Log-concave and concave distributions in reliability

Sengupta, Debasis; Nanda, Asok K.

doi:10.1002/(sici)1520-6750(199906)46:4<419::aid-nav5>3.0.co;2-b

Cited by 80 publications

(44 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, if f is log-concave, then it can have at most one jump discontinuity, and the jump can only occur at the left end-point of its support (Sengupta and Nanda 1997).…”

mentioning

confidence: 99%

The Data-Driven Newsvendor Problem: New Bounds and Insights

Levi

Perakis

Uichanco

2015

Operations Research

201

117

View full text Add to dashboard Cite

Consider the newsvendor model, but under the assumption that the underlying demand distribution is not known as part of the input. Instead, the only information available is a random, independent sample drawn from the demand distribution. This paper analyzes the sample average approximation (SAA) approach for the data-driven newsvendor problem. We obtain a new analytical bound on the probability that the relative regret of the SAA solution exceeds a threshold. This bound is significantly tighter than existing bounds, and it matches the empirical accuracy of the SAA solution observed in extensive computational experiments.This bound reveals that the demand distribution's weighted mean spread (WMS) affects the accuracy of the SAA heuristic.

show abstract

“…In fact, if f is log-concave, then it can have at most one jump discontinuity, and the jump can only occur at the left end-point of its support (Sengupta and Nanda 1997).…”

mentioning

confidence: 99%

The Data-Driven Newsvendor Problem: New Bounds and Insights

Levi

Perakis

Uichanco

2015

Operations Research

201

117

View full text Add to dashboard Cite

show abstract

“…showed that mixtures can alter the hazard from that of the component distributions. Sengupta and Nanda (1999) as well as Li, Da, and Zhao (2010) have examined the reverse hazard of mixtures.…”

Section: Reverse Hazard For Continuous Mixturesmentioning

confidence: 99%

Properties of reverse hazard functions

Chechile

2011

Journal of Mathematical Psychology

View full text Add to dashboard Cite

“…For an interpretation of the reversed hazard rate and further properties we refer the reader to [44] and the references cited there. Taking this aging notion into consideration, results of Burkschat et al [45] suggest a connection to the theory of dual generalized order statistics.…”

Section: Lemma 33 Let Xmentioning

confidence: 99%

Multivariate dependence of spacings of generalized order statistics

Burkschat

2009

Journal of Multivariate Analysis

View full text Add to dashboard Cite

Multivariate total positivity Strongly multivariate reverse regular rule Conditionally increasing in sequence Negative and positive orthant dependence Right tail increasing in sequence Increasing failure rate Reversed hazard rate Non-negativity of BLUE Dual generalized order statistics a b s t r a c t Multivariate dependence of spacings of generalized order statistics is studied. It is shown that spacings of generalized order statistics from DFR (IFR) distributions have the CIS (CDS) property. By restricting the choice of the model parameters and strengthening the assumptions on the underlying distribution, stronger dependence relations are established.For instance, if the model parameters are decreasingly ordered and the underlying distribution has a log-convex decreasing (log-concave) hazard rate, then the spacings satisfy the MTP 2 (S-MRR 2 ) property. Some consequences of the results are given. In particular, conditions for non-negativity of the best linear unbiased estimator of the scale parameter in a location-scale family are obtained. By applying a result for dual generalized order statistics, we show that in the particular situation of usual order statistics the assumptions can be weakened.

show abstract

Log-concave and concave distributions in reliability

Cited by 80 publications

References 8 publications

The Data-Driven Newsvendor Problem: New Bounds and Insights

The Data-Driven Newsvendor Problem: New Bounds and Insights

Properties of reverse hazard functions

Multivariate dependence of spacings of generalized order statistics

Contact Info

Product

Resources

About