Kullback–Leibler life time testing

“…Computation of confidence level of I-divergence contours in the case of known threshold x m is in detail elaborated in [17]. The case of unknown x m needs special attention.…”

Section: Application To Real Data -Paretomentioning

confidence: 99%

Entropy based statistical inference for methane emissions released from wetland

Sabolová

Sečkárová

Dusek

et al. 2015

Chemometrics and Intelligent Laboratory Systems

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“…The small sample properties of both homogeneity tests (against general and two component alternatives) have been studied by Stehlík and Wagner (2011). Tests for homogeneity when the shape parameter of the Weibull is unknown have been developed for complete samples by Mosler and Scheicher (2008); for a comparison of procedures, see Mosler and Haferkamp (2007); and for an alternative approach based on geometric integration, see Stehlík et al (2014). For the classical exponential mixtures and complete samples, the likelihood ratio test converges in distribution to the supremum of a square Gaussian process (see Ciuperca 2002).…”

Section: Homogeneity Testing For Censored Datamentioning

confidence: 99%

Likelihood Testing With Censored and Missing Duration Data

Stehlík

2014

Journal of Statistical Theory and Practice

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Duration data of a component, product, or system are often incomplete. We give guidelines for likelihood ratio testing for small samples with some data imperfections, that is, when some information is missing and some information is censored. We introduce the model of the missing time-to-failure mechanism, which still enables the exact likelihood ratio testing of the scale and homogeneity. Such a model encompasses well both the generalized gamma and Pareto duration time models with missing individual times to failure. The exact distribution of the likelihood ratio test for the censored sample from Weibull distribution with known shape parameter is derived and discussed. We discuss separately Type I, Type II, and progressively censored samples. We show that the Type I censoring and Type II censoring differ substantially. The construction of the pivotal quantity is possible for Type II and progressively Type II censoring; however, it is not available for the case of Type I censoring. Thus, for the latter case the usage of the exact likelihood ratio test is a natural option. We also discuss the case of the generalized gamma distribution. For the case with nuisance shape parameters we use an integrated likelihood approach. Convenient examples illustrate the methods developed in the article.

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“…Since it is related to the likelihood ratio statistics, Stehlík also calculated the exact distribution of the likelihood ratio tests and discussed the optimality of such exact tests. Recently Stehlík et al (2014) applied the exact distribution of the Kullback-Leibler I-divergence in the exponential family for optimal life time testing.…”

Section: Introductionmentioning

confidence: 99%