Multinomial Probabilities, Permanents and a Conjecture of Karlin and Rinott
نویسنده
چکیده
The probability density function of a multiparameter multinomial distribution can be expressed in terms of the permanent of a suitable matrix. This fact and certain results on conditionally negative definite matrices are used to prove a conjecture due to Karlin and Rinott.
منابع مشابه
On an Inequality of Karlin and Rinott Concerning Weighted Sums of i.i.d. Random Variables
It is convenient to define H(X) = Hα(X) = −∞ when X is discrete, e.g., degenerate. (Our notation differs from that of Karlin and Rinott 1981 here.) We study the entropy of a weighted sum, S = ∑n i=1 aiXi, of i.i.d. random variables Xi, assuming that the density f of Xi is log-concave, i.e., supp(f) = {x : f(x) > 0} is an interval and log f is a concave function on supp(f). The main result is th...
متن کاملProbit and nested logit models based on fuzzy measure
Inspired by the interactive discrete choice logit models [Aggarwal, 2019], this paper presents the advanced families of discrete choice models, such as nested logit, mixed logit, and probit models to consider the interaction among the attributes. Besides the DM's attitudinal character is also taken into consideration in the computation of choice probabilities. The proposed choice models make us...
متن کاملA Univariate Inequality for Medians
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...
متن کاملA Further Note on Runs in Independent Sequences
Given a sequence of letters generated independently from a finite alphabet, we consider the case when more than one, but not all, letters are generated with the highest probability. The length of the longest run of any of these letters is shown to be one greater than the length of the longest run in a particular state of an associated Markov chain. Using results of Foulser and Karlin (19...
متن کاملDeterminants and permanents of Hessenberg matrices and generalized Lucas polynomials
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...
متن کامل