public class Percentile extends AbstractUnivariateStatistic implements java.io.Serializable
There are several commonly used methods for estimating percentiles (a.k.a. quantiles) based on sample data. For large samples, the different methods agree closely, but when sample sizes are small, different methods will give significantly different results. The algorithm implemented here works as follows:
n
be the length of the (sorted) array and
0 < p <= 100
be the desired percentile. n = 1
return the unique array element (regardless of
the value of p
); otherwise pos = p * (n + 1) / 100
and the difference, d
between pos
and floor(pos)
(i.e. the fractional
part of pos
). If pos >= n
return the largest
element in the array; otherwiselower
be the element in position
floor(pos)
in the array and let upper
be the
next element in the array. Return lower + d * (upper - lower)
To compute percentiles, the data must be (totally) ordered. Input arrays
are copied and then sorted using Arrays.sort(double[])
.
The ordering used by Arrays.sort(double[])
is the one determined
by Double.compareTo(Double)
. This ordering makes
Double.NaN
larger than any other value (including
Double.POSITIVE_INFINITY
). Therefore, for example, the median
(50th percentile) of
{0, 1, 2, 3, 4, Double.NaN}
evaluates to 2.5.
Since percentile estimation usually involves interpolation between array
elements, arrays containing NaN
or infinite values will often
result in NaN
or infinite values returned.
Note that this implementation is not synchronized. If
multiple threads access an instance of this class concurrently, and at least
one of the threads invokes the increment()
or
clear()
method, it must be synchronized externally.
Constructor and Description |
---|
Percentile()
Constructs a Percentile with a default quantile
value of 50.0.
|
Percentile(double p)
Constructs a Percentile with the specific quantile value.
|
Percentile(Percentile original)
Copy constructor, creates a new
Percentile identical
to the original |
Modifier and Type | Method and Description |
---|---|
Percentile |
copy()
Returns a copy of the statistic with the same internal state.
|
static void |
copy(Percentile source,
Percentile dest)
Copies source to dest.
|
double |
evaluate(double[] values,
double p)
Returns an estimate of the
p th percentile of the values
in the values array. |
double |
evaluate(double[] values,
int start,
int length)
Returns an estimate of the
quantile th percentile of the
designated values in the values array. |
double |
evaluate(double[] values,
int begin,
int length,
double p)
Returns an estimate of the
p th percentile of the values
in the values array, starting with the element in (0-based)
position begin in the array and including length
values. |
double |
getQuantile()
Returns the value of the quantile field (determines what percentile is
computed when evaluate() is called with no quantile argument).
|
void |
setQuantile(double p)
Sets the value of the quantile field (determines what percentile is
computed when evaluate() is called with no quantile argument).
|
evaluate, test, test
public Percentile()
public Percentile(double p)
p
- the quantilejava.lang.IllegalArgumentException
- if p is not greater than 0 and less
than or equal to 100public Percentile(Percentile original)
Percentile
identical
to the original
original
- the Percentile
instance to copypublic double evaluate(double[] values, double p)
p
th percentile of the values
in the values
array.
Calls to this method do not modify the internal quantile
state of this statistic.
Double.NaN
if values
has length
0
p
) values[0]
if values
has length 1
IllegalArgumentException
if values
is null or p is not a valid quantile value (p must be greater than 0
and less than or equal to 100)
See Percentile
for a description of the percentile estimation
algorithm used.
values
- input array of valuesp
- the percentile value to computejava.lang.IllegalArgumentException
- if values
is null
or p is invalidpublic double evaluate(double[] values, int start, int length)
quantile
th percentile of the
designated values in the values
array. The quantile
estimated is determined by the quantile
property.
Double.NaN
if length = 0
quantile
)
values[begin]
if length = 1
IllegalArgumentException
if values
is null, or start
or length
is invalid
See Percentile
for a description of the percentile estimation
algorithm used.
evaluate
in interface UnivariateStatistic
evaluate
in class AbstractUnivariateStatistic
values
- the input arraystart
- index of the first array element to includelength
- the number of elements to includejava.lang.IllegalArgumentException
- if the parameters are not validpublic double evaluate(double[] values, int begin, int length, double p)
p
th percentile of the values
in the values
array, starting with the element in (0-based)
position begin
in the array and including length
values.
Calls to this method do not modify the internal quantile
state of this statistic.
Double.NaN
if length = 0
p
) values[begin]
if length = 1
IllegalArgumentException
if values
is null , begin
or length
is invalid, or
p
is not a valid quantile value (p must be greater than 0
and less than or equal to 100)
See Percentile
for a description of the percentile estimation
algorithm used.
values
- array of input valuesp
- the percentile to computebegin
- the first (0-based) element to include in the computationlength
- the number of array elements to includejava.lang.IllegalArgumentException
- if the parameters are not valid or the
input array is nullpublic double getQuantile()
public void setQuantile(double p)
p
- a value between 0 < p <= 100java.lang.IllegalArgumentException
- if p is not greater than 0 and less
than or equal to 100public Percentile copy()
copy
in interface UnivariateStatistic
copy
in class AbstractUnivariateStatistic
public static void copy(Percentile source, Percentile dest)
Neither source nor dest can be null.
source
- Percentile to copydest
- Percentile to copy tojava.lang.NullPointerException
- if either source or dest is null