Related papers: Fat Tailed Distributions in Catastrophe Prediction
We study the statistics of human deaths from wars, conflicts, similar man-made conflicts as well as natural disasters. The probability distribution of number of people killed in natural disasters as well as man made situations show power…
The purpose of this paper is to show that the use of heavy-tailed distributions in Financial problems is theoretically baseless and can lead to significant misunderstandings. The reason for this the authors see in an incorrect…
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
It is well known that the distribution of returns from various financial instruments are leptokurtic, meaning that the distributions have "fatter tails" than a Normal distribution, and have skew toward zero. This paper presents a graceful…
In order to account for large variance and fat tail of damage by natural disaster, we study a simple model by combining distributions of disaster and population/property with their spatial correlation. We assume fat-tailed or power-law…
The notion that natural disasters can be controlled is, of course, farcical; history is permeated with examples of countless failed attempts at this pointless task; it is synonymous with trying to build a perpetual motion machine.…
The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in…
A decision must often be made between heavy-tailed and Gaussian errors for a regression or a time series model, and the t-distribution is frequently used when it is assumed that the errors are heavy-tailed distributed. The performance of…
This paper introduces a new distribution to improve tail risk modeling. Based on the classical normal distribution, we define a new distribution by a series of heat equations. Then, we use market data to verify our model.
We introduce the Zeta Tail(a) probability distribution as a new model for random damage-event counts in risk analysis. Although readily motivated as an analogue of the Geometric(p) distribution, Zeta Tail(a) has received little attention in…
This is an epistemological approach to errors in both inference and risk management, leading to necessary structural properties for the probability distribution. Many mechanisms have been used to show the emergence of fat tails. Here we…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.
Ex ante forecast outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. Reapplying measurements of uncertainty about the estimation errors of the estimation errors of an…
A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows asymmetry of scale and also of tail power, whilst avoiding the discontinuity of the second derivative of the split-t (AST) distribution. With…
I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward,…
The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with…
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…
Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise in…
In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…