Mostrando recursos 1 - 20 de 260

  1. Asymptotics for sparse exponential random graph models

    Yin, Mei; Zhu, Lingjiong
    We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the limiting log partition function of the edge-(single)-star model. They are in sharp contrast to the corresponding asymptotics in dense exponential random graph models. Similar analysis is done for directed sparse exponential random graph models parametrized by edges and multiple outward stars.

  2. Concentration function for the skew-normal and skew-$t$ distributions, with application in robust Bayesian analysis

    Godoi, Luciana G.; Branco, Márcia D.; Ruggeri, Fabrizio
    Data from many applied fields exhibit both heavy tail and skewness behavior. For this reason, in the last few decades, there has been a growing interest in exploring parametric classes of skew-symmetrical distributions. A popular approach to model departure from normality consists of modifying a symmetric probability density function in a multiplicative fashion, introducing skewness. An important issue, addressed in this paper, is the introduction of some measures of distance between skewed versions of probability densities and their symmetric baseline. Different measures provide different insights on the departure from symmetric density functions: we analyze and discuss $L_{1}$ distance, $J$-divergence and...

  3. A bivariate optimal replacement policy with cumulative repair cost limit for a two-unit system under shock damage interaction

    Lai, Min-Tsai; Chen, Chung-Ho; Hariguna, Taqwa
    In this paper, a bivariate $(n,k)$ replacement policy with cumulative repair cost limit for a two-unit system is studied, in which the system is subjected to shock damage interaction between units. Each unit 1 failure causes random damage to unit 2 and these damages are additive. Unit 2 will fail when the total damage of unit 2 exceed a failure level $K$, and such a failure makes unit 1 fail simultaneously, resulting in a total failure. When unit 1 failure occurs, if the cumulative repair cost till to this failure is less than a predetermined limit $L$, then unit 1...

  4. $G$ method in action: Fast exact sampling from set of permutations of order $n$ according to Mallows model through Cayley metric

    Păun, Udrea
    Using $G$ method, we give a fast exact (not approximate) Markovian method for sampling from $\mathbb{S}_{n}$, the set of permutations of order $n$, according to the Mallows model through Cayley metric (a model for ranked data). This method has something in common with the cyclic Gibbs sampler and something in common with the swapping method. The number of steps of our method is equal to the number of steps of swapping method, that is, $n-1$; moreover, both methods use the best probability distributions on sampling, the swapping method uses uniform probability distributions while our method uses almost uniform probability distributions...

  5. The probability that $n$ random points in a disk are in convex position

    Marckert, Jean-François
    Pick $n$ random points $x_{1},\dots,x_{n}$ uniformly and independently in a disk and consider their convex hull $C$. Let $P_{D}^{n,m}$ be the probability that exactly $m$ points among the $x_{i}$’s are on the boundary of the convex hull of $\{x_{1},\ldots,x_{n}\}$ (so that $P_{D}^{n,n}$ is the probability that the $x_{i}$’s are in a convex position). ¶ In the paper, we provide a formula for $P_{D}^{n,m}$.

  6. On estimating the scale parameter of the selected uniform population under the entropy loss function

    Arshad, Mohd.; Misra, Neeraj
    Let $\pi_{1},\ldots,\pi_{k}$ be $k$ ($\geq2$) independent populations, where $\pi_{i}$ denotes the uniform distribution over the interval $(0,\theta_{i})$ and $\theta_{i}>0$ ($i=1,\ldots,k$) is an unknown scale parameter. Let $\theta_{[1]}\leq\cdots\leq\theta_{[k]}$ be the ordered values of $\theta_{1},\ldots,\theta_{k}$. The population $\pi_{(k)}$ ($\pi_{(1)}$) associated with the unknown parameter $\theta_{[k]}$ ($\theta_{[1]}$) is called the best (worst) population. For selecting the best population, we consider a general class of selection rules based on the natural estimators of $\theta_{i},i=1,\ldots,k$. Under the entropy loss function, we consider the problem of estimating the scale parameter $\theta_{S}$ of the population selected using a fixed selection rule from this class. We derive the...

