scholarly journals Extreme Value Theory: a New Characterization of the Distribution Function for the Mixed Method

2016 ◽  
Vol 6 (1) ◽  
pp. 71
Author(s):  
Kane Ladji ◽  
Diawara Daouda ◽  
Diallo Moumouni
Keyword(s):  
Distribution Function ◽  
Mixed Method ◽  
Conditional Distribution ◽  
Convex Combination ◽  
Value Theory ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Underlying Distribution ◽  
Generalized Pareto

Consider the sample X1, X2, ..., XN of N independent and identically distributed (iid) random variables with common cumulative distribution function (cdf)F, and let Fu be their conditional excess distribution function F. We define the ordered sample by . Pickands (1975), Balkema and de Haan (1974) posed that for a large class of underlying distribution functions F , and large u ,Fu is well approximated by the Generalized Pareto Distribution.The mixed method is a method for determining thresholds. This method consists in minimizing the variance of a convex combination of other thresholds.The objective of the mixed method is to determine by which probability distribution one can approach this conditional distribution. In this article, we propose a theorem which specifies the conditional distribution of excesses when the deterministic threshold tends to the end point.

scholarly journals Comparative characterization of PCDH19 missense and truncating variants in PCDH19-related epilepsy

2020 ◽  
Author(s):  
Mami Shibata ◽  
Atsushi Ishii ◽  
Ayako Goto ◽  
Shinichi Hirose
Keyword(s):  
Distribution Function ◽  
Intellectual Disability ◽  
Cumulative Distribution Function ◽  
Clinical Phenotype ◽  
Cytoplasmic Domain ◽  
Cumulative Distribution ◽  
Clinical Implications ◽  
Healthy Individuals ◽  
Conserved Domains

AbstractMissense and truncating variants in protocadherin 19 (PCDH19) cause PCDH19-related epilepsy. In this study, we aimed to investigate variations in distributional characteristics and the clinical implications of variant type in PCDH19-related epilepsy. We comprehensively collected PCDH19 missense and truncating variants from the literature and by sequencing six exons and intron–exon boundaries of PCDH19 in our cohort. We investigated the distribution of each type of variant using the cumulative distribution function and tested for associations between variant types and phenotypes. The distribution of missense variants in patients was clearly different from that of healthy individuals and was uniform throughout the extracellular cadherin (EC) domain, which consisted of six highly conserved domains. Truncating variants showed two types of distributions: (1) located from EC domain 1 to EC domain 4, and (2) located from EC domain 5 to the cytoplasmic domain. Furthermore, we also found that later onset seizures and milder intellectual disability occurred in patients with truncating variants located from EC domain 5 to the cytoplasmic domain compared with those of patients with other variants. Our findings provide the first evidence of two types of truncating variants in the PCDH19 gene with regard to distribution and the resulting clinical phenotype.

Statistical Analysis of Extreme Electron Fluxes in the Radiation Belts

2017 ◽  
Vol 13 (S335) ◽  
pp. 128-131
Author(s):  
Vanina Lanabere ◽  
Sergio Dasso
Keyword(s):  
Distribution Function ◽  
Space Weather ◽  
Radiation Belt ◽  
Weather Conditions ◽  
Value Theory ◽  
Cumulative Distribution ◽  
Outer Radiation Belt ◽  
Weather Events ◽  
Polar Satellite ◽  
Energy Channels

AbstractThe main aim of this work is to study the frequency of extreme Space Weather events, in particular to analyse the tails of the daily averaged electron fluxes distribution function for different channels of energy between 0.249–1.192 MeV measured at ~ 600 km of altitude with the particle detector ICARE-NG/CARMEN-1 on board argentinian polar satellite SAC-D. An extreme value theory was applied to estimate the maximum values of the electron flux in the outer radiation belt for different return levels. We found that the cumulative distribution function of the extreme electron fluxes presents a finite upper limit in (1) the core of the outer radiation belt for the lower energy channels and (2) in the inner edge of the outer radiation belt for energy channels larger than 0.653 keV. The results presented in this work are important to characterise Space Weather conditions.

scholarly journals Distribution Function, Probability Generating Function and Archimedean Generator

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2108
Author(s):  
Weaam Alhadlaq ◽  
Abdulhamid Alzaid
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Generating Functions ◽  
Probability Generating Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Archimedean Copulas ◽  
Cumulative Distribution Functions ◽  
Probability Generating Functions ◽  
Real Functions

Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that under certain conditions the cumulative distribution functions on (0, 1) and probability generating functions can be used as Archimedean generators. It is shown that most of the well-known Archimedean copulas can be generated using such distributions. Further, we introduced new Archimedean copulas.

