Information matrices for some elliptically symmetric distributions

The Fisher information matrices are derived for three of the most popular elliptically symmetric distributions: the Pearson type II, Pearson type VII and the Kotz type distributions. We hope the results could be important to the many researchers working in this area

RELIABILITY FOR SOME BIVARIATE EXPONENTIAL DISTRIBUTIONS

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr(X \u3c Y). The algebraic form for R = Pr(X \u3c Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when (X,Y) follow bivariate distributions with dependence between X and Y. In particular, explicit expressions for R are derived when the joint distribution is bivariate exponential. The calculations involve the use of special functions. An application of the results is also provided

A vector multivariate hazard rate

AbstractA vector definition of multivariate hazard rate, and associated definitions of increasing and decreasing multivariate hazard rate distributions are presented. Consequences of these definitions are worked out in a number of special cases. Relationships between hazard rate and orthant dependence are established

Comments on “On the Distribution of the Product of Independent Rayleigh Random Variables”

It is pointed out that the result in Salo et al. “The Distribution of the Product of Independent Rayleigh Random Variables” IEEE Trans. Antennas Propag., vol. 54, pp. 639–643, Feb. 2006, is a particular case of a much more general result known since the 1970s. A general technique (known as the function technique) is described that can be used derive a wide range of results similar to Salo et al

The Exact Distribution of the Multilook Magnitude

Gierull provides a statistical analysis of multilook synthetic aperture radar interferograms. Various expressions for the probability density function, cumulative distribution function, and the moments of associated statistics are derived. It appears, however, that most of these expressions are based on some approximation. In this letter, the corresponding expressions are derived in their exact form, including some elementary representations for certain expressions given by Gierull. A numerical comparison of the exact and approximate expressions is provided

Muliere and Scarsini's bivariate Pareto distribution: sums, products, and ratios

We derive the exact distributions of R = X + Y, P = X Y and W = X/(X + Y) and the corresponding moment properties when X and Y follow Muliere and Scarsini's bivariate Pareto distribution. The expressions turn out to involve special functions. We also provide extensive tabulations of the percentage points associated with the distributions. These tables -obtained using intensive computing power- will be of use to practitioners of the bivariate Pareto distribution.Trobem la distribució exacta de R = X + Y , P = X Y, W = X/(X + Y ), els corresponents moments i les seves propietats quan X, Y segueixen la distribució bivariant Pareto de Muliere i Scarsini. Les expressions fan servir funcions especials. També proporcionem tabulacions extensives dels percentils associats amb les distribucions. Aquestes taules -obtingudes emprant potents tècniques de computació intensiva-seran d'utilitat per als usuaris de la distribució de Pareto bivariant