Journal of Iranian Statistical Society
Volume:23 Issue: 1, Spring 2024

An important challenge in using progressive Type-II right censoring is to determine a removal scheme. It can be predetermined or randomly chosen per discrete distributions. This paper considers the random removal problem and proposes two scenarios for determining the removal vector without introducing any parameter to a model when progressively Type-II censored samples are available from the three-parameter Weibull distribution. The proposed scenarios are based on the normalized spacings with random and fixed coefficients according to progressively Type-II censored order statistics from an exponential distribution. The joint probability mass functions of removal vectors are provided as well as expected experimental time under the proposed two methods. Moreover, the maximum likelihood estimators (MLEs) and corrected maximum likelihood estimators (corrected MLEs) of parameters are obtained. The new approaches are compared with the patterns of removal derived from the discrete uniform and binomial distributions using a Monte Carlo simulation study. This comparison is based on their estimated biases, estimated mean squared errors and expected total time on the experiment. Finally, a real data example is given to show the practical applications of the paper.

Missing observations are practical problems that occur frequently even in a well-planned experiment and can significantly impact the statistical accuracy of the experiment. This work introduces a new class of third-order designs called augmented orthogonal uniform composite minimax loss (AOUCM) designs, which are more robust to a single missing design point as a variation of the existing third-order augmented orthogonal uniform composite designs (AOUCDs). The AOUCM designs are constructed using the minimax loss criterion. The constructed AOUCM designs are evaluated and compared with AOUCDs based on the relative D- and G-efficiency criteria, generalized scaled deviation, and the fraction of design space plot. The AOUCM designs are shown to be robust and more efficient in estimating the parameters of the third-order model. Moreover, although the AOUCDs and AOUCM designs are stable and uniformly distributed throughout the design space, the AOUCM designs have the least scaled prediction variance.

Saddlepoint techniques have proven effective across various applications due to their markable accuracy in approximating densities. In this work, through considering the integer-valued bilinear model, the saddlepoint maximum likelihood method is applied to parameter estimation. Simulation studies show that this method provides an efficient approach to parameter estimation. The analysis of practical cases highlight the usefulness and adequacy of the proposed model in applications.

This paper, using the signature technique and a generalized Farlie-Gumbel-Morgenstern (FGM) copula function, presents a generic mean residual lifetime (MRL) model for the reliability analysis of a load-sharing coherent system. The present approach differs from earlier models in that in addition to load-sharing phenomenon it simultaneously considers the effect of operating conditions on the system. Further, using the developed model and the renewal-reward argument, an age replacement policy is investigated. The proposed MRL model and the behavior of the optimal solution as the model parameters change are illustrated through numerical examples.

It is interesting to learn that the complementary dual of the Shannon entropy measure exists and has some common properties. This new measure of uncertainty has been introduced by Lad et al. (2015) and is known as extropy. Although there are some mathematical analogies between the two measures, extropy typically has different uses and interpretations than entropy. Taking into account the importance of extropy measure, and its various generalizations, in the present communication, we consider and study Kullback-Leibler based "divergence-extropy" measure between the distribution of nth upper k-record and mth upper k-record values. Characterization problems for the proposed "divergence-extropy" measure have been studied. Further, some specific lifetime distributions used in lifetime testing, physical sciences, survival analysis and reliability engineering have been studied using the proposed "divergence-extropy" measure. At the end, we study the proposed "divergence-extropy" measure between the distribution of k-record value and order statistics.

This paper examines a novel extension of the geometric distribution characterized by two parameters, that is not created based on discretizing existing continuous models. This model, due to its analytical form of the cumulative distribution function and simple structure, can be of interest from mathematical perspectives, particularly in cases where the analysis of stochastic orders is desired. In addition, it is a suitable candidate for analyzing monotone hazard rate discrete data, in view of the fact that its hazard rate function exhibits monotonicity in both increasing and decreasing directions. Additionally, the behavior of the survival function of residual lifetime is briefly addressed. The parameters of the distribution are estimated using the maximum likelihood method, and a real-world data set is scrutinized to assess the distribution's adequacy in providing satisfactory fits.

This article introduces a dual problem of widely used calibration ratio-type estimators for estimating population mean of the study variable considering auxiliary information under dual constraints using stratified systematic sampling design. Under large sample approximations, the expression for bias and variance of the proposed estimator are derived. In addition, the optimality condition for the proposed estimator and hence optimum variance expression is also obtained for the same. Moreover, a study based on real-life data is carried out to judge the performance of the proposed calibration estimator in terms of minimum relative bias and relative root mean squared error criterion. The study reveals that the calibration ratio-type estimator under dual constraints may be preferred in practice as it provides consistent and more precise parameter estimates.