Modelling Poisson marked point processes using bivariate mixture transition distributions

A class of bivariate continuous-discrete distributions is proposed to fit Poisson dynamic models in a single unified framework via bivariate mixture transition distributions (BMTDs). Potential advantages of this class over the current models include its ability to capture stretches, bursts and nonlinear patterns characterized by Internet network traffic, high-frequency financial data and many others. It models the inter-arrival times and the number of arrivals (marks) in a single unified model which benefits from the dependence structure of the data. The continuous marginal distributions of this class include as special cases the exponential, gamma, Weibull and Rayleigh distributions (for the inter-arrival times), whereas the discrete marginal distributions are geometric and negative binomial. The conditional distributions are Poisson and Erlang. Maximum-likelihood estimation is discussed and parameter estimates are obtained using an expectation–maximization algorithm, while the standard errors are estimated using the missing information principle. It is shown via real data examples that the proposed BMTD models appear to capture data features better than other competing models.     

Pareto analysis for the lifetime performance index of products on the basis of progressively first-failure-censored batches under balanced symmetric and asymmetric loss functions

One of the most important topics in manufacturing industries is the evaluation of performance lifetimes of products. Based on a given lifetime performance index, this paper deals with evaluating the performance of a process subject to a given lower specification limit. We confine ourselves to the progressively first-failure-censored data coming from a common Pareto distribution. With both the Bayesian and the non-Bayesian approaches being investigated here, we pay more attention to Bayesian estimators under balanced type loss functions. The results are presented under the balanced versions of two well-known loss functions, namely the squared error loss and the Varian's linear-exponential (LINEX) loss. Moreover, based on the Bayesian and the non-Bayesian approaches, the problem of testing hypotheses on the lifetime performance index is studied. Also, a simulation study is performed to assess the obtained results. Finally, two illustrative examples are given.     

Estimation of P(Y < X) for Weibull Distribution Under Progressive Type-II Censoring

Based on progressively Type II censored samples, we consider the estimation of R = P(Y < X) when X and Y are two independent Weibull distributions with different shape parameters, but having the same scale parameter. The maximum likelihood estimator, approximate maximum likelihood estimator, and Bayes estimator of R are obtained. Based on the asymptotic distribution of R, the confidence interval of R are obtained. Two bootstrap confidence intervals are also proposed. Analysis of a real data set is given for illustrative purposes. Monte Carlo simulations are also performed to compare the different proposed methods.     

On the moments of record values

In this paper some general relations for expectations of functions of record values are established. It is seen that these relations may be used to obtain recurrence relations for moments of record values. Bounds on expectations of record values with numerical computations are presented. Applications to the characterizations of the generalizeed exponential distribution are also given.     

Fitting probability distributions to economic growth: a maximum likelihood approach

The growth rate of the gross domestic product (GDP) usually carries heteroscedasticity, asymmetry and fat-tails. In this study three important and significantly heteroscedastic GDP series are examined. A Normal, normal-mixture, normal-asymmetric Laplace distribution and a Student's t-Asymmetric Laplace (TAL) distribution mixture are considered for distributional fit comparison of GDP growth series after removing heteroscedasticity. The parameters of the distributions have been estimated using maximum likelihood method. Based on the results of different accuracy measures, goodness-of-fit tests and plots, we find out that in the case of asymmetric, heteroscedastic and highly leptokurtic data the TAL-distribution fits better than the alternatives. In the case of asymmetric, heteroscedastic but less leptokurtic data the NM fit is superior. Furthermore, a simulation study has been carried out to obtain standard errors for the estimated parameters. The results of this study might be used in e.g. density forecasting of GDP growth series or to compare different economies.     

A discrete model for the segmentation of chains and strings

A statistical model is presented that can be used to represent a discrete breakage process. It considers a fixed length chain or string made up of n +1 pieces joined together. The chain is stressed at each connection or link andrupture occurs at some of the links. Models are developed to answer the question, “what is the expected proportion of chain segments of a given size?” The model is modified to handle those experiments where only thetotal weight of a given size segment is known. Expressions are obtained for the expected value and variance of the number of segments of a given size. The model is used to predict the expected number of segments which results when a fixed length DNA molecule chain is subjected to carcinogenic agents and is applied to industrial examples.     

On the Optimal Parameters for Reconstruction and Forecasting in Singular Spectrum Analysis

There are two main parameters in Singular Spectrum Analysis (SSA). The aim of this study is to determine whether the optimal values of these parameters are different for reconstruction and forecasting stages, and if those are worth the extra computational effort and time which they require. Here, we evaluate these issues using simulation study.     

Toward re-engineering models and algorithms of facility layout

Models and algorithms are continuously being developed for the facility layout problem in various manufacturing settings. However, there could be practices and obstacles that weaken them and adversely impact the effectiveness of the layout. Thus, they should be obliterated in order to advance the layout problem. This paper suggests a set of guidelines that are directed at the process inherent in developing layout models, algorithms, expert systems, and software applications to assist in improving them and developing better layouts. Such guidelines are lacking in the literature of facility layout. Examples on the suitability and applicability of the suggested guidelines are given.