This paper deals with the stochastic comparison of order statistics and their mixtures. For a random sample of size n from an exponential distribution with hazard rate [lambda], and for 1<=k<=n, let us denote by the distribution function of the corresponding kth order statistic. Let us consider m random samples of same size n from exponential distributions having respective hazard rates [lambda]1,...,[lambda]m. Assume that p1,...,pm>0, such that , and let U and V be two random variables with the distribution functions and , respectively....</=k<=n,>

An admissible estimator of the eigenvalues of the variance-covariance matrix is given for multivariate normal distributions with respect to the scale-invariant squared error loss.

We consider a continuous time stochastic volatility model. The model contains a stationary volatility process. We aim to estimate the multivariate density of the finite-dimensional distributions of this process. We assume that we observe the process at discrete equidistant instants of time. The...

High dimensional data routinely arises in image analysis, genetic experiments, network analysis, and various other research areas. Many such datasets do not correspond to well-studied probability distributions, and in several applications the data-cloud prominently displays non-symmetric and...

The ratio of the largest eigenvalue divided by the trace of a p×p random Wishart matrix with n degrees of freedom and an identity covariance matrix plays an important role in various hypothesis testing problems, both in statistics and in signal processing. In this paper we derive an approximate...

Principal component analysis (PCA) is one of the key techniques in functional data analysis. One important feature of functional PCA is that there is a need for smoothing or regularizing of the estimated principal component curves. Silverman's method for smoothed functional principal component...

Let be a correlated complex non-central Wishart matrix defined through , where is an complex Gaussian with non-zero mean and non-trivial covariance . We derive exact expressions for the cumulative distribution functions (c.d.f.s) of the extreme eigenvalues (i.e., maximum and minimum) of for some...

In this paper, we discuss some basic distributional and asymptotic properties of the Pearson-Kotz Dirichlet multivariate distributions. These distributions, which appear as the limit of conditional Dirichlet random vectors, possess many appealing properties and are interesting from theoretical...

The model we discuss in this paper deals with inequality in distribution in the presence of a covariate. To elucidate that dependence, we propose to consider the composition of the cumulative quantile regression (CQR) function and the Goldie concentration curve, the standardized counterpart of...