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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 Generalised logistic function ： ウィキペディア英語版 Generalised logistic function The generalised logistic function or curve, also known as Richards' curve, originally developed for growth modelling, is an extension of the logistic or sigmoid functions, allowing for more flexible S-shaped curves: :$Y(t)\; =\; A\; +\; \}$ where $Y$ = weight, height, size etc., and $t$ = time. It has five parameters: *$A$: the lower asymptote; *$K$: the upper asymptote. If $A=0$ then $K$ is called the carrying capacity; *$B$: the growth rate; *$\backslash nu\; >\; 0$ : affects near which asymptote maximum growth occurs. *$Q$: is related to the value $Y(0)$ *$C$: typically takes a value of 1. The equation can also be written: :$Y(t)\; =\; A\; +\; \}$ where $M$ can be thought of a starting time, $t\_0$ (at which $Y(t\_0)\; =\; A\; +$ ) Including both $Q$ and $M$ can be convenient: :$Y(t)\; =\; A\; +\; \}$ this representation simplifies the setting of both a starting time and the value of Y at that time. The logistic, with maximum growth rate at time $M$, is the case where $Q\; =\; \backslash nu$ = 1. ==Generalised logistic differential equation== A particular case of the generalised logistic function is: :$Y(t)\; =\; \}$ which is the solution of the so-called Richard's differential equation (RDE): :$Y^(t)\; =\; \backslash alpha\; \backslash left(1\; -\; \backslash left(\backslash frac\; \backslash right)^\; \backslash right)Y$ with initial condition :$Y(t\_0)\; =\; Y\_0$ where :$Q\; =\; -1\; +\; \backslash left(\backslash frac\; \backslash right)^$ provided that ν > 0 and α > 0. The classical logistic differential equation is a particular case of the above equation, with ν =1, whereas the Gompertz curve can be recovered in the limit $\backslash nu\; \backslash rightarrow\; 0^+$ provided that: :$\backslash alpha\; =\; O\backslash left(\backslash frac\backslash right)$ In fact, for small ν it is :$Y^(t)\; =\; Y\; r\; \backslash frac\backslash right)\; \backslash right)\}\; \backslash approx\; r\; Y\; \backslash ln\backslash left(\backslash frac\backslash right)$ The RDE suits to model many growth phenomena, including the growth of tumours. Concerning its applications in oncology, its main biological features are similar to those of Logistic curve model. 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「Generalised logistic 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.