Lifetime regression models based on a functional equation of physical nature

1987 ◽  
Vol 24 (01) ◽  
pp. 160-169 ◽  
Author(s):  
Enrique Castillo ◽  
Janos Galambos
Keyword(s):  
Functional Equation ◽  
Conditional Distribution ◽  
Regression Models ◽  
Practical Problem ◽  
Ad Hoc ◽  
Physical Nature ◽  
Value Theory ◽  
Complete Characterization ◽  
Lifetime Data

There are a number of ad hoc regression models for the statistical analysis of lifetime data, but only a few examples exist in which physical considerations are used to characterize the model. In the present paper a complete characterization of a regression model is given by solving a functional equation recurring in the literature for the case of a fatigue problem. The result is that, if the lifetime for given values of the regressor variable and the regressor variable for a given lifetime are both Weibull variables (assumptions which are well founded, at least as approximations, from extreme-value theory in some concrete applications), there are only three families of (conditional) distribution for the lifetime (or for the regressor variable). This model is then applied to a practical problem for illustration.

scholarly journals Mixed Method of Extreme Value Theory, with Application to the Calculation of the Portion of Each Claim Payable by the Reinsurer of Excess of Sinister

2016 ◽  
Vol 5 (2) ◽  
pp. 100
Author(s):  
Yingmei Xu ◽  
Kane Ladji ◽  
Diawara Daouda
Keyword(s):  
Bayesian Methods ◽  
Extreme Value Theory ◽  
Mixed Method ◽  
Simulated Data ◽  
Value Theory ◽  
Extreme Value ◽  
Graphical Methods ◽  
Insurance Company

<p>In the literature many determinists approaches (numerical and graphical methods), probability (the probability law, extreme value theory, Bayesian methods) exist for the detection of grave sinister. In this paper, we will give a new characterization of the mixed method of extreme value theory. These results are applied to the simulated data of a Malian insurance company.</p>

Characterization of ERA5 daily precipitation using the extended generalized Pareto distribution

2020 ◽  
Author(s):  
Pauline Rivoire ◽  
Olivia Martius ◽  
Philippe Naveau
Keyword(s):  
Confidence Intervals ◽  
Pareto Distribution ◽  
Daily Precipitation ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Cumulative Distribution ◽  
Simultaneous Occurrence ◽  
Lower Tail ◽  
Generalized Pareto ◽  
Return Levels

&lt;p&gt;Both mean and extreme precipitation are highly relevant and a probability distribution that models the entire precipitation distribution therefore provides important information. Very low and extremely high precipitation amounts have traditionally been modeled separately. Gamma distributions are often used to model low and moderate precipitation amounts and extreme value theory allows to model the upper tail of the distribution. However, difficulties arise when making a link between upper and lower tail. One solution is to define a threshold that separates the distribution into extreme and non-extreme values, but the assignment of such a threshold for many locations is not trivial.&amp;#160;&lt;/p&gt;&lt;p&gt;Here we apply the Extended Generalized Pareto Distribution (EGPD) used by Tencaliec &amp; al. 2019. This method overcomes the problem of finding a threshold between upper and lower tails thanks to a transition function (G) that describes the transition between the empirical distribution of precipitation and a Pareto distribution. The transition cumulative distribution function G has to be constrained by the upper tail and lower tail behavior. G can be estimated using Bernstein polynomials.&lt;/p&gt;&lt;p&gt;EGPD is used here to characterize ERA-5 precipitation. ERA-5 is a new ECMWF climate re-analysis dataset that provides a numerical description of the recent climate by combining a numerical weather model with observations. The data set is global with a spatial resolution of 0.25&amp;#176; and currently covers the period from 1979 to present.&lt;/p&gt;&lt;p&gt;ERA-5 daily precipitation is compared to EOBS, a gridded dataset spatially interpolated from observations over Europe, and to CMORPH, a satellite-based global precipitation product. Simultaneous occurrence of extreme events is assessed with a hit rate. An intensity comparison is conducted with return levels confidence intervals and a Kullback Leibler divergence test, both derived from the EGPD.&lt;/p&gt;&lt;p&gt;Overall, extreme event occurrences between ERA5 and EOBS over Europe appear to agree. The presence of overlap between 95% confidence intervals on return levels highly depends on the season and the probability of occurrence.&lt;/p&gt;

