limits can be used in conjunction with a normalizing transformation, as illustrated by the logarithmic transformation in the preceding example from Nelson (1982). Transformations to achieve approximate normality are especially important in light of the lack of robustness of the prediction limits noted earlier. 2. Some instructors may wish to contrast prediction limits with tolerance limits; the...

Let L be the zero set of a nonconstant monic polynomial with complex coe¢ cients. In the context of constructive mathematics without countable choice, it may not be possible to construct an element of L. In this paper we introduce a notion of distance from a point to a subset, more general than the usual one, that allows us to measure distances to subsets like L. To verify the correctness of th...

There has been a great deal of recent emphasis on majorization and related correlation inequalities, for example Marshall and Olkin [11' and Karlin and Rinott [2]. These inequalities have a variety of important applications. However they are based solely on mathematical expectations, for example the result below due to Karamata [3]. After stating this result we give our analog for medians. Kara...

The Pareto distribution has long been recognized as a suitable model for many non-negative socio-economic variables. Univariate and multivariate variations abound. Some unification is possible by representing the Pareto variables in terms of independent gamma distributed components. Further unification is sometimes possible since some of the frequently used multivariate Pareto models share the ...

The purpose of this paper is to graphically illustrate the parametric relationships between pairs of 35 univariate distribution families. The families are organized into a seven-by-five matrix and the relationships are illustrated by connecting related families with arrows. A simplified matrix, showing only 25 families, is designed for student use. These relationships provide rapid access to in...

در این مقاله یک مدل ریاضی برای مسئله سیستم تولیدی همکارانه ساخت بر اساس سفارش با رعایت انصاف تخصیص بار‌های تولید طراحی شده است. اهداف اصلی مدل، کمینه‌سازی هزینه‌‌های کل و حداکثر استفاده از منابع به‌منظور عادلانه شرایط عدم­قطعیت کنترل پارامتر‌های غیرقطعی روش برنامه‌ریزی فازی ‌شده نتایج نشان می‌دهد افزایش نرخ عدم‌قطعیت، می­یابد. ازآنجاکه ظرفیت کارخانه‌ها ثابت است، مقدار تقاضا، هر کارخانه نیز می­ی...

Merit factor of a binary sequence is reviewed, and constructions are described that appear to satisfy an asymptotic merit factor of 6.3421 . . .Multivariate merit factor is characterised and recursive Boolean constructions are presented which satisfy a non-vanishing asymptote in multivariate merit factor. Clifford merit factor is characterised as a generalisation of multivariate merit factor an...

FAmle is a R package that may be used in order to carry out tasks that pertain to univariate frequency analysis. Basically, two general frameworks are being entertained here: maximum likelihood and Bayesian. More precisely, for a given problem, the user may decide to estimate the unknown parameters via maximum likelihood, and to then proceed to statistical inference accordingly, or to use a ful...