China 
Africa 
Explore chapters and articles related to this topic
Probability Theory
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
for −∞<x<∞. The shape of this density function is the classic bell-shaped curve, symmetric around x=μ. Many natural random phenomena follow this distribution (approximately), and it is also the limiting distribution for several other well-known distributions. Furthermore, a result called the Central Limit Theorem says that the sum of a large number of independent and identically distributed random variables has a distribution that is approximately Normal. This is one of the most remarkable and important results in all of probability theory.
C
Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
center of projection the point within a projector from which all the light rays appear to diverge; the point in a camera towards which all the light rays appear to converge before they cross the imaging plane or photographic plate. central absolute moment for random variable x, the pth central absolute moment is given by E[|x - E[x]| p ]. See central moment, absolute moment, expectation. central limit theorem (CLT) (1) a theorem that the distribution of the sum of independent and identically distributed random variables tends toward a Gaussian distribution as the number of individual random variables approaches infinity. (2) in probability, the theorem that the density function of some function of n independent random variables tends towards a normal distribution as n tends to infinity, as long as the variances of
Stochastic analysis of dynamic stress amplification factors for slab track foundations
Published in International Journal of Rail Transportation, 2023
Hongwei Xie, Qiang Luo, Tengfei Wang, Liangwei Jiang, David P. Connolly
The amplitude of dynamic stresses on roadbed surfaces obeys a normal distribution, as Figure 5 shown. Extreme values generated from a normal random variable follow the Gumbel distribution (also known as the extreme value Type I distribution). This means the maximum values of independent and identically distributed random variables of the initial normal distribution converge to the Gumbel distribution [42]. A time history of subgrade dynamic stress is a sampling of subgrade dynamic responses at different loading positions, and the peaks occur at random locations. The DAF associated with peak stress naturally obeys the Gumbel distribution. Equation (12) shows its cumulative distribution function (CDF) F(ϕ), which is a double exponential function.
Analysis of the GI/M/c queue with N-threshold policy
Published in Quality Technology & Quantitative Management, 2022
F. P. Barbhuiya, Nitin Kumar, U. C. Gupta
In this section, we give a comprehensive description of the multi-server -policy queue. The customers arrive one at a time such that the interarrival times , , , are independent and identically distributed random variables with probability distribution function , probability density function , Laplace-Stieltjes transform (LST) and mean interarrival time . Here is the rate at which arrival occurs and . The system has multiple number of servers, i.e. where each server is independent and have exponentially distributed service time with mean . The arrivals form a single waiting line, and each server provides service individually based on FCFS (first-come, first-served) discipline.
Analysis of process flexibility designs under disruptions
Published in IISE Transactions, 2020
Erfan Mehmanchi, Hoda Bidkhori, Oleg A. Prokopyev
We consider designs based on the configuration explored in Jordan and Graves (1995) as introduced in Example 2. For each we consider and multiple . Moreover, we let and . The demands are assumed to be independent and identically distributed random variables from normal distribution with support . The normal distribution is often used in the related literature, see, e.g., the five benchmark test instances in Section 6 and the discussion in Jordan and Graves (1995). For each design and combinations of α and γ we simulate for 5000 product demands drawn from the aforementioned normal distribution.