Module org.apache.sis.util

Package org.apache.sis.math

Class Statistics

Object

Statistics

All Implemented Interfaces:

Serializable, Cloneable, Double­Consumer, Long­Consumer

public class Statistics
extends Object
implements DoubleConsumer, LongConsumer, Cloneable, Serializable

Holds some statistics derived from a series of sample values. Given a series of y₀, y₁, y₂, y₃, etc… samples, this class computes the minimum, maximum, mean, root mean square and standard deviation of the given samples.

In addition to the statistics on the sample values, this class can optionally compute statistics on the differences between consecutive sample values, i.e. the statistics on y₁-y₀, y₂-y₁, y₃-y₂, etc…, Those statistics can be fetched by a call to differences(). They are useful for verifying if the interval between sample values is approximately constant.

If the samples are (at least conceptually) the result of some y=f(x) function for x values increasing or decreasing at a constant interval Δx, then one can get the statistics on the discrete derivatives by a call to differences().scale(1/Δx).

Statistics are computed on the fly using the Kahan summation algorithm for reducing the numerical errors; the sample values are never stored in memory.

An instance of Statistics is initially empty: the count of values is set to zero, and all above-cited statistical values are set to Na­N. The statistics are updated every time an accept(double) method is invoked with a non-NaN value.

Examples

The following examples assume that a y=f(x) function is defined. A simple usage is:

Statistics stats = new Statistics("y");
for (int i=0; i<numberOfValues; i++) {
    stats.accept(f(i));
}
System.out.println(stats);

Following example computes the statistics on the first and second derivatives in addition to the statistics on the sample values:

final double x₀ = ...; // Put here the x value at i=0
final double Δx = ...; // Put here the interval between x values
Statistics stats = Statistics.forSeries("y", "∂y/∂x", "∂²y/∂x²");
for (int i=0; i<numberOfValues; i++) {
    stats.accept(f(x₀ + i*Δx));
}
stats.differences().scale(1/Δx);
System.out.println(stats);

Since:

0.3

See Also:

• Serialized Form

Constructor Summary

Constructors

Constructor	Description
Statistics(Char­Sequence name)	Constructs an initially empty set of statistics.
Statistics(Char­Sequence name, int count­Na­N, int count, double minimum, double maximum, double mean, double standard­Deviation, boolean all­Population)	Constructs a set of statistics initialized to the given values.

Method Summary

Modifier and Type	Method	Description
void	accept(double sample)	Updates statistics for the specified floating-point sample value.
void	accept(long sample)	Updates statistics for the specified integer sample value.
Statistics	clone()	Returns a clone of this statistics.
void	combine(Statistics stats)	Updates statistics with all samples from the specified stats.
int	count()	Returns the number of samples, excluding Na­N values.
int	count­Na­N()	Returns the number of Na­N samples.
Statistics	differences()	Returns the statistics on the differences between sample values, or null if none.
boolean	equals(Object object)	Compares this statistics with the specified object for equality.
static Statistics	for­Series(Char­Sequence name, Char­Sequence... difference­Names)	Constructs a new Statistics object which will also compute finite differences up to the given order.
int	hash­Code()	Returns a hash code value for this statistics.
double	maximum()	Returns the maximum sample value, or Na­N if none.
double	mean()	Returns the mean value, or Na­N if none.
double	minimum()	Returns the minimum sample value, or Na­N if none.
International­String	name()	Returns the name of the phenomenon for which this object is collecting statistics.
void	reset()	Resets this object state as if it was just created.
double	rms()	Returns the root mean square, or Na­N if none.
void	scale(double factor)	Multiplies the statistics by the given factor.
double	span()	Equivalents to maximum - minimum.
double	standard­Deviation(boolean all­Population)	Returns the standard deviation.
double	sum()	Returns the sum, or 0 if none.
String	to­String()	Returns a string representation of this statistics.

Methods inherited from class Object

finalize, get­Class, notify, notify­All, wait, wait, wait

Methods inherited from interface DoubleConsumer

and­Then

Methods inherited from interface LongConsumer

and­Then

Constructor Details

Statistics

public Statistics(CharSequence name)

Constructs an initially empty set of statistics. The count() and the sum() are initialized to zero and all other statistical values are initialized to Double.Na­N.