  7. On bivariate inverse Weibull distribution

    Kundu, Debasis; Gupta, Arjun K.
    Inverse Weibull distribution has been used quite successfully to analyze lifetime data which has non-monotone hazard function. The main aim of this paper is to introduce bivariate inverse Weibull distribution along the same line as the Marshall–Olkin bivariate exponential distribution, so that the marginals have inverse Weibull distributions. The proposed bivariate inverse Weibull distribution has four parameters and it has a singular component. Therefore, it can be used quite successfully if there are ties in the data. The joint probability density function, the joint cumulative distribution function and the joint survival function are all in closed forms. Several properties of...

  8. Improved asymptotic estimates for the contact process with stirring

    Levit, Anna; Valesin, Daniel
    We study the contact process with stirring on $\mathbb{Z}^{d}$. In this process, particles occupy vertices of $\mathbb{Z}^{d}$; each particle dies with rate 1 and generates a new particle at a randomly chosen neighboring vertex with rate $\lambda$, provided the chosen vertex is empty. Additionally, particles move according to a symmetric exclusion process with rate $N$. For any $d$ and $N$, there exists $\lambda_{c}$ such that, when the system starts from a single particle, particles go extinct when $\lambda<\lambda_{c}$ and have a chance of being present for all times when $\lambda>\lambda_{c}$. Durrett and Neuhauser proved that $\lambda_{c}$ converges to 1 as...

  9. A generating function approach to branching random walks

    Bertacchi, Daniela; Zucca, Fabio
    It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching process can be seen as a one-dimensional branching random walk. We define a multidimensional generating function associated to a given branching random walk. The present paper investigates the similarities and the differences of the generating functions, their fixed points and the implications on the underlying stochastic process, between the one-dimensional (branching process) and the multidimensional case (branching random walk). In particular, we...

  10. On the critical probability of percolation on random causal triangulations

    Cerda-Hernández, José; Yambartsev, Anatoly; Zohren, Stefan
    In this work, we study bond percolation on random causal triangulations. While in the sub-critical regime there is no phase transition, we show that for percolation on critical random causal triangulations there exists a non-trivial phase transition and we compute an upper bound for the critical probability. Furthermore, the critical value is shown to be almost surely constant.

  11. Semimartingale properties of the lower Snell envelope in optimal stopping under model uncertainty

    Treviño Aguilar, Erick
    Optimal stopping under model uncertainty is a recent topic under research. The classical approach to characterize the solution of optimal stopping is based on the Snell envelope which can be seen as the value process as time runs. The analogous concept under model uncertainty is the so-called lower Snell envelope and in this paper, we investigate its structural properties. We give conditions under which it is a semimartingale with respect to one of the underlying probability measures and show how to identify the finite variation process by a limiting procedure. An example illustrates that without our conditions, the semimartingale property...

  12. Ranked set sampling with scrambled response model to subsample non-respondents

    Ahmed, Shakeel; Shabbir, Javid
    This paper considers use of the scrambled response model in Ranked Set Sampling (RSS) for collecting information on second call to estimate population mean when non-response is due to sensitivity of the study variable. It also uses Extreme Ranked Set Sampling (ERSS) and Median Ranked Set Sampling (MRSS) to sub-sample the non-respondents. Expressions for variances of different estimators are derived. A Monte Carlo experiment is carried out to observe the efficiency of proposed estimators.

  13. Calibration estimation of adjusted Kuk’s randomized response model for sensitive attribute

    Son, Chang-Kyoon; Kim, Jong-Min
    In this paper, we consider the calibration procedure for Su et al.’s [Sociol. Methods Res. 44 (2014) DOI:10.1177/0049124114554459] adjusted Kuk randomized response (RR) technique by using auxiliary information such as gender or age group of respondents associated with the variable of interest. Our proposed calibration method can overcome the problems such as noncoverage and nonresponse. From the efficiency comparison study, we show that the calibrated adjusted Kuk’s RR estimators are more efficient than that of Su et al. [Sociol. Methods Res. 44 (2014) DOI:10.1177/0049124114554459], when the known population cell and marginal counts of auxiliary information are used for the calibration...

