Detection of outliers in the exponential distribution based on prediction

In this paper, we present a test procedure to detect outliers in the one-parameter exponential distribution based on prediction. The distribution of the test statistic is obtained. The proposed test can be used to detect more than one outlier and the required percentage points can be easily determined. Furthermore, the test provides a simple procedure to detect whether a given set of data is free from outliers or spurious observations.     

Stochastic modelling of the hybrid survival curve

In this paper, building upon the idea of cross-sectional survival probabilities developed by Brouard (Espaces Popul Soc 2(14–15):157–168, 1986), we propose using stochastic models to study the evolution of a new type of survival curves called hybrid survival curve. We find that the three-factor survival model provides a better model fitting than the two-factor survival model. Furthermore, the three time-varying parameters are highly interpretable and their respective trends can be used as an indicator for the rectangularisation of survival curve. On top of that, we demonstrate how the time-varying parameters can be extrapolated into the future to obtain projected hybrid survival curves.     

Outlier detection in linear models: a comparative study in simple linear regression

Five widely used test statistics for detecting outliers and influential observations were studied using Monte Carlo method . The test statistic based on Studentized residuals, with critical values given by Tietjen, Moore and Beckman (1973), appears to be the best procedure for detecting a single outlier in simple linear regression.     

Atypical observations in linear models

The problem of ‘atypical data point’ in the estimation of model parameters and its effect on prediction are discussed. A cross-validity procedure is then proposed to accommodate the unusual observations in the estimation and thereby to improve the prediction of future data points. Each atypical point, weighted according to cross-validitory procedure, is used in the estimation of model parameters.     

Reliability sampling plans for the two-parameter exponential distribution under progressive censoring

This paper presents reliability sampling plans for the two-parameter exponential distribution under progressive censoring. These sampling plans are quite useful to practitioners, because they provide savings in resources and in total test time. Furthermore, they off er the flexibility to remove functioning test specimens from further testing at various stages of the experimentation. In the construction of these sampling plans, the operating characteristic curve is derived using the exact distributional properties of maximum likelihood estimators. An example is given to illustrate the application of the proposed sampling plans.     

Selecting between gamma and Weibull distributions—an approach based on predictions of order statistics

A method based on the prediction of order statistics is proposed to select the underlying parent distribution. A cross-validatory predictor and the best linear unbiased predictor are considered in choosing between gamma and Weibull models when shape parameters are only known to lie within a range. The proposed approach is evaluated using a large-scale Monte Carlo study. The results clearly show that the cross-validatory predictor performs well as a robust procedure in selecting between probability densities. Two well-known data sets are used to illustrate the procedure.