Quantile based stop-loss transform and its applications

Partial moments are extensively used in actuarial science for the analysis of risks. Since the first order partial moments provide the expected loss in a stop-loss treaty with infinite cover as a function of priority, it is referred as the stop-loss transform. In the present work, we discuss distributional and geometric properties of the first and second order partial moments defined in terms of quantile function. Relationships of the scaled stop-loss transform curve with the Lorenz, Gini, Bonferroni and Leinkuhler curves are developed.     

The Govindarajulu Distribution: Some Properties and Applications

In this article, we present various distributional properties and application to reliability analysis of the Govindarajulu distribution. A quantile-based analysis is performed as the distribution function is not analytically tractable. The properties of the distribution like percentiles, L-moments, L-skewness, and kurtosis and order statistics are presented. Various reliability characteristics are derived along with some characterization theorems by relationship between reliability measures. We also make a comparative study with other competing models with reference to real data.     

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannon's measures of uncertainty proposed by Ebrahimi (1996 Ebrahimi , N. ( 1996 ). How to measure uncertainty in the residual lifetime distribution . Sankhya A 58 : 48 – 56 . [Google Scholar]) and Sankaran and Gupta (1999 Sankaran , P. G. , Gupta , R. P. ( 1999 ). Characterization of lifetime distributions using measure of uncertainty . Calcutta Statist. Assoc. Bull. 49 : 195 – 196 . [Google Scholar]), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them.     

Proportional hazards model with quantile functions

Proportional Hazards Model (PHM) introduced by Cox (1972) is extensively studied in literature. In this paper, we study reliability properties of the PHM using quantile functions. Some special properties of the quantile function, which are not shared by distribution function are explored to study various properties of the PHM. We discuss ageing properties and stochastic orders for the PHM. The quantile-based dynamic cumulative Kullback-Leibler divergence of PHM is studied. Characterizations of some important quantile densities using PHM are also proved.     

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto II and beta distributions. Further, we generalize the identities for the Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in the context of lengthbiased models are also explored.     

On some reliability aspects of Pearson family of distributions

We characterize the Pearson family of distributions by finding a relationship between the failure rate and the higher order moments of residual life. We also present a characterization theorem of IFR(DFR) class of distributions in the Pearson family.     

Multivariate discrete reversed hazard rates

In the present paper, we define and study four versions of multivariate discrete reversed hazard rates, namely scalar reversed hazard rate, vector reversed hazard rate, alternative reversed hazard rate, and conditional reversed hazard rate. Various properties of these functions are studied. Interrelationships between these reversed hazard rates are explored. We also present characterization of discrete distributions using these reversed hazard rates.     

Association Measures for Bivariate Lifetime Data

Reversed hazard rates are found to be very useful in survival and reliability studies especially in cases of parallel systems and left-censored data. We introduce four association measures using reversed hazard rates and mean waiting time. We then study the properties of these measures. Nonparametric estimators of these measures are developed. Finally, the application of these measures is illustrated with two real life data sets.     

Dependence Assessment in Human Reliability Analysis Using Evidence Theory and AHP

Dependence assessment among human errors in human reliability analysis (HRA) is an important issue. Many of the dependence assessment methods in HRA rely heavily on the expert's opinion, thus are subjective and may sometimes cause inconsistency. In this article, we propose a computational model based on the Dempster‐Shafer evidence theory (DSET) and the analytic hierarchy process (AHP) method to handle dependence in HRA. First, dependence influencing factors among human tasks are identified and the weights of the factors are determined by experts using the AHP method. Second, judgment on each factor is given by the analyst referring to anchors and linguistic labels. Third, the judgments are represented as basic belief assignments (BBAs) and are integrated into a fused BBA by weighted average combination in DSET. Finally, the CHEP is calculated based on the fused BBA. The proposed model can deal with ambiguity and the degree of confidence in the judgments, and is able to reduce the subjectivity and improve the consistency in the evaluation process.