[STATISTICS-81] Implement descriptive statistics for integer types

• Type: Improvement
• Status: Open
• Priority: Minor
• Resolution: Unresolved
• Component/s: descriptive
• difficulty-level: Easy
• Assignee: Unassigned
• Reporter: Alex Herbert
• Created: 14/Dec/23 15:43
• Updated: 01/Jan/24 10:07

Description

The descriptive module defines the DoubleStatistic as a composite interface:

public interface DoubleStatistic extends DoubleConsumer, DoubleSupplier

The implementations compute on a stream of double values, and provide factory methods to compute on a double[].

The moment based statistics use a rolling algorithm for numerical stability. The moment based statistics (mean, variance, skewness, kurtosis) perform a double pass computation over array data.

Several of the statistics can be efficiently computed for integer types using different algorithms. For example:

mean = sum(x) / n
variance = 1/n * [ sum(x^2) - (sum(x))^2 / n ]

These can operate using a single-pass and are not subject to loss of precision if the sums are accumulated with enough integer bits of precision. For a stream the sums must be able to accept up to 2^63 observations. In the case of an array the maximum number of observations is ~2^31 allowing some optimisation. Sums can avoid using BigInteger with special implementations of signed and unsigned summation arithmetic. The final statistic can be computed using extended floating-point precision (e.g. double-double).

 

Issue Links

• is a child of: STATISTICS-71 Implementation of Univariate Statistics