This is not the document you are looking for? Use the search form below to find more!

0.00 (0 votes)

For a unimodal distribution on the Real line, the celebrated mean-median-mode inequality states that they often occur in an alphabetical (or its reverse) order. Various sufficient conditions for the validity of the inequality are known. This article explicitly characterizes the three dimensional set of means, medians, and modes of unimodal distributions. It is
found that the set is pathwise connected but not convex. Some fundamental inequalities among the mean, the median and mode of unimodal distributions are also derived. These inequalities are used : (¿) to prove nonunimodality of certain distributions, and (n) for obtaining bounds on the median of a unimodal distribution. In a multivariate setting, the generalized notion of a-unimodality is used, and characterizations are given for the set of mean vectors, when the mode is fixed, or when it varies in a sphere. In particular, it is found that the set of mean vectors for generalized unimodal distributions with a specified mode and covariance matrix is an exact ellipsoid and this ellipsoid is explicitly described.

- Added:
**April, 03rd 2010** - Reads:
**939** - Downloads:
**48** - File size:
**1.04mb** - Pages:
**23**

- Username: samanta
- Name:
**samanta** - Documents:
**1258**

Related Documents

This project is a lesson in the 6th grade math unit of data analysis. The goal of this project is for the students to understand the mathematical terms of mean, median, mode, and range; and be able ...

Many sufficient conditions for inequalities about the mean, median, mode and skewness have been obtained. Runnenburg gives a result and ...

There are other statistical measures of central tendency that should not be confused with means - including the 'median' and 'mode'. Statistical analyses also commonly use measures of dispersion, ...

In mathematics the meaning of mean is same as the meaning of average or in other words meanings of mean is adding all the values and then divide these values by the total number of values are called ...

Edible coating has been used for preserving the quality and safety of fresh fruit and vegetables. The objective of this research was to evaluate the effect of soybean gum, jojoba wax, glycerol ...

RIPE Inflatable Packers on the Historical Origins and Development of Packer Technology 1800-1850

Inflatable Packers on the Historical Origins and Development of Packer Technology 1800-1850

This thesis describes a methodology for the computational learning and classification of a Systemic Functional Grammar. A machine learning algorithm is developed that allows the structure of the ...

The ongoing damage that the newer forms of HIV denialism are visiting upon our country is evidenced by the recent firing of Nozizwe Madlala-Routledge, the South African Deputy Minister of ...

This paper provides an overview of the political and economic de- cisions that helped to create the financial crisis of 2008. It begins with an overview of U.S. efforts to promote home ...

## Add New Comment