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author | Eric Wieser <wieser.eric@gmail.com> | 2018-03-16 07:46:49 (GMT) |
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committer | Eric Wieser <wieser.eric@gmail.com> | 2018-03-16 07:49:05 (GMT) |

commit | 7a3db4909498a40bdeec44c9626924e37c51ed12 (patch) | |

tree | ec575bc95d86dad9aa0c05a9f60d0a546606a90c | |

parent | f42e10405f2354e1776f89402ceae0ad0ab637bb (diff) | |

download | python-numpy-7a3db4909498a40bdeec44c9626924e37c51ed12.zip python-numpy-7a3db4909498a40bdeec44c9626924e37c51ed12.tar.gz python-numpy-7a3db4909498a40bdeec44c9626924e37c51ed12.tar.bz2 |

DOC: Move bin estimator documentation from `histogram` to `histogram_bin_edges`

-rw-r--r-- | numpy/lib/histograms.py | 182 |

1 files changed, 75 insertions, 107 deletions

diff --git a/numpy/lib/histograms.py b/numpy/lib/histograms.py index f151a60..7329246 100644 --- a/numpy/lib/histograms.py +++ b/numpy/lib/histograms.py @@ -425,6 +425,76 @@ def histogram_bin_edges(a, bins=10, range=None, weights=None): -------- histogram + Notes + ----- + The methods to estimate the optimal number of bins are well founded + in literature, and are inspired by the choices R provides for + histogram visualisation. Note that having the number of bins + proportional to :math:`n^{1/3}` is asymptotically optimal, which is + why it appears in most estimators. These are simply plug-in methods + that give good starting points for number of bins. In the equations + below, :math:`h` is the binwidth and :math:`n_h` is the number of + bins. All estimators that compute bin counts are recast to bin width + using the `ptp` of the data. The final bin count is obtained from + ``np.round(np.ceil(range / h))`. + + 'Auto' (maximum of the 'Sturges' and 'FD' estimators) + A compromise to get a good value. For small datasets the Sturges + value will usually be chosen, while larger datasets will usually + default to FD. Avoids the overly conservative behaviour of FD + and Sturges for small and large datasets respectively. + Switchover point is usually :math:`a.size \approx 1000`. + + 'FD' (Freedman Diaconis Estimator) + .. math:: h = 2 \frac{IQR}{n^{1/3}} + + The binwidth is proportional to the interquartile range (IQR) + and inversely proportional to cube root of a.size. Can be too + conservative for small datasets, but is quite good for large + datasets. The IQR is very robust to outliers. + + 'Scott' + .. math:: h = \sigma \sqrt[3]{\frac{24 * \sqrt{\pi}}{n}} + + The binwidth is proportional to the standard deviation of the + data and inversely proportional to cube root of ``x.size``. Can + be too conservative for small datasets, but is quite good for + large datasets. The standard deviation is not very robust to + outliers. Values are very similar to the Freedman-Diaconis + estimator in the absence of outliers. + + 'Rice' + .. math:: n_h = 2n^{1/3} + + The number of bins is only proportional to cube root of + ``a.size``. It tends to overestimate the number of bins and it + does not take into account data variability. + + 'Sturges' + .. math:: n_h = \log _{2}n+1 + + The number of bins is the base 2 log of ``a.size``. This + estimator assumes normality of data and is too conservative for + larger, non-normal datasets. This is the default method in R's + ``hist`` method. + + 'Doane' + .. math:: n_h = 1 + \log_{2}(n) + + \log_{2}(1 + \frac{|g_1|}{\sigma_{g_1}}) + + g_1 = mean[(\frac{x - \mu}{\sigma})^3] + + \sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}} + + An improved version of Sturges' formula that produces better + estimates for non-normal datasets. This estimator attempts to + account for the skew of the data. + + 'Sqrt' + .. math:: n_h = \sqrt n + The simplest and fastest estimator. Only takes into account the + data size. + Examples -------- >>> arr = np.array([0, 0, 0, 1, 2, 3, 3, 4, 5]) @@ -489,44 +559,8 @@ def histogram(a, bins=10, range=None, normed=False, weights=None, .. versionadded:: 1.11.0 - If `bins` is a string from the list below, `histogram` will use - the method chosen to calculate the optimal bin width and - consequently the number of bins (see `Notes` for more detail on - the estimators) from the data that falls within the requested - range. While the bin width will be optimal for the actual data - in the range, the number of bins will be computed to fill the - entire range, including the empty portions. For visualisation, - using the 'auto' option is suggested. Weighted data is not - supported