Concept

Location–scale family

Publications associées (8)

On the Informativeness of Moments in Optimal Stopping

We study a variant of the prophet inequality with limited information, where the decision maker has access only to the first 𝑘 moments of each random variable, rather than their full distributions. In this work, we show that even with full moment knowledge (i.e., 𝑘 = ∞), the best possible competitive ratio is Θ(1/log 𝑛), and that this can already be achieved with only knowledge of the first moment. While the lower bound is simple and is attained by a standard exponential bucketing algorithm, the upper bound

ACM2026

Analytical description of seepage from disconnected surface water: improved approximate solution and insights for disconnection assessment

Seepage across a streambed is typically expressed by Darcy's law, q = Kc · ΔH / wc, where Kc and wc are the hydraulic conductivity and thickness of the bed, respectively, and ΔH is the hydraulic head gradient. When the stream is “disconnected” – i.e., an unsaturated zone exists beneath it – the suction at the lower bed interface no longer follows the groundwater head. Capturing this effect requires solving a nonlinear equation that incorporates the unsaturated hydraulic conductivity (UHC) relationship of th

2026

An internally non-linear ADC for a ΣΔ accelerometer loop

Maher Kayal, Marc Pastre

If an analog-to-digital converter (ADC) is used within a ΣΔ converter such that the loop filter is mixed signal, then the ADC does not need to have the full resolution of the ΣΔ converter, and its input values will not be uniformly distributed over the input range. In this paper, we argue that the best input distribution to use as a general model is the maximumentropy distribution (for location parameters: the Gaussian distribution). We then describe an externally linear ADC with non-linearly spaced decisio

2010

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Jean-Yves Le Boudec

Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called mean field limit", or hydrodynamic limit"). A common practice, often called the ``fixed point approximation" consists in approximating the stationary behaviour of the stochastic process by the stationary points of the fluid limit. It is known that this may be incorrect in general, as the stationary behaviour of the fluid limit may not be described by its stationary points. We show

arxiv.org2010

Measurement and Analysis of Single-Hop Delay on an IP Backbone Network

Patrick Thiran

We measure and analyze the single-hop packet delay through operational routers in the Sprint Internet protocol (IP) backbone network. After presenting our delay measurements through a single router for OC-3 and OC-12 link speeds, we propose a methodology to identify the factors contributing to single-hop delay. In addition to packet processing, transmission, and queueing delay at the output link, we observe the presence of very large delays that cannot be explained within the context of a first-in first-out

2003

Computer-intensive statistical methods : saddlepoint approximations with applications in bootstrap and robust inference

Diego Kuonen

The saddlepoint approximation was introduced into statistics in 1954 by Henry E. Daniels. This basic result on approximating the density function of the sample mean has been generalized to many situations. The accuracy of this approximation is very good, particularly in the tails of the distribution and for small sample sizes, compared with normal or Edgeworth approximation methods. Before applying saddlepoint approximations to the bootstrap, this thesis will focus on saddlepoint approximations for the dist

EPFL2001

Approximation Error for Quasi-Interpolators and (Multi-) Wavelet Expansions

Michaël Unser, Thierry Blu

We investigate the approximation properties of general polynomial preserving operators that approximate a function into some scaled subspace of

L _{ 2 }

via an appropriate sequence of inner products. In particular, we consider integer shift-invariant approximations such as those provided by splines and wavelets, as well as finite elements and multi-wavelets which use multiple generators. We estimate the approximation error as a function of the scale parameter T when the function to approximate is suffic

Academic Press1999

Conditional behavior of confidence intervals

This paper studies conditional properties of equivariant confidence intervals of a location parameter. The probability of covering the true value of the location parameter conditional on the location-and-scale configuration is computed. Also, the asymptotic distribution of this coverage probability is derived. Finally, the resulting expressions are applied to various confidence bounds such as the Wilcoxon, the Student

t

and the Cauchy likelihood bound.

1994

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