Finding the parameters of a Bernoulli-Gaussian Model

<div><div><div><p>A transmission medium perturbed by an additive noise from which the estimated noise power is all information known, is better modeled as a Gaussian channel. Since the Gaussian channel is, according to Information Theory, the worst channel to transmit information through, this is the most pessimistic assumption. When noise samples are available though, choosing to model the transmission medium using a more sophisticated model pays off. The Bernoulli-Gaussian channel, would be one such a choice. Finding the three parameters that characterize the Bernoulli-Gaussian stochastic process which mathematically models the noise is a task of paramount importance. Many algorithms can be used to estimate the parameters of this model based on numerical methods. In the current work a closed form expression to estimate the model parameters is presented. All that is required besides the estimation of the power of Bernoulli-Gaussian process from the available noise samples is the estimation of two additional quantities: the expected value of the absolute value of the amplitude of the process—the first absolute moment—plus the third absolute moment, viz., the expected value of the third power of the absolute value of the process. An alternative option, often used for power line communication, is to model the transmission medium as a channel in which the noise is represented by a three parameter stochastic process called Middleton Class A. Other models (like generalized-Bernoulli-Gaussian, or Bernoulli- Gaussian with memory) might render a better medium model than the Bernoulli-Gaussian channel. Estimating the parameters of these processes is however a cumbersome task and, as we show in the current work, the rate harvested by using the simple, yet more sophisticated, Bernoulli-Gaussian channel is increased as compared to the, more pessimistic, Gaussian channel, allowing one thus to more closely approach the true capacity. The communication system design can be much improved if a well fit Bernoulli-Gaussian stochastic process is selected to model the true noise. The incorporation of the Bernoulli-Gaussian channel in the communication system model leads to a better design as corroborated by the computer simulation results presented.</p></div></div></div>

Finding the parameters of a Bernoulli-Gaussian Model

<div><div><div><p>A transmission medium perturbed by an additive noise from which the estimated noise power is all information known, is better modeled as a Gaussian channel. Since the Gaussian channel is, according to Information Theory, the worst channel to transmit information through, this is the most pessimistic assumption. When noise samples are available though, choosing to model the transmission medium using a more sophisticated model pays off. The Bernoulli-Gaussian channel, would be one such a choice. Finding the three parameters that characterize the Bernoulli-Gaussian stochastic process which mathematically models the noise is a task of paramount importance. Many algorithms can be used to estimate the parameters of this model based on numerical methods. In the current work a closed form expression to estimate the model parameters is presented. All that is required besides the estimation of the power of Bernoulli-Gaussian process from the available noise samples is the estimation of two additional quantities: the expected value of the absolute value of the amplitude of the process—the first absolute moment—plus the third absolute moment, viz., the expected value of the third power of the absolute value of the process. An alternative option, often used for power line communication, is to model the transmission medium as a channel in which the noise is represented by a three parameter stochastic process called Middleton Class A. Other models (like generalized-Bernoulli-Gaussian, or Bernoulli- Gaussian with memory) might render a better medium model than the Bernoulli-Gaussian channel. Estimating the parameters of these processes is however a cumbersome task and, as we show in the current work, the rate harvested by using the simple, yet more sophisticated, Bernoulli-Gaussian channel is increased as compared to the, more pessimistic, Gaussian channel, allowing one thus to more closely approach the true capacity. The communication system design can be much improved if a well fit Bernoulli-Gaussian stochastic process is selected to model the true noise. The incorporation of the Bernoulli-Gaussian channel in the communication system model leads to a better design as corroborated by the computer simulation results presented.</p></div></div></div>

Dynamic rain model for linear stochastic environments

To develop modem agriculture, a vision of an integral management is required, where the complexity of interactions between climatic, biological, economical, social and political factors involved in the food production must systematically be analyzed in a context of regional conditions. At the same time, it is necessary to develop the ability to forecast both the climatic variations and their possible impact on society. The minimization of this impact on agriculture through consistent practices adequate to local climates, is not only commendable, but basically necessary, besides, the usefulness of these studies in acquiring a better knowledge of those areas with an inversion risk for agricultural and cattle rising development is high. In this paper a statistical model is used to accomplish the objectives above mentioned. The rainfall variability in several areas of the Tlaxcala State (Mexico) is analyzed with due regard to both inter- and intra-annual relations, considering that the cumulative rainfall, in the former case, follows a logistic curve and in the latter it follows a linear, first order, stochastic process.

Peacocks and the Zeta distributions

We prove in this short paper that the stochastic process defined by: $$Y_{t} := \frac{X_{t+1}}{\mathbb{E}\left[ X_{t+1}\right]},\; t\geq a > 1,$$ is an increasing process for the convex order,where Χt a random variable taking values in N with probability P(Χt = n) = n-t/(𝛇(t)) and 𝛇(t) = +∞∑k=1(1/kt), ∀t > 1.

RELIABILITY OF DETERIORATED MARINE STRUCTURES BASED ON MEASURED DATA

Reliability assessment of a corroded deck of a tanker ship subjected to non-linear general corrosion wastage is performed, accounting for an initial period without corrosion due to the presence of a corrosion protection system, and a non-linear increase in wastage up to a steady state value. The reliability model is based on the analysis of corrosion depth data. Two types of uncertainties are accounted for. The first one is related to the corrosion degradation trend as a function of time, which is identified by a sequence independent data analysis. The second uncertainty is related to the variation of the corrosion degradation around its trend, which is identified as a stochastic process, and is defined based on the time series analysis. The time series determines the autocorrelation and spectral density functions of the stochastic process applying the Fast Fourier transform. The reliability estimates with respect to a corroded deck of cargo tank of a tanker ship is analysed by a time variant formulation and the effect of inspections is also incorporated employing the Bayesian updating formulation.

Quantile Process with Applications : Chirp Signal Model

<p>The parameters in the well-known chirp signal model controls the frequency fluctuations of the signals, and consequently, the estimation of the parameters has received considerable attention in the literature of statistical signal processing. In the same spirit with a broader view, this article investigates the quantile estimator of parameters involved in the chirp signal model, which enables us to provide basic features of the entire distribution of the signals. In the course of this study, we establish the limiting behaviour of the associated stochastic process, which we call quantile process. As the applications of this result, we obtain the limiting distributions of various quantile based measures of descriptive statistics, which give us summarized features of the fluctuations of the signals in various senses. Finally, along with extensive simulation study, the practicability of the proposed methodology is shown on a few benchmark real datasets closely related with various chirp signal models.<br></p>

Quantile Process with Applications : Chirp Signal Model

<p>The parameters in the well-known chirp signal model controls the frequency fluctuations of the signals, and consequently, the estimation of the parameters has received considerable attention in the literature of statistical signal processing. In the same spirit with a broader view, this article investigates the quantile estimator of parameters involved in the chirp signal model, which enables us to provide basic features of the entire distribution of the signals. In the course of this study, we establish the limiting behaviour of the associated stochastic process, which we call quantile process. As the applications of this result, we obtain the limiting distributions of various quantile based measures of descriptive statistics, which give us summarized features of the fluctuations of the signals in various senses. Finally, along with extensive simulation study, the practicability of the proposed methodology is shown on a few benchmark real datasets closely related with various chirp signal models.<br></p>