org.statcato.statistics

Class BasicStatistics

java.lang.Object

org.statcato.statistics.BasicStatistics

public class BasicStatistics
extends java.lang.Object

A collection of basic statistical functions.

Since:

1.0

Constructor Summary

Constructors

Constructor and Description
BasicStatistics()

Method Summary

Modifier and Type	Method and Description
static java.util.Vector<java.lang.Double>	changeRange(java.util.Vector<java.lang.Double> numbers, double a, double b) Adjusts a vector of numbers to fit in a specific range [a, b].
static java.lang.Double	coefficientOfVariance(java.util.Vector<java.lang.Double> numbers) Returns the coefficient of variance (standard deviation / mean * 100).
static java.util.Vector<java.lang.Double>	customStandardize(java.util.Vector<java.lang.Double> numbers, double num1, double num2) Standardizes a vector of numbers of subtracting one number and then dividing by another number for each number in the vector.
static java.lang.Double	firstQuartile(java.util.Vector<java.lang.Double> numbers) Returns the first quartile of a vector of numbers as a Double object.
static java.lang.Double	interquartileRange(java.util.Vector<java.lang.Double> numbers) Returns the interquartile range (third quartile - first quartile).
static java.lang.Double	kurtosis(java.util.Vector<java.lang.Double> numbers) Returns the unbiased kurtosis of a vector of numbers (centered at 0).
static java.lang.Double	kurtosisBiased(java.util.Vector<java.lang.Double> numbers) Returns the biased kurtosis of a vector of numbers (centered at 0).
static java.lang.Double	kurtosisBiasedCentered3(java.util.Vector<java.lang.Double> numbers) Returns the biased kurtosis of a vector of numbers (centered at 3).
static java.lang.Double	kurtosisCentered3(java.util.Vector<java.lang.Double> numbers) Returns the kurtosis of a vector of numbers (centered at 3)
static java.lang.Double	max(java.util.ArrayList<java.lang.Double> numbers) Returns the maximum of an ArrayList of numbers.
static int	max(int[] numbers) Returns the maximum of an array of integers (assume array length > 0).
static java.lang.Double	max(java.util.Vector<java.lang.Double> numbers) Returns the maximum of a vector of doubles
static java.lang.Double	mean(java.util.Vector<java.lang.Double> numbers) Returns the mean of a vector of numbers.
static java.lang.Double	median(java.util.Vector<java.lang.Double> numbers) Returns the median of a vector of numbers.
static java.lang.Double	min(java.util.ArrayList<java.lang.Double> numbers) Returns the minimum of an ArrayList of numbers.
static int	min(int[] numbers) Returns the minimum of an array of integers (assume array length > 0).
static java.lang.Double	min(java.util.Vector<java.lang.Double> numbers) Returns the minimum of a vector of numbers.
static java.lang.Object[]	mode(java.util.Vector<java.lang.Double> numbers) Finds the mode of a vector of numbers and returns a vector of the mode(s) along with the number of occurences for the mode(s).
static java.lang.Double	moment(java.util.Vector<java.lang.Double> numbers, int k) Returns the kth moment about the mean = sum[(x - mean)^k].
static java.lang.Double	MSSD(java.util.Vector<java.lang.Double> numbers) Returns the mean of successive squared differences (MSSD).
static int	Nmissing(java.util.Vector<java.lang.Double> numbers) Returns the number of missing numbers in the input vector.
static int	Nnonmissing(java.util.Vector<java.lang.Double> numbers) Returns the number of nonmissing numbers in the input vector.
static int	Ntotal(java.util.Vector<java.lang.Double> numbers) Returns the total number of numbers in the input vector.
static int	numberOfNegativeSigns(java.util.Vector<java.lang.Double> values, double k) Returns the number of the values in the given vector that are less than the given median.
static int	numberOfPositiveSigns(java.util.Vector<java.lang.Double> values, double k) Returns the number of the values in the given vector that are greater than the given median.
static java.lang.Double	percentile(java.util.Vector<java.lang.Double> numbers, double i) Returns the i'th percentile of a vector of numbers as a Double object.
static java.lang.Double	range(java.util.Vector<java.lang.Double> numbers) Returns the range of a vector of numbers.
static java.util.Vector<java.lang.Double>	removeOutliers(java.util.Vector<java.lang.Double> values) Removes the outliers from a vector of double values and returns a vector of the outliers.
static double	RyanJoinerNormalityCV(int n, double significance) Returns the critical value used in the Ryan-Joiner normality test.
static java.lang.Double	SEmean(java.util.Vector<java.lang.Double> numbers) Return the standard error of the mean (s/sqrt(n)) of a vector of numbers.
static java.lang.Double	skewness(java.util.Vector<java.lang.Double> numbers) Returns the unbiased skewness of a vector of numbers.
static java.lang.Double	skewnessBiased(java.util.Vector<java.lang.Double> numbers) Returns the biased skewness of a vector of numbers.
static java.util.Vector<java.lang.Double>	standardize(java.util.Vector<java.lang.Double> numbers) Standardizes a vector of numbers by subtracting the mean and then dividing by the standard deviation for each number in the vector.
static java.lang.Double	stdev(java.util.Vector<java.lang.Double> numbers) Returns the standard deviation of a vector of numbers.
static double	sum(java.util.Vector<java.lang.Double> numbers) Returns the sum of a vector of numbers.
static double	sumOfSquares(java.util.Vector<java.lang.Double> numbers) Returns the sum of squares of a vector of numbers.
static java.lang.Double	thirdQuartile(java.util.Vector<java.lang.Double> numbers) Returns the third quartile of a vector of numbers as a Double object.
static java.lang.Double	trimmedMean(java.util.Vector<java.lang.Double> numbers, double percent) Returns the trimmed mean of a vector doubles.
static java.lang.Double	variance(java.util.Vector<java.lang.Double> numbers) Returns the variance of a vector of numbers.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

