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 |

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)=` |
The index |

`A(1,2)=` |
The index |

`A(1,3)=` |
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`

.

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
#
``` |

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

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