The logarithmic series distribution as a failure model from the Bayesian point of view

In this presentation the logorithmic series is studied as a failure model from the Bayesian point of view. It is assumed that the location parameter behaves as a random variable with beta as its prior distribution. Based on this assumption Bayes estimators for the location parameter and reliability function are derived. By using computer simulation we compare the Bayes estimator for the parameter with the corresponding minimum variance unbiased estimator (MVUE) and the Bayes estimator for the reliability with a corresponding unbiased estimator derived from the MVUE of the probability function.     

The Burr type XII distribution as a failure model under various loss functions

Bayesian estimates of the parameter p and the reliability function for the two-parameter Burr type XII failure model under three different loss functions, absolute difference, squared error and logarithmic are derived. It is assumed that the parameter p behaves as a random variable having (i) a gamma prior and (ii) a vague prior. Monte Carlo simulations are presented to compare the Bayesian estimators and the maximum likelihood estimators of the parameter p and the reliability function. The results show that the “popular” squared error loss function is not always the best, and that the other loss functions give comparable results.     

Bayesian approach to prediction with outliers from the Burr type X model

In this paper, Bayesian prediction bounds are obtained for the future observations from the Burr type X distribution in the presence of outliers. Numerical examples are used to illustrate the procedure.     

Bayesian approach to prediction with outliers from the Burr type X model

In this paper, Bayesian prediction bounds are obtained for the future observations from the Burr type X distribution in the presence of outliers. Numerical examples are used to illustrate the procedure.     

The study of a maintenance float model with Burr failure distribution

This paper considers an operational system made up of N independent and identical units. These units are required to be in service and are supported by a maintenance float. Here, an attempt has been made to model and analyse the maintenance float problem for a Burr failure distribution. For the sake of simplicity, the repair times are assumed to follow exponential and lognormal distributions.     

Peculiarities of finding characteristic functions of the generating process in the model of stationary linear AR(2) process with negative binomial distribution

The linear random AR(2) autoregressive process having the negative binomial distribution has been considered. It has the form ξ _t + a ₁ξ _t-1 + a ₂ξ _t-2 = ? _t , t ∈ Z, where {a ₁, a ₂ ≠ 0} are the autoregressive parameters; Z = {...,-1,0,1,...} is the sequence of integers; {ξ _t ,t ∈ Z} is the random process with discrete time and independent values having the infinitely divisible distribution law that is called generating process. The method of finding the characteristic function of the generating process for linear autoregressive process having negative binomial distribution is presented. This inverse problem is solved by using properties of the characteristic function of stationary linear autoregressive process that can be presented in the Kolmogorov canonical form and as a linear stationary autoregressive process. An example of finding the Poisson spectrum of jumps and the characteristic function for the linear second order autoregressive process (AR(2)) with negative binomial distribution has been also presented.     

A maintenance inspection model for a single machine with general failure distribution

In this paper we develop a mathematical model for determining a periodic inspection schedule in a preventive maintenance program for a single machine subject to random failure. We formulate the problem as a profit maximization model with general failure time distribution. We show that under certain conditions on the probability density function of failure, a unique optimal inspection interval can be obtained. When the failure times are exponentially distributed, we propose alternative optimal and heuristic procedures to find exact and approximate inspection intervals. Our heuristic solution method is shown numerically to be more efficient than an earlier published heuristic procedure. We also investigated the sensitivity of the optimal inspection interval and expected profit per unit of time with respect to the changes in the two parameters of the Weibull time to failure distribution.     

A sparsity-based Bayesian approach for hyperspectral unmixing using normal compositional model

A new Bayesian-based method is developed for unmixing of hyperspectral images. Endmembers are assumed variable based on the Gaussian distribution. A semi-supervised scenario is considered, and as a practical aspect, the abundance vectors are assumed sparse. We propose the Dirichlet prior to represent the sparsity and derive the corresponding posteriors in Bayesian sense. Numerical results are used to evaluate different methods for both simulated and real data. It is shown that the proposed method achieves a lower error in abundance estimation and image reconstruction.     

Estimation of failure probability from a bivariate normal stress-strength distribution

Probability (P) of equipment failure consequent upon stress exceeding built-in strength has been estimated assuming a bivariate normal stress-strength distribution. The UMVUE of P when parameters other than the means are known has been derived. An alternative estimator based on maximum likelihood estimates has been proposed in the case when all the five parameters are unknown. Asymptotic variances of both these estimators have been worked out. Some relevant numerical computations have also been reported.     

Estimation of wavefield power distribution in the remotely sensed environment: Bayesian maximum entropy approach

The problem of estimating, from one random realization of the remotely sensed signal, the spatial spectrum pattern (SSP) of the wavefield sources distributed in the environment is cast in the framework of Bayesian estimation theory. The kernel spectral estimation method that is familiar, for the classical SSP estimation problem, with the Fourier transform operator and white noise in the observations is extended to incorporate spatial correlation in the data, the system-oriented model of the signal formation operator, and the maximum entropy (ME) statistical a priori information about the SSP. To derive the estimate of the SSP, we applied the Bayesian strategy for maximization of the a posteriori probability density function of the randomized ME model of the SSP. The estimator was obtained as a nonlinear adaptive algorithm that also permits a concise robust implementation. The optimal algorithm implies formation of the second-order sufficient statistics of the data and their smoothing by applying the window operator. The new formalism of the sufficient statistics and windows, explaining their adjustment to the metrics in a solution space, a priori nonparametric model and assumed correlation properties of the desired SSP, is developed. Simulation results are included to illustrate the overall performance of the proposed method in an example of application to radar image formation.     

