ede {inflection}

The Extremum Distance Estimator (EDE) for finding the inflection point of a convex/concave curve

Description

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

Usage

ede(x, y, index)

Arguments

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

Details

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

Value

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

A(1, 1)

The index j_{F_{1}} for EDE method

A(1, 2)

The index j_{F_{2}} for EDE method

A(1, 3)

The Extremum Distance Estimator (EDE) for inflection point

Note

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.

Author(s)

Demetris T. Christopoulos

References

[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

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

Examples

#
#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 
#