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 bias-reduced estimator for the mean of a heavy-tailed distribution with an infinite second moment

2013 ◽  
Vol 143 (6) ◽  
pp. 1064-1081 ◽  
Author(s):  
Brahim Brahimi ◽  
Djamel Meraghni ◽  
Abdelhakim Necir ◽  
Djabrane Yahia
Keyword(s):  
Second Moment ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed

scholarly journals Estimating the Mean of Heavy-tailed Distribution under Random Truncation

2021 ◽  
pp. 273-286
Author(s):  
Ben Dahmane Khanssa
Keyword(s):  
Asymptotic Normality ◽  
Simulation Study ◽  
Random Variable ◽  
Finite Sample ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed ◽  
Alternative Estimator ◽  
The Right ◽  
Random Truncation

Inspired by L.Peng’s work on estimating the mean of heavy-tailed distribution in the case of completed data. we propose an alternative estimator and study its asymptotic normality when it comes to the right truncated random variable. A simulation study is executed to evaluate the finite sample behavior on the proposed estimator

scholarly journals A Semi-Markov Leaky Integrate-and-Fire Model

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1022
Author(s):  
Giacomo Ascione ◽  
Bruno Toaldo
Keyword(s):  
Markov Process ◽  
Waiting Times ◽  
Markov Property ◽  
Fire Model ◽  
Integrate And Fire ◽  
Heavy Tailed Distribution ◽  
Semi Markov Process ◽  
The Mean ◽  
Heavy Tailed ◽  
Mean Variance

In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed.

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

2003 ◽  
Vol 35 (03) ◽  
pp. 793-805 ◽  
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.

scholarly journals Subsampling the mean of heavy-tailed dependent observations

2004 ◽  
Vol 25 (2) ◽  
pp. 217-234 ◽  
Author(s):  
Piotr Kokoszka ◽  
Michael Wolf
Keyword(s):  
Dependent Observations ◽  
The Mean ◽  
Heavy Tailed

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

2008 ◽  
Vol 56 (6) ◽  
pp. 137-148 ◽  
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.

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.

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