Volume 31, Issue 1

In this work, we propose to estimate the probability density function for nonnegative support using an LPE kernel with the adaptive Bayesian approach for bandwidth selection. For this, we exploit the conjugality between the LPE kernel and a prior distribution to develop the explicit form of the variable bandwidth parameter. Simulation studies are realized to evaluate the performance of the proposed adaptive Bayesian LPE kernel approach, with the classical Plug-In and UCV methods. On the other hand, we have carried out a comparative study between the proposed approach and two other adaptive Bayesian approaches with BSPE and gamma kernels. Moreover, real data sets are presented to illustrate the findings.

The multiplication of cells leads to consider the cell division model with mutation. Large cell counts therefore appear, implying that the distribution of the final number of mutant cells is a heavy tailed distribution. This distribution can be interpreted as a compound Poisson distribution, which depends on two parameters: the average number of mutations and the fitness parameter (heavy tail index). In this work, we specify some conditions that ensure a stability property of heavy-tailed distributions, namely, the distribution of random sum of random variables is a heavy-tailed distribution. We apply the obtained result to the compound Poisson distribution. To estimate the tail index, the Hill estimator and the generating function method are used. A comparative study is performed using these two estimators.

A coupled Hidden Markov Model (cHMM) is a hidden Markov model whose hidden Markov chain is bi-dimensional. In this paper, we focus to solve the likelihood and the decoding problems of a cHMM whose state space is composed of a continuous part and a discrete part. We adapt Forward, Backward and Viterbi algorithms to be able to study such cHMMs problems. Basic numerical examples are considered to show the well functioning of the elaborated algorithms for our proposal.

In the literature, maintenance plan efficacy is often assessed based on the long-term predicted maintenance cost rate, indicating a performance-centric approach. However, this criteria does not account for the fluctuation in maintenance costs over renewal cycles, and typical solutions may not be adequate from a risk management standpoint, a robustness viewpoint. This study tries to rethink standard solutions considering both performance and robustness, and thus, offer more suitable maintenance options.Specifically, using the long-term expected maintenance cost rate as the performance metric and the variance of maintenance cost per renewal cycle as the robustness metric, the study examines two representatives of time-based and condition-based maintenance approaches: a block replacement strategy and a periodic inspection and replacement strategy. Mathematical cost models are created based on the homogeneous Gamma degradation process and probability theory.Comparative study of both maintenance techniques demonstrates that the higher-performing approach carries a larger amount of risk. Consequently, a full examination of both performance and resilience is required in selecting a more dependent maintenance option. These maintenance solutions, together with the employment of the Monte Carlo Method, are contrasted against each other using a unique criteria that analyzes the degree of performance and robustness of each adaptation in maintenance decision-making.

The subject of this paper is a Monte Carlo algorithm for scalar conservation laws proposed in [L. Pareschi and M. Seaïd, A new Monte Carlo approach for conservation laws and relaxation systems, Computational Science—ICCS 2004. Part II, Lecture Notes in Comput. Sci. 3037, Springer, Berlin 2004, 276–283]. The algorithm is a stochastic particle method based on a probabilistic interpretation of the Jin–Xin relaxation formulation of conservation laws. We prove convergence as the number of particles approaches infinity, and the spatial and temporal mesh sizes approach zero, assuming that the number of particles approaches infinity at a rate sufficiently high compared to the rate that the mesh size approaches zero. For the case where the solution can take either sign, our version of the algorithm is novel. We present two numerical examples as evidence of convergence.

In this work, we introduce a new process by modifying the kernel in the time domain representation of the generalized Hermite process. This modification is constructed by means of multiplication of the kernel in the time definition of the process by an exponential tempering factor λ > 0 {\lambda>0} such that this new process is well defined. Several properties of the process are studied.