Statistical analysis of middle censored competing risks data with exponential distribution

In this paper, we consider some problems of estimation and reconstruction based on middle censored competing risks data. It is assumed that the lifetime distributions of the latent failure times are independent and exponential distributed with different parameters and also that the censoring mechanism is independent. The maximum likelihood estimators (MLEs) of the unknown parameters are obtained. We then use the asymptotic distribution of the MLEs to construct approximate confidence intervals. Based on gamma priors, Lindley's approximation method is applied to obtain the Bayesian estimates of the unknown parameters under squared error loss function. Since it is not possible to construct the credible intervals, we propose and implement the Gibbs sampling technique to construct the credible intervals. Several point reconstructors for failure time of censored units are provided. Finally, a simulation study is given by Monte-Carlo simulations to evaluate the performances of the different methods and a data set is analysed to illustrate the proposed procedures.     

Bivariate transition model for analysing ordinal and nominal categorical responses: an application to the Labour Force Survey data

In many panel studies, bivariate ordinal–nominal responses are measured and the aim is to investigate the effects of explanatory variables on these responses. A regression analysis for these types of data must allow for the correlation among responses of the same individual. To analyse such ordinal–nominal responses using a proper weighting approach, an ordinal–nominal bivariate transition model is proposed and maximum likelihood is used to find the parameter estimates. We propose a method in which the likelihood function can be partitioned to make possible the use of existing software. The approach is applied to the Labour Force Survey data in Iran, where the ordinal response, at the first period, is the duration of unemployment for unemployed people and the nominal response, in the second period, is economic activity status of these individuals. The interest is to find the reasons for staying unemployed or moving to another status of economic activity.     

A Note on the Regression of Order Statistics

This paper examines the relationships between the mean residual life functions of parallel and k-out-of-n systems with the regression of order statistics. Using these relationships, the results and properties about the mean residual life function of those systems can be used for the regression of order statistics and vice versa. Finally, the paper proposes a definition for the mean residual life function of a k-out-of-n system when the number of failed components of the system is known.     

On Properties of Reversed Mean Residual Life Order for Weighted Distributions

In this article, first, in order to compare X and X ^w (the weighted version of X with weight function w(·)) according to reversed mean residual life order, we provide an equivalent condition. We then try to provide conditions under which the reversed mean residual life order is preserved by weighted distributions. For this end, we obtain several independent results. Finally, the problem of preservation of increasing reversed mean residual life class under weighting is investigated, as well. Some examples are also given to illustrate the results.