Statistics (Apache SIS 0.8 API)

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 approximatively 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

Defined in the sis-utility module

Constructor Summary

Constructors
Constructor and Description

Statistics(CharSequence name)
Constructs an initially empty set of statistics.

Constructors
Constructor and Description
`Statistics(CharSequence name)` Constructs an initially empty set of statistics.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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

- Constructor Detail
  - 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, then this name will be shown as column header in the table formatted by StatisticsFormat.
- Method Detail
  - 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 can not 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.
    
    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).
    
    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.

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%

Class Statistics

Constructor Summary

Method Summary

Methods inherited from class Object

Constructor Detail

Statistics

Method Detail

forSeries

name

reset

accept

accept

combine

scale

countNaN

count

minimum

maximum

span

sum

mean

rms

standardDeviation

differences

toString

clone

hashCode

equals