• Corpus ID: 88513056

# Confidence intervals for average success probabilities

@article{Mattner2014ConfidenceIF,
title={Confidence intervals for average success probabilities},
author={Lutz Mattner and Christoph Tasto},
journal={arXiv: Statistics Theory},
year={2014}
}
• Published 2 March 2014
• Mathematics
• arXiv: Statistics Theory
We provide Buehler-optimal one-sided and some valid two-sided confidence intervals for the average success probability of a possibly inhomogeneous fixed length Bernoulli chain, based on the number of observed successes. Contrary to some claims in the literature, the one-sided Clopper-Pearson intervals for the homogeneous case are not completely robust here, not even if applied to hypergeometric estimation problems.
1 Citations
Extreme expectations of Bernoulli convolutions given their first few moments are attained at shifted convolutions of as few binomials
. A result of Chebyshev (1846) and Hoeﬀding (1956), on bounding an expectation of a given function with respect to a Bernoulli convolution (also called Poisson binomial law, or law of the number of

## References

SHOWING 1-10 OF 15 REFERENCES
On construction of the smallest one-sided confidence interval for the difference of two proportions
For any class of one-sided $1-\alpha$ confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the
Confidence Intervals for the Product of Two Binomial Parameters
Abstract Many more-or-less reasonable solutions to the problem of statistical estimation of the product P 1 P 2 of two binomial parameters by confidence intervals can be given. After specializing to
Description of a subfamily of the discrete pearson system as generalized-binomial distributions
• Mathematics
• 1995
In this paper we prove that a subfamily of distributions of the discrete Pearson, system, containing the Polya distribution without replacement and hence the hypergeometric distribution, can be
On the Distribution of the Number of Successes in Independent Trials
Let S be the number of successes in n independent trials, and let p i denote the probability of success in the jth trial, j = 1, 2, …, n (Poisson trials). We consider the problem of finding the
Observations on Mixed Binomials
• Mathematics
• 1974
In many situations, the probability (P) of some event is not constant over trials and the observed total number (S) of successes or errors over N trials is not distributed as a simple binomial. This
Letter to the Editor: Some comments on: On construction of the smallest one-sided confidence interval for the difference of two proportions
• Mathematics
• 2010
Letter to the Editor: Some comments on "On construction of the smallest one-sided confidence interval for the difference of two proportions" by Weizhen Wang [arXiv:1002.4945].
Monotone Convergence of Binomial Probabilities and a Generalization of Ramanujan's Equation
• Mathematics
• 1968
Abstract : The paper contains two basic theorems which generalize results of Anderson and Samuels (1967) and Jogdeo (1967). These two theorems serve as lemmas for the more detailed results of
Confidence Sets for Binary Response Models
Abstract Inequalities of Hoeffding are employed to obtain a confidence set for an arbitrary parameterized binary response model. Numerical results are demonstrated for a particular set of
Immunotherapy of osteogenic sarcoma with transfer factor
• Medicine
Cancer Immunology, Immunotherapy
• 2004
Seven of the fifteen patients with osteogenic sarcoma treated with transfer factor derived from leukocytes of their household contacts were disease-free when transfer therapy was initiated shortly after surgical removal of the primary tumor or solitary pulmonary metastases.