ARTICLE
ABSTRACT
Zielinski (2009) constructed a nonparametric interval for At-Risk-of-Poverty Rate. It appeared that the confidence level of the interval depends on the underlying distribution of the income. For some distributions (e.g. lognormal, gamma, Pareto) the confidence level may be smaller than the nominal one. The question is, what is the largest deviance from the nominal level?
In the paper, a more general problem is considered, i.e. the problem of robustness of the confidence level of the confidence interval for binomial probability. The worst distribution is derived as well as the smallest true confidence level is calculated. Some asymptotic remarks (sample size tends to infinity) are also given.
KEYWORDS
ARPR, binomial distribution, confidence interval, robustness.
REFERENCES
CLOPPER C. J., PEARSON E. S. (1934), The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial, Biometrika, 26, 404-413.
ZIELINSKI R. (2006) Exact distribution of the natural ARPR estimator in small samples from infinite populations, Statistics In Transition, 7, 881-888.
ZIELINSKI W. (2009), A nonparametric confidence interval for At-Risk-of- Poverty-Rate, Statistics in Transition new series, 10, 437-444.