  14. Multivariate versions of dimension walks and Schoenberg measures

    Alonso-Malaver, Carlos Eduardo; Porcu, Emilio; Giraldo Henao, Ramón
    This paper considers multivariate Gaussian fields with their associated matrix valued covariance functions. In particular, we characterize the class of stationary-isotropic matrix valued covariance functions on $d$-dimensional Euclidean spaces, as being the scale mixture of the characteristic function of a $d$ dimensional random vector being uniformly distributed on the spherical shell of $\mathbb{R}^{d}$, with a uniquely determined matrix valued and signed measure. This result is the analogue of celebrated Schoenberg theorem, which characterizes stationary and isotropic covariance functions associated to an univariate Gaussian fields. ¶ The elements $\mathbf{C}$, being matrix valued, radially symmetric and positive definite on $\mathbb{R}^{d}$, have a matrix valued...

  15. From heavy-tailed Boolean models to scale-free Gilbert graphs

    Hirsch, Christian
    Define the scale-free Gilbert graph based on a Boolean model with heavy-tailed radius distribution on the $d$-dimensional torus by connecting two centers of balls by an edge if at least one of the balls contains the center of the other. We investigate two asymptotic properties of this graph as the size of the torus tends to infinity. First, we determine the tail index associated with the asymptotic distribution of the sum of all power-weighted incoming and outgoing edge lengths at a randomly chosen vertex. Second, we study the behavior of chemical distances on scale-free Gilbert graphs and show the existence...

  16. Slash-elliptical nonlinear regression model

    Alcantara, Izabel Cristina; Cysneiros, Francisco José A.
    The aim of this paper is to develop nonlinear regression models with error distribution having the slash-elliptical family. A slash-elliptical random variable is defined as the quotient of two independent random variables, $Z$ and $U^{1/q}$, where $Z$ has an elliptical contoured distribution and $U$ has a uniform distribution. A key advantage of the slash-elliptical distribution is the simplicity by which the well-known elliptical contoured distribution can be modified to support increase in kurtosis. The main properties of the slash-elliptical distribution is symmetry, heavy tails and convergence to the elliptical contoured distribution as the limiting case of the shape parameter. One...

  17. A new stochastic model and its diffusion approximation

    Covo, Shai; Elalouf, Amir
    This paper considers a kind of queueing problem with a Poisson number of customers or, more generally, objects which may arrive in groups of random size. The focus is on the total quantity over time, called system size. The main result is that the process representing the system size, properly normalized, converges in finite-dimensional distributions to a centered Gaussian process (the diffusion approximation) with several attractive properties. Comparison with existing works (where the number of objects is assumed nonrandom) highlights the contribution of the present paper.

  18. Prediction of future failures for generalized exponential distribution under Type-I or Type-II hybrid censoring

    Valiollahi, R.; Asgharzadeh, A.; Kundu, D.
    In this paper, we consider the prediction of a future observation based on either Type-I or Type-II hybrid censored samples when the lifetime distribution of the experimental units is assumed to be a generalized exponential random variable. Different point and interval predictors are obtained using classical and Bayesian approaches. Monte Carlo simulations are performed to compare the performances of the different methods, and the analysis of one data set has been presented for illustrative purposes.

  19. Strong rate of tamed Euler–Maruyama approximation for stochastic differential equations with Hölder continuous diffusion coefficient

    Ngo, Hoang-Long; Luong, Duc-Trong
    We study the strong rate of convergence of the tamed Euler–Maruyama approximation for one-dimensional stochastic differential equations with superlinearly growing drift and Hölder continuous diffusion coefficients.

  20. Inference on dynamic models for non-Gaussian random fields using INLA

    Cortes, R. X.; Martins, T. G.; Prates, M. O.; Silva, B. A.
    Robust time series analysis is an important subject in statistical modeling. Models based on Gaussian distribution are sensitive to outliers, which may imply in a significant degradation in estimation performance as well as in prediction accuracy. State-space models, also referred as Dynamic Models, is a very useful way to describe the evolution of a time series variable through a structured latent evolution system. Integrated Nested Laplace Approximation (INLA) is a recent approach proposed to perform fast approximate Bayesian inference in Latent Gaussian Models which naturally comprises Dynamic Models. We present how to perform fast and accurate non-Gaussian dynamic modeling with...

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