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

## Description

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

## Usage

 `1` ```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)=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

## 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, Developing methods for identifying the inflection point of a convex/ concave curve. arXiv:1206.5478v2 [math.NA], https://arxiv.org/pdf/1206.5478v2.pdf, 2014
[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), https://www.researchgate.net/publication/304557351, 2016

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# #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 # ```

### Example output

```        j1     j2      chi
EDE 351061 648080 4.997139
user  system elapsed
0.035   0.004   0.038
```

inflection documentation built on May 29, 2017, 5:49 p.m.