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A parent pipeline aggregation which calculates the derivative of a specified metric in a parent histogram (or date_histogram)
aggregation. The specified metric must be numeric and the enclosing histogram must have min_doc_count
set to 0
(default
for histogram
aggregations).
A derivative
aggregation looks like this in isolation:
"derivative": { "buckets_path": "the_sum" }
Table 7. derivative
Parameters
Parameter Name  Description  Required  Default Value 

 The path to the buckets we wish to find the derivative for (see  Required  
 The policy to apply when gaps are found in the data (see Dealing with gaps in the data for more details)  Optional 

 format to apply to the output value of this aggregation  Optional 

The following snippet calculates the derivative of the total monthly sales
:
POST /sales/_search { "size": 0, "aggs" : { "sales_per_month" : { "date_histogram" : { "field" : "date", "calendar_interval" : "month" }, "aggs": { "sales": { "sum": { "field": "price" } }, "sales_deriv": { "derivative": { "buckets_path": "sales" } } } } } }

And the following may be the response:
{ "took": 11, "timed_out": false, "_shards": ..., "hits": ..., "aggregations": { "sales_per_month": { "buckets": [ { "key_as_string": "2015/01/01 00:00:00", "key": 1420070400000, "doc_count": 3, "sales": { "value": 550.0 } }, { "key_as_string": "2015/02/01 00:00:00", "key": 1422748800000, "doc_count": 2, "sales": { "value": 60.0 }, "sales_deriv": { "value": 490.0 } }, { "key_as_string": "2015/03/01 00:00:00", "key": 1425168000000, "doc_count": 2, "sales": { "value": 375.0 }, "sales_deriv": { "value": 315.0 } } ] } } }
No derivative for the first bucket since we need at least 2 data points to calculate the derivative  
Derivative value units are implicitly defined by the  
The number of documents in the bucket are represented by the 
A second order derivative can be calculated by chaining the derivative pipeline aggregation onto the result of another derivative pipeline aggregation as in the following example which will calculate both the first and the second order derivative of the total monthly sales:
POST /sales/_search { "size": 0, "aggs" : { "sales_per_month" : { "date_histogram" : { "field" : "date", "calendar_interval" : "month" }, "aggs": { "sales": { "sum": { "field": "price" } }, "sales_deriv": { "derivative": { "buckets_path": "sales" } }, "sales_2nd_deriv": { "derivative": { "buckets_path": "sales_deriv" } } } } } }
And the following may be the response:
{ "took": 50, "timed_out": false, "_shards": ..., "hits": ..., "aggregations": { "sales_per_month": { "buckets": [ { "key_as_string": "2015/01/01 00:00:00", "key": 1420070400000, "doc_count": 3, "sales": { "value": 550.0 } }, { "key_as_string": "2015/02/01 00:00:00", "key": 1422748800000, "doc_count": 2, "sales": { "value": 60.0 }, "sales_deriv": { "value": 490.0 } }, { "key_as_string": "2015/03/01 00:00:00", "key": 1425168000000, "doc_count": 2, "sales": { "value": 375.0 }, "sales_deriv": { "value": 315.0 }, "sales_2nd_deriv": { "value": 805.0 } } ] } } }
The derivative aggregation allows the units of the derivative values to be specified. This returns an extra field in the response
normalized_value
which reports the derivative value in the desired xaxis units. In the below example we calculate the derivative
of the total sales per month but ask for the derivative of the sales as in the units of sales per day:
POST /sales/_search { "size": 0, "aggs" : { "sales_per_month" : { "date_histogram" : { "field" : "date", "calendar_interval" : "month" }, "aggs": { "sales": { "sum": { "field": "price" } }, "sales_deriv": { "derivative": { "buckets_path": "sales", "unit": "day" } } } } } }
And the following may be the response:
{ "took": 50, "timed_out": false, "_shards": ..., "hits": ..., "aggregations": { "sales_per_month": { "buckets": [ { "key_as_string": "2015/01/01 00:00:00", "key": 1420070400000, "doc_count": 3, "sales": { "value": 550.0 } }, { "key_as_string": "2015/02/01 00:00:00", "key": 1422748800000, "doc_count": 2, "sales": { "value": 60.0 }, "sales_deriv": { "value": 490.0, "normalized_value": 15.806451612903226 } }, { "key_as_string": "2015/03/01 00:00:00", "key": 1425168000000, "doc_count": 2, "sales": { "value": 375.0 }, "sales_deriv": { "value": 315.0, "normalized_value": 11.25 } } ] } } }