TY - JOUR

T1 - Exact average coverage probabilities and confidence coefficients of confidence intervals for discrete distributions

AU - Wang, Hsiuying

PY - 2009/6/1

Y1 - 2009/6/1

N2 - 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, inf∈ θ P θ (θ (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.

AB - 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, inf∈ θ P θ (θ (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.

KW - Confidence coefficient

KW - Confidence interval

KW - Coverage probability

KW - Discrete distribution

UR - http://www.scopus.com/inward/record.url?scp=59849105766&partnerID=8YFLogxK

U2 - 10.1007/s11222-008-9077-8

DO - 10.1007/s11222-008-9077-8

M3 - Article

AN - SCOPUS:59849105766

VL - 19

SP - 139

EP - 148

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 2

ER -