A novel heavy tail distribution of logarithmic returns of cryptocurrencies

2021 ◽  
pp. 102574
Author(s):  
Quang Van Tran ◽  
Jaromir Kukal
Keyword(s):  
Heavy Tail ◽  
Tail Distribution

A Method of Over Bounding Ground Based Augmentation System (GBAS) Heavy Tail Error Distributions

2005 ◽  
Vol 58 (1) ◽  
pp. 83-103 ◽  
Author(s):  
Ronald Braff ◽  
Curtis Shively
Keyword(s):  
Local Area ◽  
Tail Probability ◽  
Heavy Tail ◽  
General Interest ◽  
Local Area Augmentation ◽  
Model Distribution ◽  
Tail Distribution ◽  
Error Distributions ◽  
Navigation Error ◽  
Normal Inverse Gaussian

The purpose of this paper is to describe a statistical method for modelling and accounting for the heavy tail fault-free error distributions that have been encountered in the Local Area Augmentation System (LAAS), the FAA's version of a ground-based augmentation system (GBAS) for GPS. The method uses the Normal Inverse Gaussian (NIG) family of distributions to describe a heaviest tail distribution, and to select a suitable NIG family member as a model distribution based upon a statistical observability criterion applied to the FAA's LAAS prototype error data. Since the independent sample size of the data is limited to several thousand and the tail probability of interest is of the order of 10−9, there is a chance of mismodelling. A position domain monitor (PDM) is shown to provide significant mitigation of mismodelling, even for the heaviest tail that could be encountered, if it can meet certain stringent accuracy and threshold requirements. Aside from its application to GBAS, this paper should be of general interest because it describes a different approach to navigation error modelling and introduces the application of the NIG distribution to navigation error analysis.

scholarly journals Large Cliques in a Power-Law Random Graph

2010 ◽  
Vol 47 (4) ◽  
pp. 1124-1135 ◽  
Author(s):  
Svante Janson ◽  
Tomasz Łuczak ◽  
Ilkka Norros
Keyword(s):  
Random Graph ◽  
Power Law ◽  
High Probability ◽  
Simple Algorithm ◽  
Heavy Tail ◽  
Degree Sequences ◽  
Constant Size ◽  
Tail Distribution ◽  
Law Degree ◽  
Large Clique

In this paper we study the size of the largest clique ω(G(n, α)) in a random graph G(n, α) on n vertices which has power-law degree distribution with exponent α. We show that, for ‘flat’ degree sequences with α > 2, with high probability, the largest clique in G(n, α) is of a constant size, while, for the heavy tail distribution, when 0 < α < 2, ω(G(n, α)) grows as a power of n. Moreover, we show that a natural simple algorithm with high probability finds in G(n, α) a large clique of size (1 − o(1))ω(G(n, α)) in polynomial time.

scholarly journals Analysis of Peak Flow Distribution for Bridge Collapse Sites

Water ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 52 ◽  
Author(s):  
Fahmidah U. Ashraf ◽  
Madeleine M. Flint
Keyword(s):  
Peak Flow ◽  
Flow Distribution ◽  
Heavy Tail ◽  
Flood Frequency ◽  
Return Periods ◽  
Peak Flows ◽  
Tail Distribution ◽  
Bridge Collapse ◽  
Flood Magnitude ◽  
Distribution Parameters

Bridge collapse risk can be evaluated more rigorously if the hydrologic characteristics of bridge collapse sites are demystified, particularly for peak flows. In this study, forty-two bridge collapse sites were analyzed to find any trend in the peak flows. Flood frequency and other statistical analyses were used to derive peak flow distribution parameters, identify trends linked to flood magnitude and flood behavior (how extreme), quantify the return periods of peak flows, and compare different approaches of flood frequency in deriving the return periods. The results indicate that most of the bridge collapse sites exhibit heavy tail distribution and flood magnitudes that are well consistent when regressed over the drainage area. A comparison of different flood frequency analyses reveals that there is no single approach that is best generally for the dataset studied. These results indicate a commonality in flood behavior (outliers are expected, not random; heavy-tail property) for the collapse dataset studied and provides some basis for extending the findings obtained for the 42 collapsed bridges to other sites to assess the risk of future collapses.

scholarly journals Large Cliques in a Power-Law Random Graph

2010 ◽  
Vol 47 (04) ◽  
pp. 1124-1135 ◽  
Author(s):  
Svante Janson ◽  
Tomasz Łuczak ◽  
Ilkka Norros
Keyword(s):  
Random Graph ◽  
Power Law ◽  
High Probability ◽  
Simple Algorithm ◽  
Heavy Tail ◽  
Degree Sequences ◽  
Constant Size ◽  
Tail Distribution ◽  
Law Degree ◽  
Large Clique

In this paper we study the size of the largest clique ω(G(n, α)) in a random graph G(n, α) on n vertices which has power-law degree distribution with exponent α. We show that, for ‘flat’ degree sequences with α &gt; 2, with high probability, the largest clique in G(n, α) is of a constant size, while, for the heavy tail distribution, when 0 &lt; α &lt; 2, ω(G(n, α)) grows as a power of n. Moreover, we show that a natural simple algorithm with high probability finds in G(n, α) a large clique of size (1 − o(1))ω(G(n, α)) in polynomial time.

scholarly journals Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models

2017 ◽  
Vol 473 ◽  
pp. 60-71 ◽  
Author(s):  
Timothy Graves ◽  
Christian L.E. Franzke ◽  
Nicholas W. Watkins ◽  
Robert B. Gramacy ◽  
Elizabeth Tindale
Keyword(s):  
Long Range ◽  
Heavy Tail ◽  
Long Range Dependence ◽  
Arfima Models ◽  
Tail Distribution ◽  
Distribution Parameters
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