Instances created by this constructor do not compute differences between sample values. If differences or discrete derivatives are wanted, use the for­Series(…) method instead.

Parameters:

name - the phenomenon for which this object is collecting statistics, or null if none. If non-null, it will be shown as column header in the table formatted by Statistics­Format.

Statistics

public Statistics(CharSequence name,
 int countNaN,
 int count,
 double minimum,
 double maximum,
 double mean,
 double standardDeviation,
 boolean allPopulation)

Constructs a set of statistics initialized to the given values. The count­Na­N and count arguments must be positive. If count is 0, all following double arguments are ignored. Otherwise the following restrictions apply:

• minimum and maximum arguments are mandatory and cannot be Na­N.
• mean argument is mandatory (cannot be NaN) if standard­Deviation is not NaN.
• mean and standard­Deviation arguments can be both Na­N if unknown, but statistics initialized that way will always return NaN from sum(), mean(), rms() and standard­Deviation(boolean) methods.

Parameters:

name - the phenomenon for which this object is collecting statistics, or null if none.

count­Na­N - the number of Na­N samples.

count - the number of samples, excluding Na­N values.

minimum - the minimum sample value. Ignored if count is zero.

maximum - the maximum sample value. Ignored if count is zero.

mean - the mean value. Ignored if count is zero.

standard­Deviation - the standard deviation. Ignored if count is zero.

all­Population - true if sample values were the totality of the population under study, or false if they were only a sampling.

Since:

1.2

Method Details

forSeries

public static Statistics forSeries(CharSequence name,
 CharSequence... differenceNames)

Constructs a new Statistics object which will also compute finite differences up to the given order. If the values to be given to the accept(…) methods are the y values of some y=f(x) function for x values increasing or decreasing at a constant interval Δx, then the finite differences are proportional to discrete derivatives.

The Statistics object created by this method know nothing about the Δx interval. In order to get the discrete derivatives, the following method needs to be invoked after all sample values have been added:

statistics.differences().scale(1/Δx);

The maximal "derivative" order is determined by the length of the difference­Names array:

• 0 if no differences are needed (equivalent to direct instantiation of a new Statistics object).
• 1 for computing the statistics on the differences between consecutive samples (proportional to the statistics on the first discrete derivatives) in addition to the sample statistics.
• 2 for computing also the statistics on the differences between consecutive differences (proportional to the statistics on the second discrete derivatives) in addition to the above.
• etc.

Parameters:

name - the phenomenon for which this object is collecting statistics, or null if none. If non-null, then this name will be shown as column header in the table formatted by Statistics­Format.

difference­Names - the names of the statistics on differences. The given array cannot be null, but can contain null elements.

Returns:

the newly constructed, initially empty, set of statistics.

See Also:

• differences()

name

public InternationalString name()

Returns the name of the phenomenon for which this object is collecting statistics. If non-null, then this name will be shown as column header in the table formatted by Statistics­Format.

Returns:

the phenomenon for which this object is collecting statistics, or null if none.

reset

public void reset()

Resets this object state as if it was just created. The count() and the sum() are set to zero and all other statistical values are set to Double.Na­N.

accept

public void accept(double sample)

Updates statistics for the specified floating-point sample value. Na­N values increment the NaN count, but are otherwise ignored.

Specified by:

accept in interface Double­Consumer

Parameters:

sample - the sample value (may be NaN).

See Also:

• accept(long)
• combine(Statistics)

accept

public void accept(long sample)

Updates statistics for the specified integer sample value. For very large integer values (greater than 2⁵² in magnitude), this method may be more accurate than the accept(double) version.

Specified by:

accept in interface Long­Consumer

Parameters:

sample - the sample value.

See Also:

• accept(double)
• combine(Statistics)

combine

public void combine(Statistics stats)

Updates statistics with all samples from the specified stats. Invoking this method is equivalent (except for rounding errors) to invoking accept(…) for all samples that were added to stats.

