اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدProbability distributions with binomial moments
117
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove that if $pgeq 1$ and $-1leq rleq p-1$ then the binomial sequence $binom{np+r}{n}$, $n=0,1,...$, is positive definite and is the moment sequence of a probability measure $ u(p,r)$, whose support is contained in $left[0,p^p(p-1)^{1-p}right]$. If $p>1$ is a rational number and $-1<rleq p-1$ then $ u(p,r)$ is absolutely continuous and its density function $V_{p,r}$ can be expressed in terms of the Meijer $G$-function. In particular cases $V_{p,r}$ is an elementary function. We show that for $p>1$ the measures $ u(p,-1)$ and $ u(p,0)$ are certain free convolution powers of the Bernoulli distribution. Finally we prove that the binomial sequence $binom{np+r}{n}$ is positive definite if and only if either $pgeq 1$, $-1leq rleq p-1$ or $pleq 0$, $p-1leq r leq 0$. The measures corresponding to the latter case are reflections of the former ones.
قيم البحث
اقرأ أيضاً
In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding bound is an im
mediate consequence of the theory. Moreover, we propose a rigorous and efficient method for probability estimation, which is an adaptive Monte Carlo estimation method based on truncated inverse binomial sampling. Our proposed method of probability estimation can be orders of magnitude more efficient as compared to existing methods in literature and widely used software.
We study the probability measure $mu_{0}$ for which the moment sequence is $binom{3n}{n}frac{1}{n+1}$. We prove that $mu_{0}$ is absolutely continuous, find the density function and prove that $mu_{0}$ is infinitely divisible with respect to the additive free convolution.
We establish an isomorphism between the center of the Heisenberg category defined by Khovanov and the algebra $Lambda^*$ of shifted symmetric functions defined by Okounkov-Olshanski. We give a graphical description of the shifted power and Schur base
s of $Lambda^*$ as elements of the center, and describe the curl generators of the center in the language of shifted symmetric functions. This latter description makes use of the transition and co-transition measures of Kerov and the noncommutative probability spaces of Biane.
In this paper we review some general properties of probability distributions which exibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such para
digms, the underlying mathematical mechanism producing the singularity and other topics such as the condensation of fluctuations, the relationships with ordinary phase-transitions, the giant response associated to anomalous fluctuations, and the interplay with Fluctuation Relations.
Many authors have studied the phenomenon of typically Gaussian marginals of high-dimensional random vectors; e.g., for a probability measure on $R^d$, under mild conditions, most one-dimensional marginals are approximately Gaussian if $d$ is large. I
n earlier work, the author used entropy techniques and Steins method to show that this phenomenon persists in the bounded-Lipschitz distance for $k$-dimensional marginals of $d$-dimensional distributions, if $k=o(sqrt{log(d)})$. In this paper, a somewhat different approach is used to show that the phenomenon persists if $k<frac{2log(d)}{log(log(d))}$, and that this estimate is best possible.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
