A Test for Constant Hazard Against a Change-Point Alternative

In this article, we consider the change-point hazard rate model which arises quite commonly in mechanical or biological systems, which experience a high hazard rate early in their lifetime due to infant mortality and then a constant or steady hazard rate after the threshold time. We first derive the corresponding mean residual life function (MRLF) and observe that the MRLF is initially increasing and then constant. Here, we derive a test statistic for exponentiality against Increasing Initially then Constant Mean Residual Life (ICMRL). We also derive the asymptotic distribution of the test statistic and compare the power of the test with other existing tests such as likelihood ratio, Weibull, and Log gamma tests considered in the literature. The test performs quite well as compared to other alternatives studied.     

On the Nonparametric Mean Residual Life Estimator in Length-biased Sampling

In this article, we discuss nonparametric estimation of a mean residual life function from length-biased data. Precisely, we prove strong uniform consistency and weak converge of the nonparametric mean residual life estimator in length-biased setting.     

Bootstrap test of hypothesis for the multi-state models in survival analysis

Abstract

In the present paper we develop bootstrap tests of hypothesis, based on simulation, for the transition probability matrix arising in the context of a multi-state model. The bootstrap test statistic is based on the paper of Tattar and Vaman (2008 Tattar, P. N., Vaman, H. J. (2008). Testing transition probability matrix of a multi-state model with censored data. Lifetime Data Anal. 14(2):216–230.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which develops a statistic for the testing problems concerning the transition probability matrix of the non homogeneous Markov process.     

Some multivariate singular unified skew-normal distributions and their application

Abstract

We introduce here the truncated version of the unified skew-normal (SUN) distributions. By considering a special truncations for both univariate and multivariate cases, we derive the joint distribution of consecutive order statistics X_{(r, ..., r + k)} = (X_(r), ..., X_{(r + K)})^T from an exchangeable n-dimensional normal random vector X. Further we show that the conditional distributions of X_{(r + j, ..., r + k)} given X_{(r, ..., r + j ? 1)}, X_{(r, ..., r + k)} given (X_(r) > t)?and X_{(r, ..., r + k)} given (X_{(r + k)} < t) are special types of singular SUN distributions. We use these results to determine some measures in the reliability theory such as the mean past life (MPL) function and mean residual life (MRL) function.     

Classical estimation of hazard rate and mean residual life functions of Pareto distribution

Abstract

In this paper we find the maximum likelihood estimates (MLEs) of hazard rate and mean residual life functions (MRLF) of Pareto distribution, their asymptotic non degenerate distribution, exact distribution and moments. We also discuss the uniformly minimum variance unbiased estimate (UMVUE) of hazard rate function and MRLF. Finally, two numerical examples with simulated data and real data set, are presented to illustrate the proposed estimates.     

Exponentiated power Lindley power series class of distributions: Theory and applications

ABSTRACT

We introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley power series (EPLPS) distribution. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the minimum lifetime value among all risks. The distribution exhibits a variety of bathtub-shaped hazard rate functions. It contains as particular cases several lifetime distributions. Various properties of the distribution are investigated including closed-form expressions for the density function, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Rényi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Finally, two data applications are given showing flexibility and potentiality of the EPLPS distribution.     

Performance of standard imputation methods for missing quality of life data as covariate in survival analysis based on simulations from the International Breast Cancer Study Group Trials VI and VII*

Abstract

Imputation methods for missing data on a time-dependent variable within time-dependent Cox models are investigated in a simulation study. Quality of life (QoL) assessments were removed from the complete simulated datasets, which have a positive relationship between QoL and disease-free survival (DFS) and delayed chemotherapy and DFS, by missing at random and missing not at random (MNAR) mechanisms. Standard imputation methods were applied before analysis. Method performance was influenced by missing data mechanism, with one exception for simple imputation. The greatest bias occurred under MNAR and large effect sizes. It is important to carefully investigate the missing data mechanism.     

Optimum M-step,step-stress design with K stress variables

Most of the available literature on accelerated life testing deals with tests that use only one accelerating variable and no other explanatory variables. Frequently, however, there is a need to use more than one accelerating or other experimental variables. Examples include a test of capacitors at higher than usual levels of temperature and voltage, and a test of circuit boards at higher than usual levels of temperature, humidity, and voltage. M-step, step-stress models are extended to include k stress variables. Optimum M-step, step-stress designs with k stress variables are found. The polynomial model is considered as a special case, and a lack of fit test is discussed. Also a goodness-of-fit test is proposed and the appropriateness of using its asymptotic chi-square distribution for small samples is shown.     

Time Series Modeling of Degradation Due to Outdoor Weathering

Environmental variables have an important effect on the reliability of many products such as coatings and polymeric composites. Long-term prediction of the performance or service life of such products must take into account the probabilistic/stochastic nature of the outdoor weather. In this article, we propose a time series modeling procedure to model the time series data of daily accumulated degradation. Daily accumulated degradation is the total amount of degradation accrued within one day and can be obtained by using a degradation rate model for the product and the weather data. The fitted model of the time series can then be used to estimate the future distribution of cumulative degradation over a period of time, and to compute reliability measures such as the probability of failure. The modeling technique and estimation method are illustrated using the degradation of a solar reflector material. We also provide a method to construct approximate confidence intervals for the probability of failure.     

A generalized scheffé method of multiple comparisons

Standard resulrs on the extrema of quotients of quadratic forms are extended to the non-negative definite case. The maximum and the set over which it is achieved are characterized explicitly both in terms of generalized inverse matrices and generalized eigenvalues. These results become the basis of Scheffe type multiple comparisons in the usual way. To demonstrate their application to statistics with singular covariance matrices, the method is detailed for Mantel-Haenszel, Breslow, and Cox statistics. An example is presented illustrating a situation where the proposed Scheffe type comparisons may be better than the pairwise method.