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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spherical contact distribution function ： ウィキペディア英語版 Spherical contact distribution function In probability and statistics, a spherical contact distribution function, first contact distribution function,〔D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. ''Stochastic geometry and its applications'', volume 2. Wiley Chichester, 1995.〕 or empty space function〔A. Baddeley, I. Bárány, and R. Schneider. Spatial point processes and their applications. ''Stochastic Geometry: Lectures given at the CIME Summer School held in Martina Franca, Italy, September 13--18, 2004'', pages 1--75, 2007.〕 is a mathematical function that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both.〔〔D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, second edition, 2003.〕 More specifically, a spherical contact distribution function is defined as probability distribution of the radius of a sphere when it first encounters or makes contact with a point in a point process. This function can be contrasted with the nearest neighbour function, which is defined in relation to some point in the point process as being the probability distribution of the distance from that point to its nearest neighbouring point in the same point process. The spherical contact function is also referred to as the contact distribution function,〔 but some authors〔 define the contact distribution function in relation to a more general set, and not simply a sphere as in the case of the spherical contact distribution function. Spherical contact distribution functions are used in the study of point processes〔〔〔D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. . Probability and its Applications (New York). Springer, New York, second edition, 2008.〕 as well as the related fields of stochastic geometry〔 and spatial statistics,〔〔J. Moller and R. P. Waagepetersen. ''Statistical inference and simulation for spatial point processes''. CRC Press, 2003.〕 which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications.〔〔〔F. Baccelli and B. Błaszczyszyn. ''Stochastic Geometry and Wireless Networks, Volume I – Theory'', volume 3, No 3-4 of ''Foundations and Trends in Networking''. NoW Publishers, 2009.〕〔F. Baccelli and B. Błaszczyszyn. ''Stochastic Geometry and Wireless Networks, Volume II – Applications'', volume 4, No 1-2 of ''Foundations and Trends in Networking''. NoW Publishers, 2009.〕 ==Point process notation== (詳細はmathematical space. Since these processes are often used to represent collections of points randomly scattered in space, time or both, the underlying space is usually ''d''-dimensional Euclidean space denoted here by $\backslash textstyle\; \backslash textbf^$, but they can be defined on more abstract mathematical spaces.〔 Point processes have a number of interpretations, which is reflected by the various types of point process notation.〔〔 For example, if a point $\backslash textstyle\; x$ belongs to or is a member of a point process, denoted by $\backslash textstyle$, then this can be written as:〔 : $\backslash textstyle\; x\backslash in\; ,$ and represents the point process being interpreted as a random set. Alternatively, the number of points of $\backslash textstyle$ located in some Borel set $\backslash textstyle\; B$ is often written as:〔〔〔 : $\backslash textstyle\; (B),$ which reflects a random measure interpretation for point processes. These two notations are often used in parallel or interchangeably.〔〔〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spherical contact distribution function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.