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Quantile-Based Reliability Analysis
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TLDR
The hazard, mean residual, variance residual, and percentile residual quantiles functions, their mutual relationships and expressions for the quantile functions in terms of these functions, and some theoretical results relating to the Hankin and Lee (2006) lambda distribution are discussed.Abstract:
This book provides a fresh approach to reliability theory, an area that has gained increasing relevance in fields from statistics and engineering to demography and insurance. Its innovative use of quantile functions gives an analysis of lifetime data that is generally simpler, more robust, and more accurate than the traditional methods, and opens the door for further research in a wide variety of fields involving statistical analysis. In addition, the book can be used to good effect in the classroom as a text for advanced undergraduate and graduate courses in Reliability and Statistics.read more
Citations
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Journal ArticleDOI
Stochastic Ageing and Dependence for Reliability
TL;DR: This book aims to introduce simulation techniques for practitioners in the financial and risk management industry at an intermediate level by having extensive simulation examples using S–PLUS or Visual Basics.
Journal ArticleDOI
Quantile uncertainty and value-at-risk model risk
TL;DR: This article develops a methodology for quantifying model risk in quantile risk estimates, and provides a novel and elegant framework whereby quantile estimates are adjusted for model risk, relative to a benchmark which represents the state of knowledge of the authority that is responsible formodel risk.
Journal ArticleDOI
Quantile based entropy function
TL;DR: A quantile based Shannon entropy function is introduced and it is shown that the residual quantile entropy function determines the quantile density function uniquely through a simple relationship.
Journal ArticleDOI
Kullback–Leibler divergence: A quantile approach
TL;DR: A quantile based definition of the Kullback–Leibler divergence is introduced and the quantile versions of Kull back–Leiberler divergence for residual and past lifetime random variables are proposed.
Journal ArticleDOI
Total time on test transforms of order n and their implications in reliability analysis
TL;DR: In this paper, the properties of total time on test transforms of order n and examine their applications in reliability analysis are studied. And the ageing properties of the baseline distribution is compared with those of transformed distributions, and a partial order based on ftth-order transforms and their implications are discussed.
References
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Book
Analysis of Survival Data
David Cox,D. Oakes +1 more
TL;DR: In this article, the authors give a concise account of the analysis of survival data, focusing on new theory on the relationship between survival factors and identified explanatory variables and conclude with bibliographic notes and further results that can be used for student exercises.
Journal ArticleDOI
Nonparametric Statistical Data Modeling
TL;DR: An approach to statistical data analysis which is simultaneously parametric and nonparametric is described, and density-quantile functions, autoregressive density estimation, estimation of location and scale parameters by regression analysis of the sample quantile function, and quantile-box plots are introduced.
Journal ArticleDOI
Bathtub and Related Failure Rate Characterizations
TL;DR: In this paper, sufficient conditions are obtained that a lifetime density has a bathtub-shaped failure rate and analogous conditions handle increasing, decreasing, and upside-down bathtub shape failure rates.
Book
Statistical Modelling with Quantile Functions
TL;DR: In this article, the authors describe the sample and the population statistical foundations of Quantile Models and their construction and their use in identification estimation validation applications, including regression quantile models and Bivariate Quantile models.
Journal ArticleDOI
Stochastic Ageing and Dependence for Reliability
TL;DR: This book aims to introduce simulation techniques for practitioners in the financial and risk management industry at an intermediate level by having extensive simulation examples using S–PLUS or Visual Basics.