Axibase Time Series Database
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Aggregation

Statistical Functions

Name Description
MIN Minimum value.
MAX Maximum value.
AVG Average value.
SUM Sum of values.
COUNT Count of values.
FIRST First value.
LAST Last value.
DELTA Difference between the last and the first value.
COUNTER Sum of positive differences between consecutive values.
PERCENTILE(n) n-th percentile, for example PERCENTILE(75) or PERCENTILE(99.5).
n is a decimal number between [0, 100].
MEDIAN Median value, same as 50% percentile.
STANDARD_DEVIATION Standard deviation calculated as an unbiased estimator of variance for the n - 1 sample.
MEDIAN_ABS_DEV Median absolute deviation calculated as median(abs(value - median(value))).
SLOPE Linear regression slope.
INTERCEPT Linear regression intercept.
WAVG Weighted average.
WTAVG Weighted time average.
THRESHOLD_COUNT Number of threshold violations.
THRESHOLD_DURATION Cumulative duration of threshold violations.
THRESHOLD_PERCENT Percentage which violate threshold.
MIN_VALUE_TIME Unix time in milliseconds of the first maximum value.
MAX_VALUE_TIME Unix time in milliseconds of the first minimum value.

References

For more details on unbiased estimator and median absolute deviation refer to NIST Engineering Handbook, sections 6.3.2 and 3.5.6 respectively.

Implementation Notes

General

The descriptive statistics are calculated for all samples in the given period. If the period contains no samples, the statistic is not calculated and is not included in the response.

COUNT

Like other functions, COUNT is not calculated if the period contains no samples. Specifically, it does not return zero values for empty periods.

DELTA

The DELTA function returns the difference between the last value in the current period and the last value in the previous period.

  • If the previous period contains no values, the function is calculated as the difference between the last and the first value in the current period.
  • If there is only one value in the current period and the previous period is empty, the function returns null which is included in the response.

COUNTER

The COUNTER function returns the sum of positive differences between consecutive samples in the current period starting with the last value in the previous period.

  • If the previous period contains no values, the calculation starts with the first value in the current period.
  • If there is only one value in the current period and the previous period is empty, the function returns null which is included in the response.
  • If all the differences between consecutive samples are non-negative, the result of the COUNTER function is equal to the DELTA function.

STANDARD_DEVIATION

Standard deviation is calculated as an unbiased estimator of variance for the n - 1 sample as described in the NIST Engineering Handbook, Section 6.3.2.

References

For more details on unbiased estimator and median absolute deviation refer to NIST Engineering Handbook, sections 6.3.2 and 3.5.6 respectively.

PERCENTILE

  • The percentile(n) function returns the number which is greater than the specified percentage n of values in the given period.
  • The n parameter must be within the [0, 100] range.
  • PERCENTILE(100) = MAX.
  • PERCENTILE(97.5) is equal to 97.5% percentile.
  • PERCENTILE(50) = MEDIAN.
  • PERCENTILE(0) = MIN.
  • The function implements the R6 method as described in the NIST Engineering Handbook, Section 2.6.2, which uses N+1 as the array size (N is the number of samples in the period) and performs linear interpolation between consecutive values.
  • NaN values are ignored from the input array.