Related papers: Pareto's 80/20 Rule and the Gaussian Distribution
In this paper we discuss an empirical phenomena known as the 20-60-20 rule. It says that if we split the population into three groups, according to some arbitrary benchmark criterion, then this particular ratio implies some sort of balance.…
A simple heuristic model, including the multiple exchanges between economic agents, is used to explain the mechanism of emerging and maintenance of social inequality in the market economy. The model allows calculating a density function of…
We formalize a generalized form of the Pareto principle - ``fraction $p$ of inputs yields fraction $1-p$ of outputs'' - as a property of non-negative gain densities $\ell \in L^1([0,1])$, working with the decreasing rearrangement to obtain…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…
We analyze three sets of income data: the US Panel Study of Income Dynamics PSID), the British Household Panel Survey (BHPS), and the German Socio-Economic Panel (GSOEP). It is shown that the empirical income distribution is consistent with…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test…
A computational model for the distribution of wealth among the members of an ideal society is presented. It is determined that a realistic distribution of wealth depends upon two mechanisms: an asymmetric flux of wealth in trading…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
This work explores the distribution of citations for the publications of top scientists. A first objective is to find out whether the 80-20 Pareto rule applies, that is if 80% of the citations to a top scientist's work concern 20% of their…
In this paper, we discuss a method to define prior distributions for the threshold of a generalised Pareto distribution, in particular when its applications are directed to heavy-tailed data. We propose to assign prior probabilities to the…
We find the perhaps surprising inequality that the weighted average of independent and identically distributed Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
The double Pareto distribution is a heavy-tailed distribution with a power-law tail, that is generated via geometric Brownian motion with an exponentially distributed observation time. In this study, we examine a modified model wherein the…
Available in the literature are properties which characterize the gamma distribution via independence of two appropriately chosen statistics. Well-known is the classical result when one of the statistics is the sample mean and the other one…
The analysis of Tables of particle properties shows that the probability distribution of the results of physical measurements is far from the conventional Gaussian $\rho(\xi)=exp(-\xi^2/2) $, but is more likely to follow the simple…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…
Let $W_1,\ldots,W_N$ be a sample of $\mathrm{Pareto}(\alpha)$ random variables normalized by their sum, such that $\sum_i W_i=1$. The $W_i$ may represent the weights of valleys in a spin glass (if $0<\alpha<1$), or the frequency of…