# 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

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 |

### 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

1 2 3 4 5 6 7 8 |