for automated bin size selection. - - 'auto' - Maximum of the 'sturges' and 'fd' estimators. Provides good - all around performance. - - 'fd' (Freedman Diaconis Estimator) - Robust (resilient to outliers) estimator that takes into - account data variability and data size. - - 'doane' - An improved version of Sturges' estimator that works better - with non-normal datasets. - - 'scott' - Less robust estimator that that takes into account data - variability and data size. - - 'rice' - Estimator does not take variability into account, only data - size. Commonly overestimates number of bins required. - - 'sturges' - R's default method, only accounts for data size. Only - optimal for gaussian data and underestimates number of bins - for large non-gaussian datasets. - - 'sqrt' - Square root (of data size) estimator, used by Excel and - other programs for its speed and simplicity. + If `bins` is a string, it defines the method used to calculate the + optimal bin width, as defined by `histogram_bin_edges`. range : (float, float), optional The lower and upper range of the bins. If not provided, range @@ -537,6 +571,9 @@ def histogram(a, bins=10, range=None, normed=False, weights=None, based on the actual data within `range`, the bin count will fill the entire range including portions containing no data. normed : bool, optional + + .. deprecated:: 1.6.0 + This keyword is deprecated in NumPy 1.6.0 due to confusing/buggy behavior. It will be removed in NumPy 2.0.0. Use the ``density`` keyword instead. If ``False``, the result will contain the @@ -585,75 +622,6 @@ def histogram(a, bins=10, range=None, normed=False, weights=None, the second ``[2, 3)``. The last bin, however, is ``[3, 4]``, which *includes* 4. - .. versionadded:: 1.11.0 - - The methods to estimate the optimal number of bins are well founded - in literature, and are inspired by the choices R provides for - histogram visualisation. Note that having the number of bins - proportional to :math:`n^{1/3}` is asymptotically optimal, which is - why it appears in most estimators. These are simply plug-in methods - that give good starting points for number of bins. In the equations - below, :math:`h` is the binwidth and :math:`n_h` is the number of - bins. All estimators that compute bin counts are recast to bin width - using the `ptp` of the data. The final bin count is obtained from - ``np.round(np.ceil(range / h))`. - - 'Auto' (maximum of the 'Sturges' and 'FD' estimators) - A compromise to get a good value. For small datasets the Sturges - value will usually be chosen, while larger datasets will usually - default to FD. Avoids the overly conservative behaviour of FD - and Sturges for small and large datasets respectively. - Switchover point is usually :math:`a.size \approx 1000`. - - 'FD' (Freedman Diaconis Estimator) - .. math:: h = 2 \frac{IQR}{n^{1/3}} - - The binwidth is proportional to the interquartile range (IQR) - and inversely proportional to cube root of a.size. Can be too - conservative for small datasets, but is quite good for large - datasets. The IQR is very robust to outliers. - - 'Scott' - .. math:: h = \sigma \sqrt[3]{\frac{24 * \sqrt{\pi}}{n}} - - The binwidth is proportional to the standard deviation of the - data and inversely proportional to cube root of ``x.size``. Can - be too conservative for small datasets, but is quite good for - large datasets. The standard deviation is not very robust to - outliers. Values are very similar to the Freedman-Diaconis - estimator in the absence of outliers. - - 'Rice' - .. math:: n_h = 2n^{1/3} - - The number of bins is only proportional to cube root of - ``a.size``. It tends to overestimate the number of bins and it - does not take into account data variability. - - 'Sturges' - .. math:: n_h = \log _{2}n+1 - - The number of bins is the base 2 log of ``a.size``. This - estimator assumes normality of data and is too conservative for - larger, non-normal datasets. This is the default method in R's - ``hist`` method. - - 'Doane' - .. math:: n_h = 1 + \log_{2}(n) + - \log_{2}(1 + \frac{|g_1|}{\sigma_{g_1}}) - - g_1 = mean[(\frac{x - \mu}{\sigma})^3] - - \sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}} - - An improved version of Sturges' formula that produces better - estimates for non-normal datasets. This estimator attempts to - account for the skew of the data. - - 'Sqrt' - .. math:: n_h = \sqrt n - The simplest and fastest estimator. Only takes into account the - data size. Examples -------- |