Let W (π) be either the number of descents or inversions of a permutation π ∈ Sn. Stein’s method is applied to bound the sup-norm distance between the distribution of W and the standard normal distribution. This appears to be the first use of Stein’s method in theory of permutation statistics. The construction of an exchangeable pair (W,W ) used in Stein’s method is non-trivial and may be of in...

Birnbaum and Saunders introduced in 1969 a two-parameter lifetime distribution which has been used quite successfully to model a wide variety of univariate positively skewed data. Diaz-Garcia and Leiva-Sanchez [9] proposed a generalized BirnbaumSaunders distribution by using an elliptically symmetric distribution in place of the normal distribution. Recently, Kundu et al. [17] introduced a biva...

We develop sampling algorithms for multivariate Archimedean copulas. For exchangeable copulas, where there is only one generating function, we first analyse the distribution of the copula itself, deriving a number of integral representations and a generating function representation. One of the integral representations is related, by a form of convolution, to the distribution whose Laplace trans...

scott and szewczyk in technometrics, 2001, have introduced a similarity measure for twodensities f1 and f2 , by1, 21 21 1 2 2( , ), ,f fsim f ff f f f< >=< >< >wheref1, f2 f1(x, θ1)f2(x, θ2)dx.+∞−∞< >=∫sim(f1, f2) has some appropriate properties that can be suitable measures for the similarity of f1 and f2 .however, due to some restrictions on the value of parameters and the kind of densities, ...

Abstract In this paper we derive new results on multivariate extremes and D -norms. particular establish characterizations of the max-domain attraction property. The limit distribution certain exceedances above high thresholds is derived, that generator a -norm ${\mathbb R}^{d}$ ? <mml:m...

abstract in recent years, many researchers have attempted to estimate the soil hydraulic functions (e.g. soil moisture characteristics curve, and hydraulic conductivity function) using particle-size distribution (psd) curve. in these studies, an accurate mathematical representation of psd is required for fitting the observed data. so far, some mathematical models were developed with different l...

3D maps including urban structures and terrain information facilitate urban searches for robots operating in various robot scenarios. However it suffers from large memory requirements and computation time to deal with point clouds collected by range sensors. It is problematic for operating rescue robots in real time. NDT (Normal Distribution Transform) grid is a suitable map model to deal with ...

In this article we introduce a new three parameter skewed distribution of which normal distribution is a special case. This distribution is obtained by using geometric sum of independent identically distributed normal random variables. We call this distribution as the geometric skew normal distribution. Different properties of this new distribution have been investigated. The probability densit...