Accord.NET Framework

## QuantileMethod Enumeration |

Different methods for computing quantiles.

Syntax

Members

Member name | Value | Description | |
---|---|---|---|

Default | 6 | The default quantile method in the framework (6). | |

R | 7 | The default method in R (7). | |

Maple | 8 | The dafault method in Maple (8). | |

Type1 | 1 | Inverse of empirical distribution function. Equivalent types in other packages: R: 1, SAS: 3, Maple: 1. | |

Type2 | 2 | The same as R-1, but with averaging at discontinuities. Equivalent types in other packages: R: 2, SAS: 5, Maple: 2. | |

Type3 | 3 | The observation numbered closest to Np. Equivalent types in other packages: R: 3, SAS: 2. | |

Type4 | 4 | Linear interpolation of the empirical distribution function. Equivalent types in other packages: R: 4, SAS: 1, SciPy: (0,1), Maple: 3. | |

Type5 | 5 | Piecewise linear function where the knots are the values midway through the steps of the empirical distribution function. R-5, SciPy-(.5,.5), Maple-4. | |

Type6 | 6 | Linear interpolation of the expectations for the order statistics for the uniform distribution on [0,1]. That is, it is the linear interpolation between points (ph, xh), where ph = h / (N + 1) is the probability that the last of (N+1) randomly drawn values will not exceed the h-th smallest of the first N randomly drawn values. Equivalence to other packages: R-6, Excel, SAS-4, SciPy-(0,0), Maple-5. | |

Type7 | 7 | Linear interpolation of the modes for the order statistics for the uniform distribution on [0,1]. Equivalence to other packages: R: 7, Excel, SciPy: (1,1), Maple: 6. | |

Type8 | 8 | Linear interpolation of the approximate medians for order statistics. Equivalence to other packages: R: 8, SciPy: (1/3,1/3), Maple: 7. | |

Type9 | 9 | The resulting quantile estimates are approximately unbiased for the expected order statistics if x is normally distributed. Equivalence to other packages: R: 9, SciPy: (3/8,3/8), Maple: 8. |

Remarks

When one has a sample drawn from an unknown population, the cumulative distribution function and quantile function of the underlying population are not known and the task becomes that of estimating the quantiles. There are several methods. Mathematica, Matlab, R and GNU Octave programming languages include nine sample quantile methods.SAS includes five sample quantile methods, SciPy and Maple both include eight, EViews includes the six piecewise linear functions, STATA includes two, and Microsoft Excel includes two. Mathematica supports an arbitrary parameter for methods that allows for other, non-standard, methods.

References:

See Also