Dynamic Modeling and Statistical Analysis of Event Times

This review article provides an overview of recent work in the modeling and analysis of recurrent events arising in engineering, reliability, public health, biomedicine and other areas. Recurrent event modeling possesses unique facets making it different and more difficult to handle than single event settings. For instance, the impact of an increasing number of event occurrences needs to be taken into account, the effects of covariates should be considered, potential association among the interevent times within a unit cannot be ignored, and the effects of performed interventions after each event occurrence need to be factored in. A recent general class of models for recurrent events which simultaneously accommodates these aspects is described. Statistical inference methods for this class of models are presented and illustrated through applications to real data sets. Some existing open research problems are described.Comment: Published at http://dx.doi.org/10.1214/088342306000000349 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program

A New Class of Life Distribution based on Laplace Transform and It’s Applications

Based on the approach of Laplace transform, a new class of life distributions called used better than aged in increasing concave denoted by (UBAC(2)L) is introduced. The implication of our proposed class of life distribution with other classes is given. Some properties of UBAC(2)L class of life distribution are studied. By using the goodness of fit methodology, a new test statistic is proposed for testing exponentiality versus UBAC(2)L class of life distribution. Critical values of our test are calculated for complete and censored data. The power of the test and pitman’s asymptotic efficiency (PAE) for some commonly used distributions in reliability are calculated. Finally, a set of real data is used as an example to elucidate the use of the proposed test statistic for practical reliability analysis

A New Class of Life Distribution based on Laplace Transform and It’s Applications

Based on the approach of Laplace transform, a new class of life distributions called used better than aged in increasing concave denoted by (UBAC(2)L) is introduced. The implication of our proposed class of life distribution with other classes is given. Some properties of UBAC(2)L class of life distribution are studied. By using the goodness of fit methodology, a new test statistic is proposed for testing exponentiality versus UBAC(2)L class of life distribution. Critical values of our test are calculated for complete and censored data. The power of the test and pitman’s asymptotic efficiency (PAE) for some commonly used distributions in reliability are calculated. Finally, a set of real data is used as an example to elucidate the use of the proposed test statistic for practical reliability analysis

Markov and Neural Network Models for Prediction of Structural Deterioration of Stormwater Pipe Assets

Storm-water pipe networks in Australia are designed to convey water from rainfall and surface runoff. They do not transport sewerage. Their structural deterioration is progressive with aging and will eventually cause pipe collapse with consequences of service interruption. Predicting structural condition of pipes provides vital information for asset management to prevent unexpected failures and to extend service life. This study focused on predicting the structural condition of storm-water pipes with two objectives. The first objective is the prediction of structural condition changes of the whole network of storm-water pipes by a Markov model at different times during their service life. This information can be used for planning annual budget and estimating the useful life of pipe assets. The second objective is the prediction of structural condition of any particular pipe by a neural network model. This knowledge is valuable in identifying pipes that are in poor condition for repair actions. A case study with closed circuit television inspection snapshot data was used to demonstrate the applicability of these two models

HIV with contact-tracing: a case study in Approximate Bayesian Computation

Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian Computation, an alternative to data imputation methods such as Markov Chain Monte Carlo integration, is proposed for making inference in epidemiological models. It is a likelihood-free method that relies exclusively on numerical simulations. ABC consists in computing a distance between simulated and observed summary statistics and weighting the simulations according to this distance. We propose an original extension of ABC to path-valued summary statistics, corresponding to the cumulated number of detections as a function of time. For a standard compartmental model with Suceptible, Infectious and Recovered individuals (SIR), we show that the posterior distributions obtained with ABC and MCMC are similar. In a refined SIR model well-suited to the HIV contact-tracing data in Cuba, we perform a comparison between ABC with full and binned detection times. For the Cuban data, we evaluate the efficiency of the detection system and predict the evolution of the HIV-AIDS disease. In particular, the percentage of undetected infectious individuals is found to be of the order of 40%

On the distributional properties of household consumption expenditures. The case of Italy.

In this paper we explore the statistical properties of the distributions of consumption expenditures for a large sample of Italian households in the period 1989-2004. Goodness-of-fit tests show that household aggregate (and age-conditioned) consumption distributions are not log-normal. Rather, their logs can be invariably characterized by asymmetric exponential-power densities. Departures from log-normality are mainly due to the presence of thick lower tails coexisting with upper tails thinner than Gaussian ones. The emergence of this irreducible heterogeneity in statistical patterns casts some doubts on the attempts to explain log-normality of household consumption patterns by means of simple models based on Gibrat's Law applied to permanent income and marginal utility.Consumption, Asymmetric Exponential-Power Distribution, Income Distribution, Log-Normal Distribution, Gibrat's Law