Characterizations of probability distributions via bivariate regression of record values

Bairamov et al. (Aust N Z J Stat 47:543-547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of non-adjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric, and harmonic means.Comment: accepted in Metrik

Thermal deformation of concentrators in an axisymmetric temperature field

Axisymmetric thermal deformations of paraboloid mirrors, due to heating, are examined for a mirror with a optical axis oriented toward the Sun. A governing differential equation is derived using Mushtari-Donnel-Vlasov simplifications, and a solution is presented which makes it possible to determine the principal deformation characteristics

ON GENERALIZED SARMANOV BIVARIATE DISTRIBUTIONS

Abstract. A class of bivariate distributions which generalizes the Sarmanov class is introduced. This class possesses a simple analytical form and desirable dependence properties. The admissible range for association parameter for given bivariate distributions are derived and the range for correlation coefficients are also presented

Characterization of exponential distribution via regression of one record value on two non-adjacent record values

We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the other next to the fixed record value, and none of them are adjacent. In particular, it turns out that the underlying distribution is exponential if and only if given the first and last record values, the expected value of the median in a sample of record values equals the sample midrange.Comment: To appear in Metrik

The color of soils as a basis for proximal sensing of their composition

The color is one of the main morphological properties of soils, as it integrally reflects their material composition. Most of the macro-, micro- and nano-morphological methods in pedology are based on the analysis of soil reflectance characteristics within the visible spectrum (i.e., soils color). The evolution of soil color study methods and the features of modern instruments are described in the report. The main directions in the development of this field of soil science as well as the achievements and problems to be addressed in the study of soil color are demonstrated by specific examples