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LAWS OF LARGE NUMBERS FOR TWO TAILED PARETO RANDOM VARIABLES
Almost sure convergence weak law of large numbers strong law of large numbers
2009/9/18
We sample m random variables from a two tailed Pareto
distribution. A two tailed Pareto distribution is a random variable whose
right tail is px−2 and whose left tail is qx−2, where p + ...
Expansions for Quantiles and Multivariate Moments of Extremes for Distributions of Pareto Type
Bell polynomials Extremes Inversion theorem Moments Pareto Quantiles
2010/3/19
Let Xnr be the rth largest of a random sample of size n from a distribution
F(x) = 1 −P∞i=0 cix− −i for > 0 and > 0. An inversion theorem is proved and used to
derive an expan...
ESTIMATING PARETO TAIL INDEX BASED ON SAMPLE MEANS
domain of attraction Pareto index strong embedding of empirical process tailbehavior
2009/2/26
We propose an estimator of the Pareto tail index m of a distribution, that competes well with the Hill, Pickands and moment estimators. Unlike the above estimators,that are based only on the extreme o...
EXPONENTIALITY VERSUS GENERALIZED PARETO——A RESISTANT AND ROBUST TEST
generalized Pareto distribution breakdown point resistance robustness broadened situations mixtures
2009/2/26
Using resistant and robust methods we propose the statistic Tn= (FU−M)/(M−FL)
for testing exponentiality versus generalized Pareto, where FU, FL and M are, respectively,
the upper and lo...
LINKING PARETO-TAIL KERNEL GOODNESS-OFFIT STATISTICSWITH TAIL INDEX AT OPTIMAL THRESHOLD AND SECOND ORDER ESTIMATION
extreme value statistics Pareto-type distribution goodness-of-fit threshold selection
2009/2/25
In this paper the relation between goodness-of-fit testing and the optimal selection of
the sample fraction for tail estimation, for instance using Hill’s estimator, is examined.
We consider this pr...
Muliere and Scarsini’s bivariate Pareto distribution：sums，products，and ratios
incomplete beta function Gauss hypergeometric function Muliere and Scarsini’s bivariate Pareto distribution products of random variables ratios of random variables sums of random variables
2009/2/23
We derive the exact distributions of R = X + Y, P = X Y and W = X/(X + Y) and the corresponding
moment properties when X and Y follow Muliere and Scarsini’s bivariate Pareto distribution. The express...