A new bivariate distribution is proposed in this paper using the univariate modified Weibull extension distribution. The proposed distribution is referred to as the bivariate Modified Weibull Extension (BMWE) distribution. The BMWE distribution is of Marshall-Olkin type. We discuss some of the statistical properties of the BMWE  distribution.  Applications of this distribution to dependent competing risks data are discussed.  The maximum likelihood estimators (MLE) of the model parameters using both bivariate data and dependent competing risks data are discussed. These MLE's cannot be obtained in closed form. Therefore, numerical optimization methods are  applied. A simulation study is carried out to investigate the performance of the estimation technique. Two real data sets;  one bivariate data set and another dependent competing risks data set, are analyzed using the proposed distribution for illustrative and comparison purposes.

This paper studies the statistical inferences of the unknown parameters of some reliability models using progressively hybrid censoring of type-I and type-II. We apply the maximum likelihood and Bayesian approaches to perform the statistical inferences of the parameters when the data follow Weibull, power Lindley, and Sarhan-Tadj-Hamilton distributions. Bayes method is implemented under the squared error loss function when the parameters are independent and follow gamma prior distributions with known hyperparameters. The maximum likelihood estimates cannot be obtained in an analytic form. Therefore we use the R function "optim"to find those estimates. Also, the joint posterior distribution of the unknown parameters cannot be obtained in closed form. Therefore, we will use the Markov Chain Monte Carlo method to approximate the Bayesian analysis. We constructed the highest posterior density intervals of the model parameters. We analyzed three real data sets for illustration and comparison purposes. We found out that Sarhan-Tadj-Hamilton distribution fits those three real data sets better than Weibull and Power Lindley distribution using both complete and progressively hybrid censored samples. We used expected experimentation time to discuss the optimal test plans. Simulation studies are performed to investigate the proposed methods. Based on the simulation results, we could conclude that Bayesian method does not provide better estimations than the maximum likelihood method.

Atlantic halibut (Hippoglossus hippoglossus) support an economically important fishery on the eastern coast of Canada. Like other species that are not well sampled by trawl surveys, halibut in this area are monitored using longline surveys. These surveys present challenges that can make obtaining indices of abundance difficult. Issues include gear saturation, which can result in a non-linear relationship between catch per unit effort and local abundance. The current approach to obtain a relative index consists of fitting a multinomial exponential model to a subset of hooks from each survey station. While this approach accounts for hook competition, it does not account for the presence of spatial patterns. We therefore extend the multinomial exponential model to include spatial random fields for both Atlantic halibut and non-target species, set-specific soak time, and data from the hooks. Furthermore, we propose a method for aggregating the resulting spatially varying indices to obtain an annual index for the entirety of the modelled area. This novel approach identifies Atlantic halibut hotspots in multiple years, while simultaneously providing relative abundance indices for 2017 through 2020. These outcomes demonstrate the widespread applicability of our methods for improving the scientific advice upon which fisheries management decisions are based.

This paper deals with the estimation of reliability R = P[Y < X] when X and Y are two independent random variables with atwo-parameter bathtub shaped failure rate distribution with the samesecond shape parameter. Likelihood and Bayesian methods are proposedto make inferences about R. We obtain the likelihood interval andasymptotic confidence interval for R, and we consider Bayesianpoint estimates of R under both absolute and squared error loss,using either gamma or uniform priors for the three unknown modelparameters. An equal tail Bayesian credible interval for R isinvestigated. Analysis of a real data set is presented forillustrative purposes, and Monte Carlo simulations are performed tocompare: (1) the performance of Bayes estimates under two differentloss functions; and (2) the maximum likelihood and Bayesian methods.

A two-parameter distribution was revisited by Chen (2000) [7]. This distribution can have a bathtub-shaped or increasing failure rate function which enables it to fit real lifetime data sets. Maximum likelihood and Bayes estimates of the two unknown parameters are discussed in this paper. It is assumed in the Bayes case that the unknown parameters have gamma priors. Explicit forms of Bayes estimators cannot be obtained. Different approximations are used to establish point estimates and two sided Bayesian probability intervals for the parameters. Monte Carlo simulations are applied to the comparison between the maximum likelihood estimates and the approximate Bayes estimates obtained under non-informative prior assumptions. Analysis of a real data set is also been presented for illustrative purposes.

Global warming is predicted to result in a rise in sea level which will lead to increased flood risk. Two other factors that will affect high water are the existing trends in mean sea level and changing tides. We illustrate here that in the Bay of Fundy and Gulf of Maine these two are related. An analysis of long-term sea level records shows that, independent of global warming related to climate change, sea level and tidal range have been increasing in this system. Our numerical model investigation indicates that recent changes in sea level, attributed in part to post-glacial rebound, are giving rise to increasing tides. The combined effects of modern sea level rise, global warming induced sea level rise, and the expanded tidal range they induce, will produce a significant increase in the high water level, much greater than that found when considering modern climate-induced sea level changes in isolation. We are predicting a dramatic increase in the risk of flooding at higher high water during the twenty-first century.