Generalized Gaussian mixture models as a nonparametric Bayesian approach for clustering using class-specific visual features

Recently, there has been a growing interest in the problem of learning mixture models from data. The reasons and motivations behind this interest are clear, since finite mixture models offer a formal approach to the important problems of clustering and data modeling. In this paper, we address the problem of modeling non-Gaussian data which are largely present, and occur naturally, in several computer vision and image processing applications via the learning of a generative infinite generalized Gaussian mixture model. The proposed model, which can be viewed as a Dirichlet process mixture of generalized Gaussian distributions, takes into account the feature selection problem, also, by determining a set of relevant features for each data cluster which provides better interpretability and generalization capabilities. We propose then an efficient algorithm to learn this infinite model parameters by estimating its posterior distributions using Markov Chain Monte Carlo (MCMC) simulations. We show how the model can be used, while comparing it with other models popular in the literature, in several challenging applications involving photographic and painting images categorization, image and video segmentation, and infrared facial expression recognition.     

The Mukherjee-Islam failure model

This paper provides an extensive discussion on the model given by Mukherjee and Islam [Nav. Res. Log. Quart.30, 487–491 (1983)]. In the first section, a discussion is given on the usefulness of the model as an inventory model, and also the property of forgetfulness is discussed. In the next section, we discuss the range of this distribution, giving some useful suggestions.     

The reflex klystron as a negative resistance type amplifier

A reflex klystron has been tested as a narrow-band amplifier at 11,000 mc. The performance is predicted rather accurately from simple theory and steady gain can now be obtained in the 30-db region with a bandwidth of the order of megacycles. A noise figure of 40 db was measured and the saturation power output was the same as the output of an oscillator. A circulator was used in these tests to separate input from output and we consider it important to use this component with any type of negative resistance type amplifier.     

Bayesian analysis of the parameters of a doubly truncated weibull distribution

This paper deals with the estimation of the reliability function and parameters of a doubly truncated Weibull distribution using point and credible/highest posterior density intervals. Bayesian estimates, which obtained, compared with their corresponding classical counterparts.     

Segmental probability distribution model approach for isolatedMandarin syllable recognition

A segmental probability distribution model (SPDM) approach is proposed for fast and accurate recognition of isolated Mandarin syllables. Instead of the conventional frame-based approach such as the hidden Markov model (HMM), the model matching process in the proposed SPDM is evaluated segment-by-segment based on information-theoretic distance measurements. The training and recognition procedures for the SPDM are developed first. Several distance measurement criteria, including the Chernoff distance, Bhattacharyya distance, Patrick-Fisher (1969) distance, divergence and a Bayesian-like distance, are used, and formulations and comparative results are discussed. Experimental results show that, compared to the widely used sub-unit based continuous density HMM, the proposed method leads to an improvement of 15.27% in the error rate, with a 12-fold increase in recognition speed and less than three quarters of the mixture requirements     

Fitting a multivariate failure time distribution

A class of continuous multivariate distributions is reviewed. It is derived in a survival/reliability context, where the dependence is modeled as random effects, viz, by an unobserved covariate common to the components in a system and assumed to follow a positive stable distribution. Accounting for censored data is straightforward. The class is well fitted to proportional hazard models, and distributions of minima are simple. An important subfamily is the multivariate Weibull distributions. The theory is illustrated with an example     

Multiscale Bayesian segmentation using a trainable context model

Multiscale Bayesian approaches have attracted increasing attention for use in image segmentation. Generally, these methods tend to offer improved segmentation accuracy with reduced computational burden. Existing Bayesian segmentation methods use simple models of context designed to encourage large uniformly classified regions. Consequently, these context models have a limited ability to capture the complex contextual dependencies that are important in applications such as document segmentation. We propose a multiscale Bayesian segmentation algorithm which can effectively model complex aspects of both local and global contextual behavior. The model uses a Markov chain in scale to model the class labels that form the segmentation, but augments this Markov chain structure by incorporating tree based classifiers to model the transition probabilities between adjacent scales. The tree based classifier models complex transition rules with only a moderate number of parameters. One advantage to our segmentation algorithm is that it can be trained for specific segmentation applications by simply providing examples of images with their corresponding accurate segmentations. This makes the method flexible by allowing both the context and the image models to be adapted without modification of the basic algorithm. We illustrate the value of our approach with examples from document segmentation in which test, picture and background classes must be separated.     

Bayesian sequential estimation of two parameters of a Weibull distribution

Weibull distribution is one of the most widely used model for failure data in reliability studies. In this paper a sequential estimation procedure for estimating the parameters of Weibull distribution is proposed, which is, in principle similar to Kalman filtering. The main advantage of this approach is that it shows the variation of parameters over a time as new failure data becomes available to the analyst for estimation. Also once an available data has been used, the method does not require that data for further processing as and when the new data becomes available for updating the estimates of parameters. Its use in Quality control asa control chart has been indicated and the procedure is illustrated with the help of examples.     

Bayesian prediction for the range with a burr distribution and a random sample size

This paper is concerned with the problem of predicting the future range with the two-parameter Burr distribution, given a sample of a random size and using the Bayesian approach. We consider two possible distributions of the random sample size and the results so obtained have been illustrated numerically, using iterative techniques and computer facilities.     

Approximations for the probability in the tails of the binomial distribution (Corresp.)

Upper and lower bounds for the probability in the tails of a binomial distribution are investigated. New bounds are obtained which are computationally simple and, in the case of the lower bound, significantly better than previously known bounds.