In the transformation semigroup (X, S) we introduce the height of a closed nonempty invariant subset of X, define the transformed dimension of nonempty subset S of X and obtain some results and relations.

Very often statisticians have to deal with the problem of sample size calculation. However this is one of the most difficult questions to be answered since it depends on many considerations, assumptions and restrictions on the real problem being solved. In this paper we develop some methods, based on credible intervals, to calculate sample sizes for proportions and correlations.

This paper proposes a regression model where the response is beta distributed using a parameterization of the beta law that is indexed by mean and dispersion parameters. The proposed model is useful for situations where the variable of interest is continuous and restricted to the interval (0, 1) and is related to other variables through a regression structure. The regression parameters of the b...

The present paper integrates neoclassical offer curves and production theory, introducing utility maximization and trade levels into the comparative static factor proportions model. The paper analyzes production conditions that determine the Metzler paradox that a tariff could lower the tariff inclusive import price. The model provides a more complete link between neoclassical and factor propor...

Recent work has shown that, despite being craniodentally more derived, Australopithecus africanus had more apelike limb-size proportions than A. afarensis. Here, we test whether the A. africanus hand, as judged by metacarpal shaft and articular proportions, was similarly apelike. More specifically, did A. africanus have a short and narrow first metacarpal (MC1) relative to the other metacarpals...

An equivalence test example will set the stage for the discussion of the terminology that follows. Suppose that the response rate of the standard treatment of a disease is 0.70. Unfortunately, this treatment is expensive and occasionally exhibits serious side-effects. A promising new treatment has been developed to the point where it can be tested. One of the first questions that must be answer...

Body proportion was studied in Turner's syndrome by measurement of standing an sitting heights in relation to chronological and bone age. The mean standard deviation score for standing height was -3.8. Disproportionate growth of the legs was not a major determinant of short stature, either before or after oestrogen replacement.