Parameters:

stats - the statistics to be added to this.

scale

public void scale(double factor)

Multiplies the statistics by the given factor. The given scale factory is also applied recursively on the differences statistics, if any. Invoking this method transforms the statistics as if every values given to the accept(…) had been first multiplied by the given factor.

This method is useful for computing discrete derivatives from the differences between sample values. See differences() or for­Series(…) for more information.

Parameters:

factor - the factor by which to multiply the statistics.

countNaN

public int countNaN()

Returns the number of Na­N samples. Na­N samples are ignored in all other statistical computation. This method count them for information purpose only.

Returns:

the number of NaN values.

count

public int count()

Returns the number of samples, excluding Na­N values.

Returns:

the number of sample values, excluding NaN.

minimum

public double minimum()

Returns the minimum sample value, or Na­N if none.

Returns:

the minimum sample value, or NaN if none.

maximum

public double maximum()

Returns the maximum sample value, or Na­N if none.

Returns:

the maximum sample value, or NaN if none.

span

public double span()

Equivalents to maximum - minimum. If no samples were added, then returns Na­N.

Returns:

the span of sample values, or NaN if none.

sum

public double sum()

Returns the sum, or 0 if none. May also be NaN if that value was explicitly specified to the constructor.

Returns:

the sum, or 0 if none.

mean

public double mean()

Returns the mean value, or Na­N if none.

Returns:

the mean value, or NaN if none.

rms

public double rms()

Returns the root mean square, or Na­N if none.

Returns:

the root mean square, or NaN if none.

standardDeviation

public double standardDeviation(boolean allPopulation)

Returns the standard deviation. If the sample values given to the accept(…) methods have a uniform distribution, then the returned value should be close to sqrt(span² / 12). If they have a Gaussian distribution (which is the most common case), then the returned value is related to the error function.

As a reminder, the table below gives the probability for a sample value to be inside the mean ± n × deviation range, assuming that the distribution is Gaussian (first column) or assuming that the distribution is uniform (second column).

Probability values for some standard deviations

n	Gaussian	uniform
0.5	69.1%	28.9%
1.0	84.2%	57.7%
1.5	93.3%	86.6%
2.0	97.7%	100%
3.0	99.9%	100%

Parameters:

all­Population - true if sample values given to accept(…) methods were the totality of the population under study, or false if they were only a sampling.

Returns:

the standard deviation.

differences

public Statistics differences()

Returns the statistics on the differences between sample values, or null if none. For example if the sample values given to the accept(…) methods were y₀, y₁, y₂ and y₃, then this method returns statistics on y₁-y₀, y₂-y₁ and y₃-y₂.

The differences between sample values are related to the discrete derivatives as below, where Δx is the constant interval between the x values of the y=f(x) function:

Statistics derivative = statistics.differences();
derivative.scale(1/Δx); // Shall be invoked only once.
Statistics secondDerivative = derivative.differences();
// Do not invoke scale(1/Δx) again.

This method returns a non-null value only if this Statistics instance has been created by a call to the for­Series(…) method with a non-empty difference­Names array. More generally, calls to this method can be chained up to difference­Names.length times for fetching second or higher order derivatives, as in the above example.

Returns:

the statistics on the differences between consecutive sample values, or null if not calculated by this object.

See Also:

• for­Series(Char­Sequence, Char­Sequence[])
• scale(double)

toString

public String toString()

Returns a string representation of this statistics. This string will span multiple lines, one for each statistical value. For example:

     Number of values:     8726
     Minimum value:       6.853
     Maximum value:       8.259
     Mean value:          7.421
     Root Mean Square:    7.846
     Standard deviation:  6.489

Overrides:

to­String in class Object

Returns:

a string representation of this statistics object.

See Also:

• Statistics­Format

clone

public Statistics clone()

Returns a clone of this statistics.

Overrides:

clone in class Object

Returns:

a clone of this statistics.

hashCode

public int hashCode()

Returns a hash code value for this statistics.

Overrides:

hash­Code in class Object

equals

public boolean equals(Object object)

Compares this statistics with the specified object for equality.

Overrides:

equals in class Object

Parameters:

object - the object to compare with.

Returns:

true if both objects are equal.