python - How to qcut with non unique bin edges?

Question

My question is the same as this previous one:

Binning with zero values in pandas

however, I still want to include the 0 values in a fractile. Is there a way to do this? In other words, if I have 600 values, 50% of which are 0, and the rest are let's say between 1 and 100, how would I categorize all the 0 values in fractile 1, and then the rest of the non-zero values in fractile labels 2 to 10 (assuming I want 10 fractiles). Could I convert the 0's to nan, qcut the remaining non nan data into 9 fractiles (1 to 9), then add 1 to each label (now 2 to 10) and label all the 0 values as fractile 1 manually? Even this is tricky, because in my data set in addition to the 600 values, I also have another couple hundred which may already be nan before I would convert the 0s to nan.

Update 1/26/14:

I came up with the following interim solution. The problem with this code though, is if the high frequency value is not on the edges of the distribution, then it inserts an extra bin in the middle of the existing set of bins and throws everything a little (or a lot) off.

def fractile_cut(ser, num_fractiles):
    num_valid = ser.valid().shape[0]
    remain_fractiles = num_fractiles
    vcounts = ser.value_counts()
    high_freq = []
    i = 0
    while vcounts.iloc[i] > num_valid/ float(remain_fractiles):
        curr_val = vcounts.index[i]
        high_freq.append(curr_val)
        remain_fractiles -= 1
        num_valid = num_valid - vcounts[i]
        i += 1
    curr_ser = ser.copy()
    curr_ser = curr_ser[~curr_ser.isin(high_freq)]
    qcut = pd.qcut(curr_ser, remain_fractiles, retbins=True)
    qcut_bins = qcut[1]
    all_bins = list(qcut_bins)
    for val in high_freq:
        bisect.insort(all_bins, val)
    cut = pd.cut(ser, bins=all_bins)
    ser_fractiles = pd.Series(cut.labels + 1, index=ser.index)
    return ser_fractiles

Answer 1

The problem is that pandas.qcut chooses the bins/quantiles so that each one has the same number of records, but all records with the same value must stay in the same bin/quantile (this behaviour is in accordance with the statistical definition of quantile).

The solutions are:

1 - Use pandas >= 0.20.0 that has this fix. They added an option duplicates='raise'|'drop' to control whether to raise on duplicated edges or to drop them, which would result in less bins than specified, and some larger (with more elements) than others.

2 - Decrease the number of quantiles. Less quantiles means more elements per quantile

3 - Rank your data with DataFrame.rank(method='first'). The ranking assigns a unique value to each element in the dataframe (the rank) while keeping the order of the elements (except for identical values, which will be ranked in order they appear in the array, see method='first')

Example:

pd.qcut(df, nbins) <-- this generates "ValueError: Bin edges must be unique"

Then use this instead:

pd.qcut(df.rank(method='first'), nbins)

4 - Specify a custom quantiles range, e.g. [0, .50, .75, 1.] to get unequal number of items per quantile

5 - Use pandas.cut that chooses the bins to be evenly spaced according to the values themselves, while pandas.qcut chooses the bins so that you have the same number of records in each bin