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This paper deals with joint estimation of the mean and dispersion parameters in the analysis of proportions. We consider a parametric model, namely the extended beta-binomial model, and several semiparametric procedures. We study large-sample efficiency and small-sample bias and efficiency properties of the estimates of the mean and intraclass correlation parameters. Estimation and efficiency calculations are presented for the regression model. However, for simplicity, numerical large-sample efficiency and small-sample bias and efficiency calculations are performed for the two-parameter model only. Numerical efficiency results are presented in terms of graphs. Estimated asymptotic efficiencies of various estimates are also compared for two data sets. Our findings suggest that for the estimation of the mean (regression) parameters the quasilikelihood procedure performs best. However, for the joint estimation, the Gaussian likelihood estimates perform best. RESUMECet article traite de I'estimation conjuguCe de la moyenne et des paramitres de dispersion au cours de I'analyse de proportions. Nous considirons un modtle paramttrique, c'est h dire le modtle beta-binomial ttendu, et plusieurs procedures semi-paramitriques. Nous ttudions I'efficacitt des grands Cchantillons et le biais des petits Cchantillons, ainsi que les propnttts d'efficience des valeurs estimtes de la moyenne et des paramitres de corrilation intra-classe. Des calculs d'estimation et d'efficience sont prtsentts pour le modtle de rigression. Toutefois, ? i des fins de simplicitt, les calculs numtriques de I'efficacitt des grands Cchantillons et du biais des petits tchantillons sont effectuts seulement pour le modtle i deux paramitres. Les n5sultats numtriques de I'efficacitisont prisentts sous forme de graphiques. Les efficiences asymptotiques estimtes de difftrentes valeurs estimtes sont Cgalement comparkes pour deux ensembles de donntes. Nos dtcouvertes suggtrent que, pour I'estimation des paramitres de la moyenne (rtgression), la procidure de quasivraisemblance donne les rCsultats les plus satisfaisants. Cependant. pour I'estimation conjugute, ce sont les valeurs estimtes de vraisemblance gaussiennes qui ont la meilleure performance.

The Goel-Okumoto software reliability model, also known as the Exponential Nonhomogeneous Poisson Process, is one of the earliest software reliability models to be proposed. From literature, it is evident that most of the study that has been done on the Goel-Okumoto software reliability model is parameter estimation using the MLE method and model fit. It is widely known that predictive analysis is very useful for modifying, debugging and determining when to terminate software development testing process. However, there is a conspicuous absence of literature on both the classical and Bayesian predictive analyses on the model. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model. Driven by the requirement of highly reliable software used in computers embedded in automotive, mechanical and safety control systems, industrial and quality process control, real-time sensor networks, aircrafts, nuclear reactors among others, we address four issues in single-sample prediction associated closely with software development process. We have adopted Bayesian methods based on non-informative priors to develop explicit solutions to these problems. An example with real data in the form of time between software failures will be used to illustrate the developed methodologies.

This paper implements the method of estimating functions (EF) in the modelling and forecasting of financial returns volatility. This estimation approach incorporates higher order moments which are common in most financial time series, into modelling, leading to a substantial gain of information and overall efficiency benefits. The two models considered in this paper provide a better in-sample-fit under the estimating functions approach relative to the traditional maximum likelyhood estimation (MLE) approach when fitted to empirical time series. On this ground, the EF approach is employed in the first order EGARCH and GJR-GARCH models to forecast the volatility of two market indices from the USA and Japanese stock markets. The loss functions, mean square error (MSE) and mean absolute error (MAE), have been utilized in evaluating the predictive ability of the EGARCH vis-à-vis the GJR-GARCH model.

This paper discusses the Bayesian approach to estimation and prediction of the reliability of software systems during the testing process. A Non-Homogeneous Poisson Process (NHPP) arising from the Musa-Okumoto (1984) software reliability model is proposed for the software failures. The Musa-Okumoto NHPP reliability model consists of two components-the execution time component and the calendar time component, and is a popular model in software reliability analysis. The predictive analyses of software reliability model are of great importance for modifying, debugging and determining when to terminate software development testing process. However, Bayesian and Classical predictive analyses on the Musa-Okumoto (1984) NHPP model is missing on the literature. This paper addresses four software reliability issues in single-sample prediction associated closely with development testing program. Bayesian approach based on non-informative prior was adopted to develop explicit solutions to these problems. Examples based on both real and simulated data are presented to illustrate the developed theoretical prediction results.