Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Interval estimation for log‐normal mean with applications to water quality

Abstract: Large samples based confidence interval is frequently used by environmental scientists as an approximate data summary about the log-normal regression mean It has been shown by simulation that the coverage probability of such an interval is below the intended nominal level for small samples To overcome this difficulty, a complicated small sample corrected interval has been recently proposed in the literature which substantially improves the coverage probability In this paper, similar improvement are obtained by simply replacing the quantile of the normal distribution by the appropriate quantile of Student t distribution as will be demonstrated in this paper by simulation The advantage of our proposed interval is its simplicity and thus will be easier to use in applications As an illustration, we use the method to study the relationship between the flow and concentration of total phosphorous (TP) at four upstream/downstream sampling locations on the Fraser River of British Columbia Our interests in developing intervals for the mean TP level at each location as well as the ratio of the mean at a downstream location to that at an upstream location Such study is important in tracing the evolution of pollutants in an ecosystem and thus in setting policies for pollution control Copyright © 2006 John Wiley & Sons, Ltd

Exact average coverage probabilities and confidence coefficients of confidence intervals for discrete distributions

Abstract: For a confidence interval (L(X),U(X)) of a parameter θ in one-parameter discrete distributions, the coverage probability is a variable function of θ. The confidence coefficient is the infimum of the coverage probabilities, infθPθ( θe(L(X), U(X))). Since we do not know which point in the parameter space the infimum coverage probability occurs at, the exact confidence coefficients are unknown. Beside confidence coefficients, evaluation of a confidence intervals can be based on the average coverage probability. Usually, the exact average probability is also unknown and it was approximated by taking the mean of the coverage probabilities at some randomly chosen points in the parameter space. In this article, methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions are proposed. With these methodologies, both exact values can be derived.

Performance evaluation of recent procedures for steady-state simulation analysis

Abstract: The performance of the batch-means procedure ASAP3 and the spectral procedure WASSP is evaluated on test problems with characteristics typical of practical applications of steady-state simulation analysis procedures. ASAP3 and WASSP are sequential procedures designed to produce a confidence-interval estimator for the mean response that satisfies user-specified half-length and coverage-probability requirements. ASAP3 is based on an inverse Cornish-Fisher expansion for the classical batch-means t-ratio, whereas WASSP is based on a wavelet estimator of the batch-means power spectrum. Regarding closeness of the empirical coverage probability and average half-length of the delivered confidence intervals to their respective nominal levels, both procedures compared favorably with the Law-Carson procedure and the original ASAP algorithm. Regarding the average sample sizes required for decreasing levels of maximum confidence-interval half-length, ASAP3 and WASSP exhibited reasonable efficiency in the test problems.

Inference on a distribution function from ranked set samples

Abstract: Consider independent observations $$(X_i,R_i)$$ with random or fixed ranks $$R_i$$, while conditional on $$R_i$$, the random variable $$X_i$$ has the same distribution as the $$R_i$$-th order statistic within a random sample of size k from an unknown distribution function F. Such observation schemes are well known from ranked set sampling and judgment post-stratification. Within a general, not necessarily balanced setting we derive and compare the asymptotic distributions of three different estimators of the distribution function F: a stratified estimator, a nonparametric maximum-likelihood estimator and a moment-based estimator. Our functional central limit theorems generalize and refine previous asymptotic analyses. In addition, we discuss briefly pointwise and simultaneous confidence intervals for the distribution function with guaranteed coverage probability for finite sample sizes. The methods are illustrated with a real data example, and the potential impact of imperfect rankings is investigated in a small simulation experiment.