On descriptive confidence intervals for the mean of asymmetric populations
| Autor: | Valentin Rousson, Edwin Choi |
|---|---|
| Přispěvatelé: | University of Zurich, Rousson, V |
| Rok vydání: | 2003 |
| Předmět: |
Statistics and Probability
education.field_of_study Population 610 Medicine & health 10060 Epidemiology Biostatistics and Prevention Institute (EBPI) Robust confidence intervals Confidence interval Standard deviation Skewness Statistics 1804 Statistics Probability and Uncertainty Tolerance interval 2613 Statistics and Probability Statistics Probability and Uncertainty education Statistic CDF-based nonparametric confidence interval Mathematics |
| Zdroj: | Journal of Nonparametric Statistics. 15:553-563 |
| ISSN: | 1029-0311 1048-5252 |
| DOI: | 10.1080/10485250310001604677 |
| Popis: | Given a sample of n observations with sample mean X¯ and standard deviation S drawn independently from a population with unknown mean μ, it is well known that the skewness of the statistic n −1/2(X¯ − μ)/S is of the opposite sign to the skewness of the population. As a consequence, an equal-tailed confidence interval for μ may be used for descriptive purposes, since the relative position of X¯ in the interval provides visual information about the skewness of the population. In this paper, we are interested in confidence intervals for the mean which share this descriptive property. We formally define two simple classes of intervals where the degree of asymmetry around X¯ monotonically depends on the sample skewness through a parameter λ with values between 0 and 1. These classes contain the symmetric ordinary-z (or the ordinary-t) confidence interval as a special case. We show how to determine this parameter λ in order to obtain an equal-tailed confidence interval for μ which is second order accurate. Whil... |
| Databáze: | OpenAIRE |
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