We propose a new adjustment for constructing an improved version of the Wald interval for linear combinations of binomial proportions, which addresses the presence of extremal samples. A comparative simulation study was carried out to investigate the performance of this new variant with respect to the exact coverage probability, expected interval length and mesial and distal non-coverage probabilities. Additionally, we discuss the application of a criterion for interpreting interval location in the case of small samples and/or in situations in which extremal observations exist. The confidence intervals obtained from the new variant performed better for some evaluation measures.keywrods:Approximate confidence intervals Linear combination of binomial proportions Restricted models (Newcombe-Zou, Peskun and score methods) Unrestricted model (Wald method) Interval location

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The mapping defined by inter-nucleotide distances (InD) provides a reversible numerical representation of the primary structure of DNA. If nucleotides were independently placed along the genome, a finite mixture model of four geometric distributions could be fitted to the InD where the four marginal distributions would be the expected distributions of the four nucleotide types. We analyze a finite mixture model of geometric distributions (f 2 ), with marginals not explicitly addressed to the nucleotide types, as an approximation to the InD. We use BIC in the composite likelihood framework for choosing the number of components of the mixture and the EM algorithm for estimating the model parameters. Based on divergence profiles, an experimental study was carried out on the complete genomes of 45 species to evaluate f 2 . Although the proposed model is not suited to the InD, our analysis shows that divergence profiles involving the empirical distribution of the InD are also exhibited by profiles involving f 2 . It suggests that statistical regularities of the InD can be described by the model f 2 . Some characteristics of the DNA sequences captured by the model f 2 are illustrated. In particular, clusterings of subgroups of eukaryotes (primates, mammalians, animals and plants) are detected.

Evaluation of the coverage probability and, more recently, of the intervalar location of confidence intervals, is a useful procedure if exact and asymptotic methods for constructing confidence intervals are used for some populacional parameter. In this paper, a simple graphical procedure is presented to execute this kind of evaluation in confidence methods for linear combinations of k independent binomial proportions. Our proposal is based on the representation of the mesial and distal non-coverage probabilities on a plane. We carry out a simulation study to show how this graphical representation can be interpreted and used as a basis for the evaluation of intervalar location of confidence interval methods.