Truncating Estimation for the Mean Change-Point in Heavy-Tailed Dependent Observations

UNSTRUCTURED Current research is an attempt to understand the CoVID-19 pandemic curve through statistical approach of probability density function with associated skewness and kurtosis measures, change point detection and polynomial fitting to estimate infected population along with 30 days projection. The pandemic curve has been explored for above average affected countries, six regions and global scale during 64 days of 22nd January to 24th March, 2020. The global cases infection as well as recovery rate curves remained in the ranged of 0 ‒ 9.89 and 0 ‒ 8.89%, respectively. The confirmed cases probability density curve is high positive skewed and leptokurtic with mean global infected daily population of 6620. The recovered cases showed bimodal positive skewed curve of leptokurtic type with daily recovery of 1708. The change point detection helped to understand the CoVID-19 curve in term of sudden change in term of mean or mean with variance. This pointed out disease curve is consist of three phases and last segment that varies in term of day lengths. The mean with variance based change detection is better in differentiating phases and associated segment length as compared to mean. Global infected population might rise in the range of 0.750 to 4.680 million by 24th April 2020, depending upon the pandemic curve progress beyond 24th March, 2020. Expected most affected countries will be USA, Italy, China, Spain, Germany, France, Switzerland, Iran and UK with at least infected population of over 0.100 million. Infected population polynomial projection errors remained in the range of -78.8 to 49.0%.

Download Full-text

A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows

Advances in Applied Probability ◽

10.1017/s0001867800012544 ◽

2003 ◽

Vol 35 (03) ◽

pp. 793-805 ◽

Cited By ~ 1

Author(s):

Sem Borst ◽

Bert Zwart

Keyword(s):

Service Rate ◽

Opposite Case ◽

Peak Rate ◽

Workload Distribution ◽

The Mean ◽

Heavy Tailed ◽

Insight Into

We determine the exact large-buffer asymptotics for a mixture of light-tailed and heavy-tailed input flows. Earlier studies have found a ‘reduced-load equivalence’ in situations where the peak rate of the heavy-tailed flows plus the mean rate of the light-tailed flows is larger than the service rate. In that case, the workload is asymptotically equivalent to that in a reduced system, which consists of a certain ‘dominant’ subset of the heavy-tailed flows, with the service rate reduced by the mean rate of all other flows. In the present paper, we focus on the opposite case where the peak rate of the heavy-tailed flows plus the mean rate of the light-tailed flows is smaller than the service rate. Under mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a somewhat ‘dual’ reduced system, multiplied by a certain prefactor. The reduced system now consists of only the light-tailed flows, with the service rate reduced by the peak rate of the heavy-tailed flows. The prefactor represents the probability that the heavy-tailed flows have sent at their peak rate for more than a certain amount of time, which may be interpreted as the ‘time to overflow’ for the light-tailed flows in the reduced system. The results provide crucial insight into the typical overflow scenario.

Download Full-text

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

SSRN Electronic Journal ◽

10.2139/ssrn.2013083 ◽

2012 ◽

Author(s):

Brahim Brahimi ◽

Djamel Meraghni ◽

Necir Abdelhakim ◽

Yahia Djabrane

Keyword(s):

Second Moment ◽

Heavy Tailed Distribution ◽

The Mean ◽

Heavy Tailed

Download Full-text

Comparison of power of modified Jarque-Bera normality tests and selected tests of normality

Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis ◽

10.11118/actaun200856060137 ◽

2008 ◽

Vol 56 (6) ◽

pp. 137-148 ◽

Cited By ~ 1

Author(s):

Luboš Střelec

Keyword(s):

Stock Exchange ◽

Financial Time Series ◽

Simulation Studies ◽

Test Paper ◽

Monthly Average ◽

Financial Time ◽

Uniform Distributions ◽

Source Data ◽

The Mean ◽

Heavy Tailed

The aim of this paper is to modify the classical Jarque-Bera test and the robust Jarque-Bera test of normality. We use the median as an estimator instead of the mean in the classical Jarque-Bera test and in the robust Jarque-Bera test. This leads to the modified Jarque-Bera test and the modified robust Jarque-Bera test. Paper also demonstrates results of simulation studies of power of such tests with the various alternatives – light tailed alternatives as exponential, lognormal and gamma distribution, heavy tailed alternatives as Cauchy, Laplace, t3, t5 and logistic distributions and short tailed alternatives as beta and uniform distributions. These tests of normality are also used for normality testing of selected datasets of financial time series. Source data include logarithmic returns of monthly average prices of Prague stock exchange index PX and monthly average prices of CZK/EUR exchange rate in the period from 2000 to 2007.

Download Full-text

A robust method for shift detection in time series

Biometrika ◽

10.1093/biomet/asaa004 ◽

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.

Download Full-text

Limit theorems in change-point problems with multivariate long-range dependent observations

Statistics & Decisions ◽

10.1524/stnd.21.3.283.23432 ◽

2003 ◽

Vol 21 (3-2003) ◽

pp. 283-300 ◽

Cited By ~ 6

Author(s):

Lihong Wang

Keyword(s):

Long Range ◽

Change Point ◽

Limit Theorems ◽

Dependent Observations

Download Full-text

Variance asymptotics and central limit theorems for volumes of unions of random closed sets

Advances in Applied Probability ◽

10.1017/s0001867800011745 ◽

2002 ◽

Vol 34 (03) ◽

pp. 520-539 ◽

Cited By ~ 6

Author(s):

Tomasz Schreiber

Keyword(s):

Central Limit ◽

Borel Measure ◽

Strong Law ◽

Closed Sets ◽

Random Closed Sets ◽

Large Numbers ◽

Multidimensional Ball ◽

Mean Width ◽

The Mean ◽

Heavy Tailed

Let X, X 1, X 2, … be a sequence of i.i.d. random closed subsets of a certain locally compact, Hausdorff and separable base space E. For a fixed normalised Borel measure μ on E, we investigate the behaviour of random variables μ(E \ (X 1 ∪ ∙ ∙ ∙ ∪ X n )) for large n. The results obtained include a description of variance asymptotics, strong law of large numbers and a central limit theorem. As an example we give an application of the developed methods for asymptotic analysis of the mean width of convex hulls generated by uniform samples from a multidimensional ball. Another example deals with unions of random balls in ℝ d with centres distributed according to a spherically-symmetric heavy-tailed law.

Download Full-text