Maxima of Dirichlet and triangular arrays of gamma variables
نویسندگان
چکیده
Consider a rowwise independent triangular array of gamma random variables with varying parameters. Under several different conditions on the shape parameter, we show that the sequence of row-maximums converges weakly after linear or power transformation. Depending on the parameter combinations, we obtain both Gumbel and non-Gumbel limits. The weak limits for maximum of the coordinates of certain Dirichlet vectors of increasing dimension are also obtained using the gamma representation.
منابع مشابه
Maxima of the Cells of an Equiprobable Multinomial
Consider a sequence of multinomial random vectors with increasing number of equiprobable cells. We show that if the number of trials increases fast enough, the sequence of maxima of the cells after a suitable centering and scaling converges to the Gumbel distribution. While results are available for maxima of triangular arrays of independent random variables with certain types of distribution, ...
متن کاملRelative order and type of entire functions represented by Banach valued Dirichlet series in two variables
In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...
متن کاملAmorphous Silicon Flat Panel Imagers for Medical Application
A new gamma camera based on hydrogenated amorphous silicon (a-Si:H) pixel arrays to be used in nuclear medicine is introduced. Various performance characteristics of a-Si:H imagers are reviewed and compared with those of currently used equipment. An important component in the a-Si:H imager is the scintillator screen. A new approach for fabrication of high resolution CsI(Tl) scintillator layers,...
متن کاملLecture 7 : Triangular arrays and Lévy processes
Previous lectures detailed the central limit theorem for dealing with triangular arrays of random variables: under certain conditions, the row sums of these triangular arrays converge in distribution to a standard normal. By extension, we thus have seen conditions that lead the row sums to converge to N(μ, σ) for general μ, σ. Today, we introduce a more general condition for triangular arrays o...
متن کاملDirichlet series and approximate analytical solutions of MHD flow over a linearly stretching sheet
The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary cond...
متن کامل