In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...

in the analysis of spatial point patterns, complete spatial randomness (csr) hypothesis,which is a restriction of a homogenous poisson process to study region a, operates as a dividinghypothesis between “regular” and “aggregated” patterns. meanwhile, many alternatives to csr inaggregated patterns are extensions of homogenous poisson processes themselves. therefore, when thecsr hypothesis is rej...

Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...

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