China
Africa
Explore chapters and articles related to this topic
Contradictory Perspectives of Testing
Published in Kim H. Pries, Jon M. Quigley, Testing Complex and Embedded Systems, 2018
Sometimes the Cauchy distribution bears a resemblance to a very peaked normal distribution. The Cauchy distribution does not have any moments—it has no mean and it has no variance. Even so, the Cauchy distribution possesses a strong central tendency. We do not want to jump to the conclusion that we have a normal distribution based solely on a strong central tendency; for example, Figure 6.2 (a Minitab plot) shows that a Cauchy distribution looks somewhat like a normal distribution under certain conditions. It is much better if we understand the mechanisms for failure. We know that a relatively random set of different failure mechanisms will often produce a normal distribution. So, let’s go into our analysis knowing that information rather than assuming that information.
Statistical Preliminaries
Published in Jaakko Astola, Pauli Kuosmanen, Fundamentals of Nonlinear Digital Filtering, 2020
Jaakko Astola, Pauli Kuosmanen
It is also completely specified if the parameters μ and σ are known. The parameter μ gives the location of the distribution and the parameter σ indicates scale, i.e., the broadness of the distribution. However, a random variable with a Cauchy distribution does not even have the expectation, not to speak of the variance, because ∫−∞∞ξfC(ξ)dξ
PIM Suppression Technology for Microwave Components
Published in Wanzhao Cui, Jun Li, Wei Huan, Xiang Chen, Passive Intermodulation, 2022
Tiancun Hu, He Bai, Qi Wang, Lu Tian
The peak, mode and median of the above probability distribution are 0. However, the mean, variance and moments of the Cauchy distribution are not defined, which is not conducive to subsequent analysis. As shown in Figure 6.5, the probability density curves are plotted in logarithmic form, which can be seen to be more different on the sides away from the median, and the tails of the Cauchy distribution are heavier.
Path Planning for Multiple Targets Interception by the Swarm of UAVs based on Swarm Intelligence Algorithms: A Review
Published in IETE Technical Review, 2021
Abhishek Sharma, Shraga Shoval, Abhinav Sharma, Jitendra Kumar Pandey
In a recent study, the authors proposed a robust Cauchy-mutated PIOA for path planning of multiple UAVs [107]. Mathematically, Cauchy distribution is the continuous probability distribution without variance and expectation. The author examined the robustness of the proposed algorithm by exploring it in a different environment such as plateau topography and plateau wind-driven environment.
Exponentially weighted moving average Lepage-type schemes based on the lower-order percentile of the run-length metrics and their use in monitoring time-occupancy in Google applications
Published in Quality Technology & Quantitative Management, 2023
Kok Ming Chan, Zhi Lin Chong, Amitava Mukherjee
In this subsection, we compare the performance characteristics of the distribution for all schemes under a zero-state shift (denoted as -), where a process change occurs at the start of Phase-II monitoring under Design I. The - performance of various schemes is compared by evaluating their - percentile () with a smaller being preferred since practitioners are 95% confident in claiming that the will identify faster. Four different distributions were considered as follows: The symmetric thin-tailed normal distribution denoted as , with a probability density function (PDF) of , .The symmetric heavy-tailed Laplace distribution denoted as , with a PDF of , .The asymmetric shifted exponential distribution denoted as , with a PDF of , .The symmetric very-heavy tailed Cauchy distribution denoted as , with a PDF of , .