We consider the problem of estimation the population mean of the study variate Y in presence of measurement errors when information on an auxiliary character X is known. A class of estimators for population means using information on an auxiliary variate X is defined. Expressions for its asymptotic bias and mean square error are obtained. Optimum conditions are obtained for which the mean...

The generation of random variates is an important tool that required in many applications. Various software programs or packages contain generators for standard distributions like the normal, exponential Gamma, e.g., programming language R and SciPy NumPy Python. However, it not uncommon sampling from new/non-standard required. Instead deriving specific such situations, so-called automatic blac...

We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers the second kind that we studied previous work. prove bi-variate polynomial version some known results on standard Bernoulli polynomials, as addition formula and binomial formula. also result allows us to obtain identities from identities, use this several involving products and/or polynomials....

The High-Dimensional Model Representation (HDMR) technique is a family of approaches to efficiently interpolate high-dimensional functions. RS(Random Sampling)-HDMR is a practical form of HDMR based on randomly sampling the overall function, and utilizing orthonormal polynomial expansions to approximate the RS-HDMR component functions. The determination of the expansion coefficients for the com...

Incorporating graph-based techniques in the analysis of multivariate signals is becoming a standard method to understand the interdependency of activity recorded at different sites. The new research frontier in this field includes the important problem of how to assess dynamic changes of signal activity. We present a unified framework of multivariate signals and network science through the grap...