Communication in Statistics- Theory and Methods · 2008 · 164 citations · 14 references
Natural SciencesRisk ManagementStatisticsStochastic ModelingUncertainty QuantificationHazard FunctionsNonparametric StatisticsProbability DistributionsReliabilityReliability ModelingCumulative Distribution FunctionsPercentile EstimationQuantile DependenceQuantile RegressionReliability Function
Quantile functions are equivalent alternatives to distribution functions in modeling and analysis of statistical data. The present article discusses the role of quantile functions in reliability studies. We present the hazard, mean residual, variance residual, and percentile residual quantile functions, their mutual relationships and expressions for the quantile functions in terms of these functions. Further, some theoretical results relating to the Hankin and Lee (2006 Hankin , R. K. S. , Lee , A. ( 2006 ). A new family of non-negative distributions . Austral. N.Z. J. Statist. 48 : 67 – 78 .[Crossref], [Web of Science ®] , [Google Scholar]) lambda distribution are discussed.
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