| viXra.org > Statistics > 2609 |
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| viXra.org > Statistics > 2609 |
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[2] viXra:2609.0017 [pdf] submitted on 2026-09-07 05:26:48
Authors: Harris V. Georgiou
Comments: 21 Pages.
In Urban Search & Rescue (USAR) operations after large-scale earthquakes, time is of essence for the survival of trapped victims. There are too many parameters that define the conditions, severity and survivability window for each victim entombed under debris. Hence, worksite assessment and triage is primarily an empirical procedure that is based on incomplete and mostly qualitative information. On the other hand, if statistical rescue data from previous USAR missions are available, appropriate probabilistic models can be developed for estimated rescue counts and live victims remaining over time. This study explores the availability of such historic data and, based on these, several probabilistic models are designed. These include Exponential and Weibull for inter-rescue times, non-homogenous Poisson for rescue counts and Generalized Extreme Value (GEV) for the tails of the underlying data distributions. All the models converge to very similar results for survival windows and in accordance to real rescue data. Namely, the 95% and 99% quantiles point to 115-118 hours (4.8-4.9 days) and 177-181 hours (7.4-7.5 days), respectively. A mixed-model approach is proposed for more accurate approximations, selecting GEV for the beginning (up to day 2) and ending phases (days 5-8), Weibull for the middle (days 3-4) and non-homogenous Poisson everywhere else (days 2-3, 4-5), with a relative approximation error no more than 4.5% compared to real rescue data throughout the typical USAR operational period of eight days. Finally, the GEV model is also used for investigating the effect of under-reporting live rescues during the first 24-hour window of USAR operations, providing hints of a factor at the order of 1-in-5 to 1-in-8 or more, especially during the first six hours. These results provide valuable insights for better planning and team deployment in such USAR missions after large-scale earthquakes.
Category: Statistics
[1] viXra:2609.0009 [pdf] submitted on 2026-09-06 22:07:09
Authors: Teo Banica
Comments: 400 Pages.
This is an advanced introduction to the various types of normal random variables, with most of the needed preliminaries included. We first discuss the probability basics, standard central limits, and the theory of the usual, real normal variables, with examples, illustrations and numerous formulae. Then we go on a similar discussion regarding the complex normal variables, and the Rayleigh variables too. We then move to arbitrary dimensions, with a discussion regarding the Gaussian vectors, and related probability laws, featuring some functional analysis, and geometry and physics too. Finally, we provide an introduction to the quantum versions of the normal variables, and notably to those coming from free probability and random matrices.
Category: Statistics
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