Search results for "Combinatorics"
showing 10 items of 1770 documents
EMERGENCE OF TRAVELLING WAVES IN SMOOTH NERVE FIBRES
2008
International audience; An approximate analytical solution characterizing initial condi- tions leading to action potential ¯ring in smooth nerve ¯bres is determined, using the bistable equation. In the ¯rst place, we present a non-trivial sta- tionary solution wave. Then, we extract the main features of this solution to obtain a frontier condition between the initiation of the travelling waves and a decay to the resting state. This frontier corresponds to a separatrix in the projected dynamics diagram depending on the width and the amplitude of the stationary wave.
Optimal signed-rank tests based on hyperplanes
2005
Abstract For analysing k -variate data sets, Randles (J. Amer. Statist. Assoc. 84 (1989) 1045) considered hyperplanes going through k - 1 data points and the origin. He then introduced an empirical angular distance between two k -variate data vectors based on the number of hyperplanes (the so-called interdirections ) that separate these two points, and proposed a multivariate sign test based on those interdirections. In this paper, we present an analogous concept (namely, lift-interdirections ) to measure the regular distances between data points. The empirical distance between two k -variate data vectors is again determined by the number of hyperplanes that separate these two points; in th…
An alternative representation of Altham's multiplicative-binomial distribution
1998
Abstract Cox (1972) introduced a log-linear representation for the joint distribution of n binary-dependent responses. Altham (1978) derived the distribution of the sum of such responses, under a multiplicative, rather than log-linear, representation and called it multiplicative-binomial. We propose here an alternative form of the multiplicative-binomial, which is derived from the original Cox's representation and is characterized by intuitively meaningful parameters, and compare its first two moments with those of the standard binomial distribution.
A Log-Rank Test for Equivalence of Two Survivor Functions
1993
We consider a hypothesis testing problem in which the alternative states that the vertical distance between the underlying survivor functions nowhere exceeds some prespecified bound delta0. Under the assumption of proportional hazards, this hypothesis is shown to be (logically) equivalent to the statement [beta[log(1 + epsilon), where beta denotes the regression coefficient associated with the treatment group indicator, and epsilon is a simple strictly increasing function of delta. The testing procedure proposed consists of carrying out in terms of beta (i.e., the standard Cox likelihood estimator of beta) the uniformly most powerful level alpha test for a suitable interval hypothesis about…
Bayesian subset selection for additive and linear loss function
1979
Given k independent samples of common size n from k populations πj,…,πk with distribution the problem is to select a non-empty subset form {πj,…,πk}, which is associated with "good" (large) θ-values. We consider this problem from a Bayesian approach. By choosing additive and especially linear loss functions we try to fill a gap lying in between the results of Deely and Gupta (1968) and more recent papers due to Goel and Rubin (1977), Gupta and Hsu (1978) and other authors. It is shown that under acertain "normal model" Seal's procedure turns out to be Bayes w.r.t. an unrealistic loss function where as Gupta's maximunl means procedure turns out to be ( for large n) asymptotically Bayes w.r. …
The asymptotic covariance matrix of the Oja median
2003
The Oja median, based on a sample of multivariate data, is an affine equivariant estimate of the centre of the distribution. It reduces to the sample median in one dimension and has several nice robustness and efficiency properties. We develop different representations of its asymptotic variance and discuss ways to estimate this quantity. We consider symmetric multivariate models and also the more narrow elliptical models. A small simulation study is included to compare finite sample results to the asymptotic formulas.
Random Logistic Maps II. The Critical Case
2003
Let (X n )∞ 0 be a Markov chain with state space S=[0,1] generated by the iteration of i.i.d. random logistic maps, i.e., X n+1=C n+1 X n (1−X n ),n≥0, where (C n )∞ 1 are i.i.d. random variables with values in [0, 4] and independent of X 0. In the critical case, i.e., when E(log C 1)=0, Athreya and Dai(2) have shown that X n → P 0. In this paper it is shown that if P(C 1=1)<1 and E(log C 1)=0 then (i) X n does not go to zero with probability one (w.p.1) and in fact, there exists a 0<β<1 and a countable set ▵⊂(0,1) such that for all x∈A≔(0,1)∖▵, P x (X n ≥β for infinitely many n≥1)=1, where P x stands for the probability distribution of (X n )∞ 0 with X 0=x w.p.1. A is a closed set for (X n…
A GALTON-WATSON BRANCHING PROCESS IN VARYING ENVIRONMENTS WITH ESSENTIALLY CONSTANT OFFSPRING MEANS AND TWO RATES OF GROWTH1
1983
Summary A Galton-Watson process in varying environments (Zn), with essentially constant offspring means, i.e. E(Zn)/mnα∈(0, ∞), and exactly two rates of growth is constructed. The underlying sample space Ω can be decomposed into parts A and B such that (Zn)n grows like 2non A and like mnon B (m > 4).
A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context
1998
Abstract For data in a two-way contingency table with ordered margins, we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities. This leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log-likelihood ratio tests. The usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases. I…
Entropic descriptor of a complex behaviour
2009
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum possible value Smax and its minimum possible value Smin. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length-scale dependence of the entropic descriptor makes it an adequate complexity-measure, able to disting…