org.apache.commons.statistics.descriptive.IntStandardDeviation Maven / Gradle / Ivy
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* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
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*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
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* See the License for the specific language governing permissions and
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*/
package org.apache.commons.statistics.descriptive;
/**
* Computes the standard deviation of the available values. The default implementation uses the
* following definition of the sample standard deviation:
*
* \[ \sqrt{ \tfrac{1}{n-1} \sum_{i=1}^n (x_i-\overline{x})^2 } \]
*
*
where \( \overline{x} \) is the sample mean, and \( n \) is the number of samples.
*
*
* - The result is {@code NaN} if no values are added.
*
- The result is zero if there is one value in the data set.
*
*
* The use of the term \( n − 1 \) is called Bessel's correction. Omitting the square root,
* this provides an unbiased estimator of the variance of a hypothetical infinite population. If the
* {@link #setBiased(boolean) biased} option is enabled the normalisation factor is
* changed to \( \frac{1}{n} \) for a biased estimator of the sample variance.
* Note however that square root is a concave function and thus introduces negative bias
* (by Jensen's inequality), which depends on the distribution, and thus the corrected sample
* standard deviation (using Bessel's correction) is less biased, but still biased.
*
*
The implementation uses an exact integer sum to compute the scaled (by \( n \))
* sum of squared deviations from the mean; this is normalised by the scaled correction factor.
*
*
\[ \frac {n \times \sum_{i=1}^n x_i^2 - (\sum_{i=1}^n x_i)^2}{n \times (n - 1)} \]
*
*
Supports up to 263 (exclusive) observations.
* This implementation does not check for overflow of the count.
*
*
This class is designed to work with (though does not require)
* {@linkplain java.util.stream streams}.
*
*
This implementation is not thread safe.
* If multiple threads access an instance of this class concurrently,
* and at least one of the threads invokes the {@link java.util.function.IntConsumer#accept(int) accept} or
* {@link StatisticAccumulator#combine(StatisticResult) combine} method, it must be synchronized externally.
*
*
However, it is safe to use {@link java.util.function.IntConsumer#accept(int) accept}
* and {@link StatisticAccumulator#combine(StatisticResult) combine}
* as {@code accumulator} and {@code combiner} functions of
* {@link java.util.stream.Collector Collector} on a parallel stream,
* because the parallel implementation of {@link java.util.stream.Stream#collect Stream.collect()}
* provides the necessary partitioning, isolation, and merging of results for
* safe and efficient parallel execution.
*
* @see Standard deviation (Wikipedia)
* @see Bessel's correction
* @see Jensen's inequality
* @see IntVariance
* @since 1.1
*/
public final class IntStandardDeviation implements IntStatistic, StatisticAccumulator {
/** Sum of the squared values. */
private final UInt128 sumSq;
/** Sum of the values. */
private final Int128 sum;
/** Count of values that have been added. */
private long n;
/** Flag to control if the statistic is biased, or should use a bias correction. */
private boolean biased;
/**
* Create an instance.
*/
private IntStandardDeviation() {
this(UInt128.create(), Int128.create(), 0);
}
/**
* Create an instance.
*
* @param sumSq Sum of the squared values.
* @param sum Sum of the values.
* @param n Count of values that have been added.
*/
private IntStandardDeviation(UInt128 sumSq, Int128 sum, int n) {
this.sumSq = sumSq;
this.sum = sum;
this.n = n;
}
/**
* Creates an instance.
*
* The initial result is {@code NaN}.
*
* @return {@code IntStandardDeviation} instance.
*/
public static IntStandardDeviation create() {
return new IntStandardDeviation();
}
/**
* Returns an instance populated using the input {@code values}.
*
* @param values Values.
* @return {@code IntStandardDeviation} instance.
*/
public static IntStandardDeviation of(int... values) {
// Small arrays can be processed using the object
if (values.length < IntVariance.SMALL_SAMPLE) {
final IntStandardDeviation stat = new IntStandardDeviation();
for (final int x : values) {
stat.accept(x);
}
return stat;
}
// Arrays can be processed using specialised counts knowing the maximum limit
// for an array is 2^31 values.
long s = 0;
final UInt96 ss = UInt96.create();
// Process pairs as we know two maximum value int^2 will not overflow
// an unsigned long.
final int end = values.length & ~0x1;
for (int i = 0; i < end; i += 2) {
final long x = values[i];
final long y = values[i + 1];
s += x + y;
ss.addPositive(x * x + y * y);
}
if (end < values.length) {
final long x = values[end];
s += x;
ss.addPositive(x * x);
}
// Convert
return new IntStandardDeviation(UInt128.of(ss), Int128.of(s), values.length);
}
/**
* Updates the state of the statistic to reflect the addition of {@code value}.
*
* @param value Value.
*/
@Override
public void accept(int value) {
sumSq.addPositive((long) value * value);
sum.add(value);
n++;
}
/**
* Gets the standard deviation of all input values.
*
*
When no values have been added, the result is {@code NaN}.
*
* @return standard deviation of all values.
*/
@Override
public double getAsDouble() {
return IntVariance.computeVarianceOrStd(sumSq, sum, n, biased, true);
}
@Override
public IntStandardDeviation combine(IntStandardDeviation other) {
sumSq.add(other.sumSq);
sum.add(other.sum);
n += other.n;
return this;
}
/**
* Sets the value of the biased flag. The default value is {@code false}. The bias
* term refers to the computation of the variance; the standard deviation is returned
* as the square root of the biased or unbiased sample variance. For further
* details see {@link IntVariance#setBiased(boolean) IntVarianceVariance.setBiased}.
*
*
This flag only controls the final computation of the statistic. The value of
* this flag will not affect compatibility between instances during a
* {@link #combine(IntStandardDeviation) combine} operation.
*
* @param v Value.
* @return {@code this} instance
* @see IntVariance#setBiased(boolean)
*/
public IntStandardDeviation setBiased(boolean v) {
biased = v;
return this;
}
}