4,568 research outputs found
A General size-biased distribution
We generalize a size-biased distribution related to the Riemann xi function
using the work of Ferrar. Some analysis and properties of this more general
distribution are offered as well
Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex.
The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it characterizes the size biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.zonoid, zonotope, linear dependence, compositional variables, multivariate size biased distribution, concordance order, Marshall-Olkin distribution.
New Proposed Length-Biased Weighted Exponential and Rayleigh Distribution with Application
The concept of length-biased distribution can be employed in development of proper models for lifetime data. Length-biased distribution is a special case of the more general form known as weighted distribution. In this paper we introduce a new class of length-biased of weighted exponential and Rayleigh distributions(LBW1E1D), (LBWRD).This paper surveys some of the possible uses of Length - biased distribution  We study the some of its statistical properties with application of these new distribution. Keywords: length- biased weighted Rayleigh distribution, length- biased weighted exponential distribution,  maximum likelihood estimation
Efficient BER simulation of orthogonal space-time block codes in Nakagami-m fading
In this contribution, we present a simple but efficient importance sampling technique to speed up Monte Carlo simulations for bit error rate estimation of orthogonal space-time block codes on spatially correlated Nakagami-m fading channels. While maintaining the actual distributions for the channel noise and the data symbols, we derive a convenient biased distribution for the fading channel that is shown to result in impressive efficiency gains up to multiple orders of magnitude
New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods
We prove abstract bounds on the Wasserstein and Kolmogorov distances between
non-randomly centered random sums of real i.i.d. random variables with a finite
third moment and the standard normal distribution. Except for the case of mean
zero summands, these bounds involve a coupling of the summation index with its
size biased distribution as was previously considered in \cite{GolRin96} for
the normal approximation of nonnegative random variables. When being
specialized to concrete distributions of the summation index like the Binomial,
Poisson and Hypergeometric distribution, our bounds turn out to be of the
correct order of magnitude.Comment: 40 pages, to appear in ALEA - Latin American Journal of Probability
and Mathematical Statistic
Using Bayes formula to estimate rates of rare events in transition path sampling simulations
Transition path sampling is a method for estimating the rates of rare events
in molecular systems based on the gradual transformation of a path distribution
containing a small fraction of reactive trajectories into a biased distribution
in which these rare trajectories have become frequent. Then, a multistate
reweighting scheme is implemented to postprocess data collected from the staged
simulations. Herein, we show how Bayes formula allows to directly construct a
biased sample containing an enhanced fraction of reactive trajectories and to
concomitantly estimate the transition rate from this sample. The approach can
remediate the convergence issues encountered in free energy perturbation or
umbrella sampling simulations when the transformed distribution insufficiently
overlaps with the reference distribution.Comment: 11 pages, 8 figure
Storage capacity of a constructive learning algorithm
Upper and lower bounds for the typical storage capacity of a constructive
algorithm, the Tilinglike Learning Algorithm for the Parity Machine [M. Biehl
and M. Opper, Phys. Rev. A {\bf 44} 6888 (1991)], are determined in the
asymptotic limit of large training set sizes. The properties of a perceptron
with threshold, learning a training set of patterns having a biased
distribution of targets, needed as an intermediate step in the capacity
calculation, are determined analytically. The lower bound for the capacity,
determined with a cavity method, is proportional to the number of hidden units.
The upper bound, obtained with the hypothesis of replica symmetry, is close to
the one predicted by Mitchinson and Durbin [Biol. Cyber. {\bf 60} 345 (1989)].Comment: 13 pages, 1 figur
World Heritage: Where are we? An empirical analysis
A statistical analysis of the UNESCO World Heritage List is presented. The World Heritage Convention intends to protect global heritage of outstanding value to mankind, but there has been great concern about the missing representativity of the member countries. There is a strongly biased distribution of Sites according to a country’s population, area or per capita income. The paper reveals the facts but refrains from judging whether the existing distribution is appropriate or not. This task must be left to the discussion in the World Heritage Convention.Global public goods, world heritage, international organizations, international political economy, culture, UNESCO
Organization and evolution of synthetic idiotypic networks
We introduce a class of weighted graphs whose properties are meant to mimic
the topological features of idiotypic networks, namely the interaction networks
involving the B-core of the immune system. Each node is endowed with a
bit-string representing the idiotypic specificity of the corresponding B cell
and a proper distance between any couple of bit-strings provides the coupling
strength between the two nodes. We show that a biased distribution of the
entries in bit-strings can yield fringes in the (weighted) degree distribution,
small-worlds features, and scaling laws, in agreement with experimental
findings. We also investigate the role of ageing, thought of as a progressive
increase in the degree of bias in bit-strings, and we show that it can possibly
induce mild percolation phenomena, which are investigated too.Comment: 13 page
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