Search results for " Probability"

Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy

2020

A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time u an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that at a larger time t the system is found to be failed. Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement evaluated at x &isin

Random cutout sets with spatially inhomogeneous intensities

2015

We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.

Curve packing and modulus estimates

2018

A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c > 0$. We strengthen Marstrand's result by showing that for $p > 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} > 0$.

On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables

2021

In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.

Circular law for sparse random regular digraphs

2020

Fix a constant $C\geq 1$ and let $d=d(n)$ satisfy $d\leq \ln^{C} n$ for every large integer $n$. Denote by $A_n$ the adjacency matrix of a uniform random directed $d$-regular graph on $n$ vertices. We show that, as long as $d\to\infty$ with $n$, the empirical spectral distribution of appropriately rescaled matrix $A_n$ converges weakly in probability to the circular law. This result, together with an earlier work of Cook, completely settles the problem of weak convergence of the empirical distribution in directed $d$-regular setting with the degree tending to infinity. As a crucial element of our proof, we develop a technique of bounding intermediate singular values of $A_n$ based on studyi…

Order statistics-based parametric classification for multi-dimensional distributions

2013

Traditionally, in the field of Pattern Recognition (PR), the moments of the class-conditional densities of the respective classes have been used to perform classification. However, the use of phenomena that utilized the properties of the Order Statistics (OS) were not reported. Recently, in [10,8], we proposed a new paradigm named CMOS, Classification by the Moments of Order Statistics, which specifically used these quantifiers. It is fascinating that CMOS is essentially ''anti''-Bayesian in its nature because the classification is performed in a counter-intuitive manner, i.e., by comparing the testing sample to a few samples distant from the mean, as opposed to the Bayesian approach in whi…

On the fractional probabilistic Taylor's and mean value theorems

2016

In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution if and only if it is exponential. The nth-order fractional equilibrium density is then used to prove a fractional probabilistic Taylor's theorem based on derivatives of Riemann-Liouville type. A fractional analogue of the probabilistic mean value theorem is thus developed for pairs of nonnegative rand…

Weighted-average least squares estimation of generalized linear models

2018

The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models (GLMs). We study the large-sample properties of the WALS estimator for GLMs under a local misspecification framework that allows the development of asymptotic model averaging theory. We also investigate t…

2020

Piping erosion is one form of water erosion that leads to significant changes in the landscape and environmental degradation. In the present study, we evaluated piping erosion modeling in the Zarandieh watershed of Markazi province in Iran based on random forest (RF), support vector machine (SVM), and Bayesian generalized linear models (Bayesian GLM) machine learning algorithms. For this goal, due to the importance of various geo-environmental and soil properties in the evolution and creation of piping erosion, 18 variables were considered for modeling the piping erosion susceptibility in the Zarandieh watershed. A total of 152 points of piping erosion were recognized in the study area that…

Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects

2021

Jyväskylästä kirjoitettiin: Käyn läpi Extra-Vipusessa ristiriitaisiksi luokitettuja yhteisjulkaisuja. Julkaisu " Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects" on meillä laitettu A2 ja teillä A1. Meillä varmaan päädytty tuohon A2:een kun tiivistelmässä sanotaan "Building on a systematic review of six leading management journals..". Mutta mitä mieltä olette, kumpi olisi parempi? Transforming variables before analysis or applying a transformation as a part of a generalized linear model are common practices in organizational research. Several methodological articles addressing the topic, either directly or indirectly, have been published in the rec…