Unimodal Time-symmetric Dynamics

Time-symmetric Cycles

The main result of this note is that given any two time-symmetric cycles, one can find a time-symmetric extension of one by the other. This means that given a time-symmetric cycle, both time-symmetric doubles and square roots can be found. 1. Introduction. In [4], the idea of time-symmetric cycles was introduced. The basic idea underlying the definition of these cycles is that the dynamics asso...

On a New Bimodal Normal Family

The unimodal distributions are frequently used in the theorical statistical studies. But in applied statistics, there are many situations in which the unimodal distributions can not be fitted to the data. For example, the distribution of the data outside the control zone in quality control or outlier observations in linear models and time series may require to be a bimodal. These situations, oc...

Unimodal Polynomials Arising from Symmetric Functions

We present a general result that, using the theory of symmetric functions, produces several new classes of symmetric unimodal polynomials. The result has applications to enumerative combinatorics including the proof of a conjecture by R. Stanley.

The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities

M ay 2 00 8 On the elicitation of continuous , symmetric , unimodal distributions

In this brief note, we highlight some difficulties that can arise when fitting a continuous, symmetric, unimodal distribution to a set of expert’s judgements. A simple analysis shows it is possible to fit a Cauchy distribution to an expert’s beliefs when their beliefs actually follow a normal distribution. This example stresses the need for careful distribution fitting and for feedback to the e...