Dynamic reliability prediction of vehicular suspension structure with damping random uncertainties

2018 ◽  
Vol 25 (3) ◽  
pp. 549-558
Author(s):  
Wei Wang ◽  
Yuling Song ◽  
Jun Chen ◽  
Shuaibing Shi
Keyword(s):  
Monte Carlo ◽  
Maximum Amplitude ◽  
Value Theory ◽  
Extreme Value ◽  
Distribution Functions ◽  
Monte Carlo Integration ◽  
Underlying Distribution ◽  
Dynamic Reliability ◽  
Suspension Structure ◽  
Failure Probabilities

This research is conducted such that a two degrees of freedom nonlinear stochastic vibration model of vehicular suspension structure with random bilinear damping forces and cubic nonlinear restoring forces is established. Based on extreme value theory (EVT) and Monte Carlo integration method (MCIM), a novel method of predicting the failure probabilities of the maximum amplitude responses of suspension structure is proposed. The extreme value distribution functions of amplitude responses, which are analytical expressed by underlying amplitude distribution functions, are acquired by using EVT. In order to obtain the analytical expressions of the underlying distribution functions, histograms are used to estimate their distribution forms. Under the log-normal distribution assumption, the means and standard deviations of the underlying distributions are calculated by using MCIM, and then by setting up amplitude failure levels, the extreme distribution functions and failure probabilities of amplitude responses are obtained. The Monte Carlo simulation method-based numerical analyses give enormous supports to use of the proposed prediction means.

scholarly journals Characterization of time-resolved laser differential phase using 3D complementary cumulative distribution functions

2012 ◽  
Vol 37 (10) ◽  
pp. 1769 ◽  
Author(s):  
Anthony J. Walsh ◽  
John A. O’Dowd ◽  
Vivian M. Bessler ◽  
Kai Shi ◽  
Frank Smyth ◽  
...  
Keyword(s):  
Distribution Functions ◽  
Cumulative Distribution ◽  
Time Resolved ◽  
Differential Phase ◽  
Cumulative Distribution Functions

scholarly journals Non-uniform Estimates in the Approximation by the Irwin Law

2016 ◽  
Vol 55 (1) ◽  
pp. 112-118
Author(s):  
Kazimieras Padvelskis ◽  
Ruslan Prigodin
Keyword(s):  
Distribution Function ◽  
Remainder Term ◽  
Cumulative Distribution Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Type Condition ◽  
Uniform Estimates ◽  
Cumulative Distribution Functions ◽  
Cumulant Method ◽  
The Difference

We consider an approximation of a cumulative distribution function F(x) by the cumulative distributionfunction G(x) of the Irwin law. In this case, a function F(x) can be cumulative distribution functions of sums (products) ofindependent (dependent) random variables. Remainder term of the approximation is estimated by the cumulant method.The cumulant method is used by introducing special cumulants, satisfying the V. Statulevičius type condition. The mainresult is a nonuniform bound for the difference |F(x)-G(x)| in terms of special cumulants of the symmetric cumulativedistribution function F(x).

Modeling the wind speed in North Morocco

2021 ◽  
pp. 0309524X2110639
Author(s):  
Zuhair Bahraoui
Keyword(s):  
Distribution Function ◽  
Wind Speed ◽  
Ground Cover ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Distribution Functions ◽  
Value Distribution ◽  
Generalized Extreme Value Distribution ◽  
Generalized Extreme Value

The change of the wind speed is strictly related to several natural factors such as local topographical and the ground cover variations, then any adjustment has to take into account the statistical variation for each specific region under study. Unlike the Weibull distribution, which is most used in wind speed modeling, we investigate two alternative distribution functions for wind speed by using the extreme value theory. The generalized Champernowne distribution function and the mixture Log-normal-Pareto distribution function are considered. We demonstrate that the proper generalized extreme value distribution gives a good fit for wind speed in the North Moroccan. In order to validate the models, a comparison of the produced aggregate wind energy in the aeolian wind turbine was being established. The empirical study shows that the generalized extreme value distribution reflects better the intensity of the wind power energy.

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