**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Skewness

Summary

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined.
For a unimodal distribution, negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution, but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat.
Introduction
Consider the two distributions in the figure just below. Within each graph, the values on the right side of the distribution taper differently from the values on the left side. These tapering sides are called tails, a

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people

Related units

No results

No results

Related publications (10)

Loading

Loading

Loading

Related lectures (25)

Related courses (14)

FIN-415: Probability and stochastic calculus

This course gives an introduction to probability theory and stochastic calculus in discrete and continuous time. We study fundamental notions and techniques necessary for applications in finance such as option pricing, hedging, optimal portfolio choice and prediction problems.

FIN-407: Financial econometrics

This course aims to give an introduction to the application of machine learning to finance. These techniques gained popularity due to the limitations of traditional financial econometrics methods tackling big data. We will review and compare traditional methods and machine learning algorithms.

CS-422: Database systems

This course is intended for students who want to understand modern large-scale data analysis systems and database systems. It covers a wide range of topics and technologies, and will prepare students to be able to build such systems as well as read and understand recent research publications.

Related concepts (57)

Median

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be t

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mat

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function

Pension funds only quite recently have explored alternative assets, prodded by financial crises that devastated equity returns and led to low bond returns. We assess the addition of alternative assets to pension fund portfolios in terms of the total benefit derived from diversification, addition of positive skewness, and the elimination of left tails in returns. During 1994-2012, adding portfolios of hedge funds produced significantly higher total benefits than adding real estate, commodities, foreign equities, mutual funds, funds of funds, as well as some counter cyclical and non-cyclical assets. Conditioning on past total benefits improves the out-of sample performance even further. (C) 2016 Elsevier B.V. All rights reserved.

Giovanni Barone-Adesi, Loriano Mancini

We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics enhancing the model flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.

2008The Small-World phenomenon, well known under the phrase "six degrees of separation", has been for a long time under the spotlight of investigation. The fact that our social network is closely-knitted and that any two people are linked by a short chain of acquaintances was confirmed by the experimental psychologist Stanley Milgram in the sixties. However, it was only after the seminal work of Jon Kleinberg in 2000 that it was understood not only why such networks exist, but also why it is possible to efficiently navigate in these networks. This proved to be a highly relevant discovery for peer-to-peer systems, since they share many fundamental similarities with the social networks; in particular the fact that the peer-to-peer routing solely relies on local decisions, without the possibility to invoke global knowledge. In this thesis we show how peer-to-peer system designs that are inspired by Small-World principles can address and solve many important problems, such as balancing the peer load, reducing high maintenance cost, or efficiently disseminating data in large-scale systems. We present three peer-to-peer approaches, namely Oscar, Gravity, and Fuzzynet, whose concepts stem from the design of navigable Small-World networks. Firstly, we introduce a novel theoretical model for building peer-to-peer systems which supports skewed node distributions and still preserves all desired properties of Kleinberg's Small-World networks. With such a model we set a reference base for the design of data-oriented peer-to-peer systems which are characterized by non-uniform distribution of keys as well as skewed query or access patterns. Based on this theoretical model we introduce Oscar, an overlay which uses a novel scalable network sampling technique for network construction, for which we provide a rigorous theoretical analysis. The simulations of our system validate the developed theory and evaluate Oscar's performance under typical conditions encountered in real-life large-scale networked systems, including participant heterogeneity, faults, as well as skewed and dynamic load-distributions. Furthermore, we show how by utilizing Small-World properties it is possible to reduce the maintenance cost of most structured overlays by discarding a core network connectivity element – the ring invariant. We argue that reliance on the ring structure is a serious impediment for real life deployment and scalability of structured overlays. We propose an overlay called Fuzzynet, which does not rely on the ring invariant, yet has all the functionalities of structured overlays. Fuzzynet takes the idea of lazy overlay maintenance further by eliminating the need for any explicit connectivity and data maintenance operations, relying merely on the actions performed when new Fuzzynet peers join the network. We show that with a sufficient amount of neighbors, even under high churn, data can be retrieved in Fuzzynet with high probability. Finally, we show how peer-to-peer systems based on the Small-World design and with the capability of supporting non-uniform key distributions can be successfully employed for large-scale data dissemination tasks. We introduce Gravity, a publish/subscribe system capable of building efficient dissemination structures, inducing only minimal dissemination relay overhead. This is achieved through Gravity's property to permit non-uniform peer key distributions which allows the subscribers to be clustered close to each other in the key space where data dissemination is cheap. An extensive experimental study confirms the effectiveness of our system under realistic subscription patterns and shows that Gravity surpasses existing approaches in efficiency by a large margin. With the peer-to-peer systems presented in this thesis we fill an important gap in the family of structured overlays, bringing into life practical systems, which can play a crucial role in enabling data-oriented applications distributed over wide-area networks.