The concept of statistical convergence in $2$-normed spaces for double sequence was introduced in [S. Sarabadan and S. Talebi, {it Statistical convergence of double sequences  in $2$-normed spaces }, Int. J. Contemp. Math. Sci. 6 (2011) 373--380]. In the first, we introduce concept strongly statistical convergence in $2$-normed spaces and generalize some results. Moreover,  we define the conce...

Mixture models provide a method of modeling a complex probability distribution in terms of simpler structures. In particular, the method of mixture of regressions has received considerable attention due to its modeling flexibility and availability of convenient computational algorithms. While the theoretical justification has been successfully worked out from the frequentist point of view, its ...

Let fn denote a kernel density estimator of a bounded continuous density f in the real line. Let Ψ(t) be a positive continuous function such that ‖Ψf‖∞<∞. Under natural smoothness conditions, necessary and sufficient conditions for the sequence √ nhn 2 log h−1 n supt∈R ∣∣Ψ(t)(fn(t)−Efn(t))∣∣ (properly centered and normalized) to converge in distribution to the double exponential law are obtaine...

For nonlinear random operator equations where the distributions of the stochastic inputs are approximated by sequences of random variables converging in distribution and where the underlying deterministic equations are simultaneously approximated, we prove a result about tightness and convergence in distribution of the approximate solutions. We apply our result to a random differential equation...

Erdős posed the problem of how many random subsets need to be chosen from a set of n elements, each element appearing in each subset with probability p = 1/2, in order that at least one subset is contained in another. Rényi answered this question, but could not determine the limiting probability distribution for the number of subset counts because the higher moments diverge to infinity. The mod...

confirmation of convergence hypothesis among provinces, its role in removing divergence among regions and achieving regional convergence is one of the important issues in macroeconomics. the aim of the present study is to examine absolute and conditional income convergence hypotheses among iranian provinces during the period 2000-2010 using panel data. the hypotheses are tested for the whole pr...