Department of Statistics / Institutionen för statistik (-2002)

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T. o. m. 2002

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    A note on the first moment of extreme order statistics from the normal distribution
    (2000) Petzold, Max; Department of Statistics
    In this note some well known asymptotic results for moments of order statistics from the normal distribution are treated. The results originates from the work of Cramér. A bias correction for finite sample sizes is proposed for the expected value of the largest observation.
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    A small sample limitation for estimators based on order statistics
    (2000) Petzold, Max; Department of Statistics
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    A comprative study of some approaches for constructing tolerance limits
    (2000) Petzold, Max; Department of Statistics
    In a dose finding study the aim is to come up with a safe and efficient drug administration. By comparing the obtained tolerance limits with predetermined desired concentration limits, i.e. the therapeutic window, one may be able to adjust the drug dosage. For drugs with a therapeutic window situated at high concentrations close to toxic levels, one has to balance between attaining a high proportion of the population at efficient high levels on one hand and the risks of an overdose on the other hand. In such cases it is important to use the proper estimation approach for the upper tolerance limit. Here a conservative estimation approach intended for a drug with potentially adverse side effects with minor overdoses is compared with an approach intended for a drug with harmless side effects. It is shown that the conservative approach can be considerably less efficient when used in the latter case, a disadvantage that is rarely discussed when proposing conservative estimators. The properties of the two approaches are evaluated using well-known parametric and non-parametric estimators in a simulation study for small and moderate sample sizes.