Asymptotics and Well-Posedness of the Derived Distribution Density in a Study of Biovariability
Burgei, Wesley A.
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In our recent work (Wang, Burgei, and Zhou, 2018) we studied the hearing loss injury among subjects in a crowd with a wide spectrum of heterogeneous individual injury susceptibility due to biovariability. The injury risk of a crowd is defined as the average fraction of injured. We examined mathematically the injury risk of a crowd vs the number of acoustic impulses the crowd is exposed to, under the assumption that all impulses act independently in causing injury regardless of whether one is preceded by another. We concluded that the observed dose-response relation can be explained solely on the basis of biovariability in the form of heterogeneous susceptibility. We derived an analytical solution for the distribution density of injury susceptibility, as a power series expansion in terms of scaled log individual non-injury probability. While theoretically the power series converges for all argument values, in practical computations with IEEE double precision, at large argument values, the numerical accuracy of the power series summation is completely wiped out by the accumulation of round-off errors. In this study, we derive a general asymptotic approximation at large argument values, for the distribution density. The combination of the power series and the asymptotics provides a practical numerical tool for computing the distribution density. We then use this tool to verify numerically that the distribution obtained in our previous theoretical study is indeed a proper density. In addition, we will also develop a very efficient and accurate Pade approximation for the distribution density.
The article of record as published may be found at http://dx.doi.org/10.4236/am.2018.96046
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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Wang, Hongyoun; Burgei, Wesley; Zhou, Hong (Scientific Research Publishing, 2018);In our recent work (Wang, Burgei, and Zhou, 2018) we studied the hearing loss injury among subjects in a crowd with a wide spectrum of heterogeneous individual injury susceptibility due to biovariability. The injury risk ...
Wang, Hongyun; Burgei, Wesley A.; Zhou, Hong (Scientific Research Publishing Inc., 2018);We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crowd vs ...
Interpreting Dose-Response Relation for Exposure to Multiple Sound Impulses in the Framework of Immunity Wang, Hongyun; Burgei, Wesley A.; Zhou, Hong (Scientific Research Publishing SCIRP, 2017);Hearing loss is a common military health problem and it is closely related to exposures to impulse noises from blast explosions and weapon firings. In a study based on test data of chinchillas and scaled to humans (Military ...