On a heavy-tailed distribution and the stability of an equilibrium in a distributed delay symmetric network

2021 ◽  
Vol 152 ◽  
pp. 111330
Author(s):  
Israel Ncube
Keyword(s):  
Distributed Delay ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed ◽  
The Stability

scholarly journals A Bias-Reduced Estimator for the Mean of a Heavy-Tailed Distribution with an Infinite Second Moment

2012 ◽  
Author(s):  
Brahim Brahimi ◽  
Djamel Meraghni ◽  
Necir Abdelhakim ◽  
Yahia Djabrane
Keyword(s):  
Second Moment ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed

scholarly journals A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay K Singh ◽  
Umesh Singh
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Statistical Properties ◽  
New Right ◽  
Data Sets ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

Heavy-tailed distributions for building stock data

2018 ◽  
Vol 46 (7) ◽  
pp. 1281-1296 ◽  
Author(s):  
Patrick Erik Bradley ◽  
Martin Behnisch
Keyword(s):  
Power Law ◽  
Building Stock ◽  
Underlying Distribution ◽  
Large Cities ◽  
Statistical Framework ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed Distribution ◽  
Event Histories ◽  
Heavy Tailed ◽  
Log Normal

The question of inferring the owner of a set of building stocks (e.g. from which country the buildings are taken) from building-related quantities like number of buildings or types of building event histories necessitates the knowledge of their distributions in order to compare them. If the distribution function is a power law, then a version of the 80/20 rule can be applied to describe the variable. This distribution is an example of a heavy-tailed distribution; another example is the log-normal distribution. Heavy-tailed distributions have the property that studying the effects of the few large values already yields most of the overall effect of the whole quantity. For example, if reducing the CO2 emissions of the buildings of a country is the issue, then in case of a heavy-tailed distribution, only the effects of the relatively few large cities need to be considered. It is shown that the number of buildings in German municipalities or counties or the number of building-related event histories of a certain vanished building stock follow a heavy-tailed distribution and give evidence for the type of underlying distribution. The methodology used is a recent statistical framework for discerning power law and other heavy-tailed distributions in empirical data.

scholarly journals Development of Temperature Process Control Method Using Smith Predictor

2019 ◽  
Vol 111 ◽  
pp. 06016
Author(s):  
Nikolajs Bogdanovs ◽  
Romualds Beļinskis ◽  
Ernests Petersons ◽  
Andris Krūmiņš ◽  
Artūrs Brahmanis
Keyword(s):  
Time Delay ◽  
Control Method ◽  
Distributed Delay ◽  
Heating System ◽  
Smith Predictor ◽  
Hot Water ◽  
Test Bed ◽  
Hot Water Supply ◽  
The Stability ◽  
System With Time Delay

The analysis of a problem of development of control systems for objects with big time delay is carried out in this work. For such objects it is difficult to provide high-quality control, because the control is carried on the last status of object’s output. The main setup methods of PID regulators have been examined. Based on this analysis the technique of complete synthesis of the regulator of higher level is given in order to regulate building’s heating system. This work offers a new method of object’s control with distributed delay. As the test bed for the offered structure of control the valve of hot water supply in a heat-node is used. Using the test bed the stability of the system with time delay have been studied, which is controlled by the PID-regulator assisted by Smith Predictor used to compensate the dead time.

scholarly journals A robust method for shift detection in time series

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 647-660
Author(s):  
H Dehling ◽  
R Fried ◽  
M Wendler
Keyword(s):  
Time Series ◽  
Nonparametric Test ◽  
Test Statistic ◽  
Moment Conditions ◽  
Limit Theory ◽  
Dependent Observations ◽  
U Statistics ◽  
Shift Detection ◽  
Heavy Tailed ◽  
The Stability

Summary We present a robust and nonparametric test for the presence of a changepoint in a time series, based on the two-sample Hodges–Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes in the case of short-range dependent observations. Using this theory, we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on U-statistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so any transform of the observed process can be used to test the stability of higher-order characteristics such as variability, skewness and kurtosis.

scholarly journals RPM-Oriented Query Rewriting Framework for E-commerce Keyword-Based Sponsored Search (Student Abstract)

2020 ◽  
Vol 34 (10) ◽  
pp. 13769-13770
Author(s):  
Xiuying Chen ◽  
Daorui Xiao ◽  
Shen Gao ◽  
Guojun Liu ◽  
Wei Lin ◽  
...  
Keyword(s):  
Statistical Models ◽  
Large Scale ◽  
Query Rewriting ◽  
Sponsored Search ◽  
Search System ◽  
Oriented Sample ◽  
Search Models ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

Sponsored search optimizes revenue and relevance, which is estimated by Revenue Per Mille (RPM). Existing sponsored search models are all based on traditional statistical models, which have poor RPM performance when queries follow a heavy-tailed distribution. Here, we propose an RPMoriented Query Rewriting Framework (RQRF) which outputs related bid keywords that can yield high RPM. RQRF embeds both queries and bid keywords to vectors in the same implicit space, converting the rewriting probability between each query and keyword to the distance between the two vectors. For label construction, we propose an RPM-oriented sample construction method, labeling keywords based on whether or not they can lead to high RPM. Extensive experiments are conducted to evaluate performance of RQRF. In a one month large-scale real-world traffic of e-commerce sponsored search system, the proposed model significantly outperforms traditional baseline.

scholarly journals Asymptotic Probabilities of an Exceedance Over Renewal Thresholds with an Application to Risk Theory

2005 ◽  
Vol 42 (01) ◽  
pp. 153-162 ◽  
Author(s):  
Christian Y. Robert
Keyword(s):  
Random Walk ◽  
Stopping Time ◽  
Random Variables ◽  
Risk Theory ◽  
Heavy Tailed Distribution ◽  
Negative Drift ◽  
Heavy Tailed ◽  
Independent And Identically Distributed

Let (Y n , N n ) n≥1 be independent and identically distributed bivariate random variables such that the N n are positive with finite mean ν and the Y n have a common heavy-tailed distribution F. We consider the process (Z n ) n≥1 defined by Z n = Y n - Σ n-1, where It is shown that the probability that the maximum M = max n≥1 Z n exceeds x is approximately as x → ∞, where F' := 1 - F. Then we study the integrated tail of the maximum of a random walk with long-tailed increments and negative drift over the interval [0, σ], defined by some stopping time σ, in the case in which the randomly stopped sum is negative. Finally, an application to risk theory is considered.

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