Set Change Rate Measure
A Set Change Rate Measure is a change rate measure for sets.
References
2008
- (Upton & Cook, 2008) ⇒ Graham Upton, and Ian Cook. (2008). “A Dictionary of Statistics, 2nd edition revised." Oxford University Press. ISBN:0199541450
- http://www.oxfordreference.com/view/10.1093/acref/9780199541454.001.0001/acref-9780199541454-e-702
- QUOTE: A curve describing the growth of a [[population]. Let [math]\displaystyle{ y }[/math] denote the size of the population at time L with c denoting the ultimate size and b denoting the growth rate [the parameter that governs the rate at which the population approaches its maximum value). Simple two-parameter possibilities include: :[math]\displaystyle{ y = ce^{-e^{-bt} } }[/math] (the Gompertz equation) :[math]\displaystyle{ y = c (1 - e^{-bt}) }[/math] (the Mitscherlich equation) :[math]\displaystyle{ y = ct/(b + t) }[/math] (the Michaelis-Menten equation)
Taking reciprocals in the last of these gives the Lineweaver-Burk equation :[math]\displaystyle{ \frac{1}{y} = \frac{1}{c} + \frac{b}{c} \times \frac{1}{t} }[/math] which is a simple linear model.
A more general growth equation is the generalized logistic equation, also called the Richards equation: :[math]\displaystyle{ y = a+ c \{1 + de^{-b(t-t_m)} \}^{-1/d} }[/math] which describes gowth from a low of [math]\displaystyle{ a }[/math] to a high of [math]\displaystyle{ c }[/math], with [math]\displaystyle{ t_m }[/math] being the time of maximum growth and [math]\displaystyle{ d }[/math] controlling whether that time occurs when the value of [math]\displaystyle{ y }[/math] is nearer [math]\displaystyle{ a }[/math] or [math]\displaystyle{ c }[/math].