A variant of the Thomson problem, which is about placing a set of points uniformly on the surface of a sphere, is that of generating uniformly distributed points on the sphere that are endowed with antipodal symmetry, i.e., if x is an element of the point set then -x is also an element of that point set. Point sets with antipodal symmetry are of special importance to many scientific and enginee...

In the present study, we propose a new family of distributions namely Pareto-X family. A sub model proposed called Pareto-Weibull (PW) distribution is discussed. The maximum likelihood estimators parameters are obtained. Different distributional properties described. order to assess applicability model, two real-life applications from environmental and biological study considered. practical sho...

We have investigated the population distribution of Chinese cities from 1997 to 2006. The rank-size distributions of Chinese cities deviate from the Pareto distribution. For city size distribution of each year we can find a population threshold Pc that characterizes the boundary of the deviation. The cities with population more than Pc follow the Pareto distribution, while the smaller cities de...

Knowledge concerning the family of univariate continuous distributions with density function f and distribution function F defined through the relation f(x) = F (x)(1 − F (x)), α, β ∈ R, is reviewed and modestly extended. Symmetry, modality, tail behaviour, order statistics, shape properties based on the mode, L-moments and — for the first time — transformations between members of the family ar...

Pär Holmberg January 28, 2006 Abstract This paper derives a Supply Function Equilibrium (SFE) of a pay-as-bid auction (discriminatory auction), such as the balancing market for electric power in Britain. It is shown that a SFE always exists if the hazard rate of the perfectly inelastic demand is monotonically decreasing and marginal costs are non-decreasing. With demand following a Pareto distr...