Testing Goodness of Fit of Parametric AFT and PH Models with Residuals

In this article, we consider the problems of testing the goodness of fit of the parametric accelerated failure time model and the Cox proportional hazards model. We consider omnibus test statistics based on residuals. The statistical distributions of Kolmogorov, Cramer-von Mises–Smirnov, and Anderson–Darling statistics are all investigated by means of Monte Carlo simulations. Type-I, Type-II, and independent random censoring situations are all considered in this study. A Monte Carlo power study has also been carried out for these tests to distinguish between various baseline models, which reveals that the Anderson–Darling test performs better than the others.     

Selection procedures based on normal and nonnormal variables with single and multiple characters

The performance of selection procedures using a single screening variable are assessed in the presence of nonnormality, in particular mixtures of bivariate normal distributions and the bivariate Edgeworth series distribution.

Screening with multiple characters in the normal situation is studied using principal components.     

Stochastic comparisons and properties of conditional generalized order statistics

Generalized order statistics introduced by Kamps [1995. A concept of generalized order statistics. J. Statist. Plann. Inference 48, 1–23] provides a unified approach to a variety of models concerning ordered random variables. This paper carries out stochastic comparisons of conditional generalized order statistics in terms of the likelihood ratio order and the hazard rate order from two samples, and establishes some stochastic monotonicity properties. The main results strengthen and generalize the corresponding results established recently in the literature. Finally, some applications of the main results are given as well.     

Expectation–maximization algorithm for system-based lifetime data with unknown system structure

AStA Advances in Statistical Analysis - In science and engineering, we are often interested in learning about the lifetime characteristics of the system as well as those of the components that made...     

Moments of order statistics from a non-overlapping mixture model with applications to truncated laplace distribution

We employ two different approaches to derive single and product moments of order statistics from a truncated Laplace distribution. A direct evaluation method establishes recurrence relations whereas the more general non-overlapping mixture model incorporates the truncated Laplace distribution as a special case. The results are thereafter applied to estimate location and scale parameters of such distributions.     

Two sided acceptance sampling plans based on mml estimators

Alternative estimators that are robust to non-normality in the symmetric thick tailed situation are shown to yield much better results tl)an do [Xbar] and s. The particular estimators suggested in this paper are the Modified Maximum Likelihood estimators of Tiku (1967).     

Inference for the Birnbaum–Saunders Lifetime Regression Model with Applications

The Birnbaum–Saunders distribution is a positively skewed distribution that is frequently used for analyzing lifetime data. Regression analysis is widely used in this context when some covariates are involved in the life-test. In this article, we discuss the maximum likelihood estimation of the model parameters and associated inference. We discuss the likelihood-ratio tests for some hypotheses of interest as well as some interval estimation methods. A Monte Carlo simulation study is then carried out to examine the performance of the proposed estimators and the interval estimation methods. Finally, some numerical data analyses are done for illustrating all the inferential methods developed here.     

Estimation for one- and two-parameter exponential distributions under multiple type-II censoring

In this paper, we derive explicit best linear unbiased estimators for one- and two-parameter exponential distributions when the available sample is multiply Type-II censored. Further, after noting that the maximum likelihood estimators do not exist explicitly, we propose some linear estimators by approximating the likelihood equations appropriately. Some illustrative examples from life-testing experiments are also presented.     

Recurrence relations for single and product moments of record values from generalized pareto distribution

In this paper we establish some recurrence relations satisfied by single and product moments of upper record values from the generalized Pareto distribution. It is shown that these relations may be used to obtain all the single and product moments of all record values in a simple recursive manner. We also show that similar results established recently by Balakrishnan and Ahsanullah (1993) for the upper record values from the exponential distribution may be deduced by letting the shape parameter p tend to 0.     

Statistical evidence in contingency tables analysis

The likelihood ratio is used for measuring the strength of statistical evidence. The probability of observing strong misleading evidence along with that of observing weak evidence evaluate the performance of this measure. When the corresponding likelihood function is expressed in terms of a parametric statistical model that fails, the likelihood ratio retains its evidential value if the likelihood function is robust [Royall, R., Tsou, T.S., 2003. Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions. J. Roy. Statist. Soc. Ser. B 65, 391–404]. In this paper, we extend the theory of Royall and Tsou [2003. Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions. J. Roy. Statist. Soc., Ser. B 65, 391–404] to the case when the assumed working model is a characteristic model for two-way contingency tables (the model of independence, association and correlation models). We observe that association and correlation models are not equivalent in terms of statistical evidence. The association models are bounded by the maximum of the bump function while the correlation models are not.