Heavy-tailed distribution ≈ Heavy-tailed distribution
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Understanding Heavy Tails of Flood Peak Distributions Open
Statistical distributions of flood peak discharge often show heavy tail behavior, that is, extreme floods are more likely to occur than would be predicted by commonly used distributions that have exponential asymptotic behavior. This heavy…
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The Fundamentals of Heavy Tails Open
Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterio…
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The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications Open
In this paper, we propose a generalization of the so-called truncated inverse Weibull-generated family of distributions by the use of the power transform, adding a new shape parameter. We motivate this generalization by presenting theoreti…
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The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data Open
In this article, the “truncated-composed” scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and pro…
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Heavy-Tailed Log-Logistic Distribution: Properties, Risk Measures and Applications Open
Heavy tailed distributions have a big role in studying risk data sets. Statisticians in many cases search and try to find new or relatively new statistical models to fit data sets in different fields. This article introduced a relatively n…
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Instance optimal learning of discrete distributions Open
We consider the following basic learning task: given independent draws from an unknown distribution over a discrete support, output an approximation of the distribution that is as accurate as possible in L1 distance (equivalently, total va…
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The generalized Cauchy family of distributions with applications Open
A family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value,…
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The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data Open
Heavy-tailed distributions play a prominent role in actuarial and financial sciences. In this paper, we introduce a family of distributions that we refer to as exponential T-X (ETX) family. Based on the proposed approach, a new extension o…
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The Inverse Weibull Generator of Distributions: Properties and Applications Open
In this paper, we introduce a new family of univariate distributions with two extra positive parameters generated from inverse Weibull random variable called the inverse Weibull generated (IW-G) family. The new family provides a lot of new…
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Characterizations of Continuous Distributions by Truncated Moment Open
A probability distribution can be characterized through various methods. In this paper, some new characterizations of continuous distribution by truncated moment have been established. We have considered standard normal distribution, Stude…
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Optimal heavy tail estimation – Part 1: Order selection Open
The tail probability, P, of the distribution of a variable is important for risk analysis of extremes. Many variables in complex geophysical systems show heavy tails, where P decreases with the value, x, of a variable as a power law with a…
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The Generalized Odd Gamma-G Family of Distributions: Properties and Applications Open
Recently, new continuous distributions have been proposed to apply in statistical analysis. In this paper, the Generalized Odd Gamma-G distribution is introduced. In particular, G has been considered as the Uniform distribution and some st…
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Determining Distribution for the Product of Random Variables by Using Copulas Open
Determining distributions of the functions of random variables is one of the most important problems in statistics and applied mathematics because distributions of functions have wide range of applications in numerous areas in economics, f…
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A New Family of Distributions Based on the Generalized Pearson Differential Equation with Some Applications Open
Recently, a generalization of the Pearson differential equation has appeared in the literature, from which a vast majority of continuous probability density functions (pdf’s) can be generated, known as the generalized Pearson system of con…
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Method for generating distributions and classes of probability distributions: the univariate case Open
In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from pre-de…
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The accumulative law and its probability model: an extension of the Pareto distribution and the log-normal distribution Open
The divergence between the Pareto distribution and the log-normal distribution has been observed persistently over the past couple of decades in complex network research, economics, and social sciences. To address this, we here propose an …
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Weak properties and robustness of t-Hill estimators Open
We describe a novel method of heavy tails estimation based on transformed score (t-score). Based on a new score moment method we derive the t-Hill estimator, which estimates the extreme value index of a distribution function with regularly…
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Nonlocal Probability Theory: General Fractional Calculus Approach Open
Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based o…
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Alpha-Power Exponentiated Inverse Rayleigh distribution and its applications to real and simulated data Open
The main goal of the current paper is to contribute to the existing literature of probability distributions. In this paper, a new probability distribution is generated by using the Alpha Power Family of distributions with the aim to model …
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Multivariate stable densities and distribution functions : general and elliptical case Open
Paper presented at: Deutsche Bundesbank’s 2005 Annual Fall Conference.
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On Generalized Gamma Distribution and Its Application to Survival Data Open
The generalized gamma distribution is a continuous probability distribution with three parameters. It is a generalization of the two-parameter gamma distribution. Since many distributions commonly used for parametric models in survival ana…
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GARCH Model With Fat-Tailed Distributions and Bitcoin Exchange Rate Returns Open
In the era of diminishing power from US dollar and increasing competition among world currencies, Bitcoin, as a completely new concept as a medium of exchange, has received increasing attentions over the world. Nowadays, Bitcoin also becom…
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A New Class of Heavy‐Tailed Distributions: Modeling and Simulating Actuarial Measures Open
Statistical distributions play a prominent role for modeling data in applied fields, particularly in actuarial, financial sciences, and risk management fields. Among the statistical distributions, the heavy‐tailed distributions have proven…
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Extreme versions of Wang risk measures and their estimation for heavy-tailed distributions Open
Among the many possible ways to study the right tail of a real-valued random variable, a particularly general one is given by considering the family of its Wang distortion risk measures. This class of risk measures encompasses various inte…
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Fitting phase–type scale mixtures to heavy–tailed data and distributions Open
We consider the fitting of heavy tailed data and distributions with a special attention to distributions with a non–standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions intro…
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Optimal Randomness for Stochastic Configuration Network (SCN) with Heavy-Tailed Distributions Open
Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained…
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Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes Open
We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has $L^1$ norm close to one and power law tail of the form $x^{-(1+α)}$, with $α\in(0,1)$. We in particular prove that when $α\in(1…
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Inference for heavy tailed stationary time series based on sliding blocks Open
© 2018, Institute of Mathematical Statistics. All right reserved. The block maxima method in extreme value theory consists of fitting an extreme value distribution to a sample of block maxima extracted from a time series. Traditionally, th…
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Transmuted Probability Distributions: A Review Open
Transmutation is the functional composition of the cumulative distribution function (cdf) of one distribution with the inverse cumulative distribution function (quantile function) of another. Shaw and Buckley(2007), first apply this concep…
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The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data Open
Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function,…