The two-parameter linear failure rate distribution has been used quite successfully to analyze lifetime data. Recently, a new three-parameter distribution, known as the generalized linear failure rate distribution, has been introduced by exponentiating the linear failure rate distribution. The generalized linear failure rate distribution is a very flexible lifetime distribution, and the probability density function of the generalized linear failure rate distribution can take different shapes. Its hazard function also can be increasing, decreasing and bathtub shaped. The main aim of this paper is to introduce a bivariate generalized linear failure rate distribution, whose marginals are generalized linear failure rate distributions. It is obtained using the same approach as was adopted to obtain the Marshall–Olkin bivariate exponential distribution. Different properties of this new distribution are established. The bivariate generalized linear failure rate distribution has five parameters and the maximum likelihood estimators are obtained using the EM algorithm. A data set is analyzed for illustrative purposes. Finally, some generalizations to the multivariate case are proposed.

In this paper, we apply a transition model to the data-set on stomach cancer mortality in Japan for the period 1955-2000. The data had been collected as a table of age- and period-specific mortality data at the Japanese Ministry of Health and Welfare.(http://wwwdbtk.mhlw.go.jp/toukei/index.html)An age-period-cohort model is often used to analyze cancer mortality data. However, that model is non-identifiable due to over parameterization. Applying a transition model to these data overcomes that problem. We propose a prediction method based on a transition model.

Statistical inference for the parameters in three competing risks models is considered in this paper. It is assumed that there are more than two causes of failure. The maximum likelihood procedure is used to derive point and asymptotic confidence interval estimates of the unknown parameters. The risks due to each cause of failure are investigated. Two sets of data are analyzed in order to (1) illustrate how the model can be applied and (2) test the hypothesis that the causes of failure follow the Chen distribution rather than the exponential distribution, or the Weibull distribution.

This paper investigates the asymptotic properties of the likelihood ratio statistic for testing homogeneity in a bivariate normal mixture model with known covariance. The asymptotic null distributions of the likelihood ratio statistic and a modified likelihood ratio statistic are obtained in explicit form. The distributions are identical. The results of a small simulation study to approximate the null distribution are presented.

This article reports on the analysis of sea level records from the Bay of Fundy/Gulf of Maine. Descriptive statistical methods are used to illustrate the increase in mean sea level, seasonal variance and nodal variation. Frequency domain time series methods are used to model increasing tidal amplitude, and to characterize features of sea level spectra. Copyright (C) 2004 John Wiley Sons, Ltd.

This paper investigates the asymptotic properties of the likelihood ratio statistic for testing homogeneity in normal mixture models in the presence of a structural parameter. The asymptotic null distributions of the ordinary likelihood ratio statistic and the modified likelihood ratio statistic are the same, having the probability density function(pdf) (1/2)g(1)(x)+(1/2)g(2)(x) where g(1)(x) and g(2)(x) are the probability density functions of X-2(1) and X-2(2) respectively. For the ordinary likelihood ratio statistic, we employ the assumption that min {alpha(1,) alpha(2}) greater than or equal to epsilon for some 1/2 > epsilon > 0, where alpha(1) and alpha(2) axe the coefficients of the mixtures.

Generalized M (or GM) estimation has been extended to the case of a nonlinear regression model with autoregressive and heteroscedastic errors. The robustness properties of the GM estimators have been investigated based on the time-series analog of Hampel's influence function. The asymptotic properties of these estimators have been studied in some detail.

The four papers presented as part of this Case Study all address the issue of finding association between the genetic information given by markers and the occurrence of Inflammatory Bowel Disease. The basic data consist of the genotypes at a number of markers along chromosome 6 where the markers are usually chosen from regions of the DNA that do not code for protein and are highly variable (polymorphic) in the sense that the alleles at a locus vary among the population. The idea is to try to find whether the alleles at any of the markers are associated with the presence of the disease. If there is evidence of association, this suggests that a disease gene may be found in the neighbourhood of the marker, i.e., be linked to the marker. It should be noted that it is quite possible that more than one gene may be involved in the disease, and that the presence of the disease could be determined by interactions among various genes. The data available for this study can be broken down into two data sets. There are two areas suspected of harbouring the disease gene which are covered by the markers DRBl and DBQ1. In the first data set, we have the four alleles from the two markers for the Toronto population and from two control groups of Jewish individuals and one control group of Caucasian individuals. In the Toronto cases, data are available on the affected children, on their parents and on some nonaffected sibs. For the second data set, we have data from an additional 25 markers on a subset of the Toronto cases. In the four papers, there are basically three distinct approaches used to analyze the data. The first and most basic

With time series data, there is often the issue of finding accurate approximations for the variance of such quantities as the sample autocovariance function or spectral estimate. Smith and Field (J. Time. Ser. Anal 14: 381–395, 1993) proposed a variance estimate motivated by resampling in the frequency domain. In this paper we present some results on the cumulants of this and other frequency domain estimates obtained via symbolic computation. The statistics of interest are linear combinations of products of discrete Fourier transforms. We describe an operator which calculates the joint cumulants of such statistics, and use the operator to deepen our understanding of the behaviour of the resampling based variance estimate. The operator acts as a filter for a general purpose operator described in Andrews and Stafford (J.R. Statist. Soc. B55, 613–627).