The normal distribution in some constrained sample spaces
نویسندگان
چکیده
Phenomena with a constrained sample space appear frequently in practice. This is the case, for example, with strictly positive data, or with compositional data, such as percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models that better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated. MSC: 60A10, 60E10, 62E10.
منابع مشابه
Optimal Solution in a Constrained Distribution System
We develop a method to obtain an optimal solution for a constrained distribution system with several items and multi-retailers. The objective is to determine the procurement frequency as well as the joint shipment interval for each retailer in order to minimize the total costs. The proposed method is applicable to both nested and non-nested policies and ends up with an optimal solution. To solv...
متن کاملEstimating a Bounded Normal Mean Relative to Squared Error Loss Function
Let be a random sample from a normal distribution with unknown mean and known variance The usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. In many practical situations, is known in advance to lie in an interval, say for some In this case, the maximum likelihood estimator...
متن کاملSplittable stochastic project scheduling with constrained renewable resource
This paper discusses the problem of allocation of constrained renewable resource to splittable activities of a single project. If the activities of stochastic projects can be split, these projects may be completed in shorter time when the available resource is constrained. It is assumed that the resource amount required to accom-plish each activity is a discrete quantity and deterministic. The ...
متن کاملCompleteness in Probabilistic Metric Spaces
The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...
متن کاملA New Approximation for the Null Distribution of the Likelihood Ratio Test Statistics for k Outliers in a Normal Sample
Usually when performing a statistical test or estimation procedure, we assume the data are all observations of i.i.d. random variables, often from a normal distribution. Sometimes, however, we notice in a sample one or more observations that stand out from the crowd. These observation(s) are commonly called outlier(s). Outlier tests are more formal procedures which have been developed for detec...
متن کامل