ede: The Extremum Distance Estimator (EDE) for finding the...
In dchristop/inflection: Finds the Inflection Point of a Curve

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Implementation of EDE method as defined in [1] and [2] by giving a simple output of the method.

1	ede(x, y, index)

`x`	The numeric vector of x-abscissas, must be of length at least 4.
`y`	The numeric vector of the noisy or not y-ordinates, must be of length at least 4.
`index`	If data is convex/concave then index=0 If data is concave/convex then index=1

We also obtain the x_{F_{1}},x_{F_{2}} points, see [1], [2].

A matrix of size 1 x 3 is returned with elements:

`A(1,1)=i_1`	The index j_{F_{1}} for EDE method
`A(1,2)=i_1`	The index j_{F_{2}} for EDE method
`A(1,3)=χ_{D}`	The Extremum Distance Estimator (EDE) for inflection point

This function is for real big data sets, more than one million rows. It is the fastest available method, see [2] for comparison to other methods.

Demetris T. Christopoulos

[1]Demetris T. Christopoulos (2014). Developing methods for identifying the inflection point of a convex/concave curve. arXiv:1206.5478v2 [math.NA]. https://arxiv.org/pdf/1206.5478v2.pdf

[2]Demetris T. Christopoulos (2016). On the efficient identification of an inflection point.International Journal of Mathematics and Scientific Computing, (ISSN: 2231-5330), vol. 6(1). https://veltech.edu.in/wp-content/uploads/2016/04/Paper-04-2016.pdf

See also the iterative version bede and iterations plot using findipiterplot.

#
#Fisher-pry model with heavy noise, unequal spaces
#and 1 million cases:
N=10^6+1;
set.seed(2017-05-11);x=sort(runif(N,0,10));y=5+5*tanh(x-5)+runif(N,-1,1);
#
ptm <- proc.time()
tede=ede(x,y,0);tede;proc.time() - ptm
#         j1     j2      chi
# EDE 351061 648080 4.997139
# user  system elapsed 
# 0.01    0.00    0.01 
#