The Extremum Distance Estimator (EDE) for Finding the Inflection Point of a Convex/Concave Curve

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Description

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

Usage

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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_F1 and x_F2 points, see [1], [2].

Value

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

A(1,1)=i1

The index jF1 for EDE method

A(1,2)=i2

The index jF2 for EDE method

A(1,3)=chi_S

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.
New function in version 1.2

Author(s)

Demetris T. Christopoulos

References

[1]Demetris T. Christopoulos, Developing methods for identifying the inflection point of a convex/ concave curve. arXiv:1206.5478v2 [math.NA],2012.
[2]Demetris T. Christopoulos, On the efficient identification of an inflection point, International Journal of Mathematics and Scientific Computing, (ISSN: 2231-5330), vol. 6(1), 2016.

See Also

See also the iterative version bede.

Examples

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#Fisher-pry model with heavy noise, unequal spaces
#and 1 million cases:
N=10^6+1;
set.seed(2016-06-09);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
#