dy.dx: Partial Derivative dy/dx

Description Usage Arguments Value Author(s) References Examples

Description

Returns the numerical partial derivate of y wrt x for a point of interest.

Usage

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dy.dx(x, y, order = NULL, s.t.n = 0.99, eval.point = median(x),
  deriv.order = 1, h = 0.05, noise.reduction = "mean",
  deriv.method = "FS")

Arguments

x

Independent Variable

y

Dependent Variable

order

Controls the number of partial moment quadrant means. Defaults to order='max' which generates a more accurate derivative for well specified cases.

s.t.n

Signal to noise parameter, sets the threshold of NNS.dep which reduces "order" when order=NULL. Defaults to 0.99 to ensure high dependence for higher "order" and endpoint determination.

eval.point

Independent variable point to be evaluated. Defaults to eval.point=median(x). Set to eval.points="overall" to find an overall partial derivative estimate.

deriv.order

For second derivative estimate of f(x), set deriv.order=2. Defaults to first derivative.

h

Percentage step used for finite step method. Defaults to h=.01 representing a 5 percent step from the value of the independent variable.

noise.reduction

In low signal to noise situations, noise.reduction="median" uses medians instead of means for partitions, while noise.reduction="mode" uses modes instead of means for partitions. noise.reduction="off" allows for maximum possible fit in NNS.reg. Default setting is noise.reduction="mean".

deriv.method

Determines the partial derivative from the coefficient of the NNS.reg output when deriv.method="NNS" or generates a partial derivative using the finite step method deriv.method="FS" (Defualt).

Value

Returns the value of the partial derivative estimate for the given order.

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" http://amzn.com/1490523995

Examples

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x<-seq(0,2*pi,pi/100); y<-sin(x)
dy.dx(x,y,eval.point=1.75)


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