated corrosion pool was used for the accelerated corrosion process. Reinforced concrete beams were used for an under monotonic bending test. The contribution of the actual corrosion levels of transverse and longitudinal reinforcement bars to the total corrosion levels were obtained from reinforcement bars fully extracted from concrete. Flexural strength, bond-slip, and moment-curvature relationships were examined for uncorroded and corroded reinforced concrete beams. A new model was developed to predict the flexural strength of corroded reinforced concrete beams. The proposed model for predicting the residual flexural strength of corroded beams was compared with test data published in previous studies. Furthermore, a novel model is presented for improved predictions between the actual and theoretically estimated corrosion mass losses, based on Faraday’s law, with the aid of fully extracted reinforcement bars. The model used to predict the flexural strength of corroded reinforced concrete beams with large sizes demonstrated good agreement with current and previously published literature data. In the case of corroded beams comprising differing amounts of polypropylene fibers, the performance of the corroded beams was limited by a fiber volume fraction of 1.5% at low corrosion levels.

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date_range 2018

language English

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