BasicStatistics

public BasicStatistics()

Method Detail

customStandardize

public static java.util.Vector<java.lang.Double> customStandardize(java.util.Vector<java.lang.Double> numbers,
                                                                   double num1,
                                                                   double num2)

Standardizes a vector of numbers of subtracting one number and then dividing by another number for each number in the vector.

Parameters:

numbers - vector of doubles

num1 - double value to subtract from each number in the vector

num2 - double value by which each number in the vector is divided. Assumed to be non-zero.

Returns:

a vector of standardized double values

standardize

public static java.util.Vector<java.lang.Double> standardize(java.util.Vector<java.lang.Double> numbers)

Standardizes a vector of numbers by subtracting the mean and then dividing by the standard deviation for each number in the vector.

Parameters:

numbers - a vector of double values

Returns:

vector of standardized double values

changeRange

public static java.util.Vector<java.lang.Double> changeRange(java.util.Vector<java.lang.Double> numbers,
                                                             double a,
                                                             double b)

Adjusts a vector of numbers to fit in a specific range [a, b]. A number n is adjusted as a + (n - min)(b - a) / (max - min).

Parameters:

numbers - a vector of double values

a - minimum value of the range

b - maximum value of the range. Assumed greater than a.

Returns:

vector of double values with a range [a, b]

Nnonmissing

public static int Nnonmissing(java.util.Vector<java.lang.Double> numbers)

Returns the number of nonmissing numbers in the input vector.

Parameters:

numbers - vector of doubles

Returns:

number of nonmissing numbers

Nmissing

public static int Nmissing(java.util.Vector<java.lang.Double> numbers)

Returns the number of missing numbers in the input vector.

Parameters:

numbers - vector of doubles

Returns:

number of missing numbers

Ntotal

public static int Ntotal(java.util.Vector<java.lang.Double> numbers)

Returns the total number of numbers in the input vector. Stops counting after the last nonmissing number in the vector.

Parameters:

numbers - vector of doubles

Returns:

total number of numbers in the vector

mean

public static java.lang.Double mean(java.util.Vector<java.lang.Double> numbers)

Returns the mean of a vector of numbers.

Parameters:

numbers - vector of doubles

Returns:

mean of the numbers, or null if the vector is empty

sum

public static double sum(java.util.Vector<java.lang.Double> numbers)

Returns the sum of a vector of numbers.

Parameters:

numbers - vector of doubles

Returns:

sum

stdev

public static java.lang.Double stdev(java.util.Vector<java.lang.Double> numbers)

Returns the standard deviation of a vector of numbers.

Parameters:

numbers - vector of doubles

Returns:

standard deviation, or null if the vector has less than two numbers

variance

public static java.lang.Double variance(java.util.Vector<java.lang.Double> numbers)

Returns the variance of a vector of numbers.

Parameters:

numbers -

Returns:

variance, or null if the vector has less than two numbers

moment

public static java.lang.Double moment(java.util.Vector<java.lang.Double> numbers,
                                      int k)

Returns the kth moment about the mean = sum[(x - mean)^k].

Parameters:

numbers - vector of doubles

k - order

Returns:

kth moment

min

public static java.lang.Double min(java.util.Vector<java.lang.Double> numbers)

Returns the minimum of a vector of numbers.

Parameters:

numbers - vector of doubles

Returns:

minimum value, or null if the vector is empty

min

public static java.lang.Double min(java.util.ArrayList<java.lang.Double> numbers)

Returns the minimum of an ArrayList of numbers.

Parameters:

numbers - ArrayList of doubles

Returns:

minimum value, or null if numbers is empty

min

public static int min(int[] numbers)

Returns the minimum of an array of integers (assume array length > 0).

Parameters:

numbers - array of integers, assumed non-empty

Returns:

minimum

max

public static java.lang.Double max(java.util.Vector<java.lang.Double> numbers)

Returns the maximum of a vector of doubles

Parameters:

numbers - vector of doubles

Returns:

maximum value, or null if the vector is empty

max

public static java.lang.Double max(java.util.ArrayList<java.lang.Double> numbers)

Returns the maximum of an ArrayList of numbers.

Parameters:

numbers - ArrayList of doubles

Returns:

maximum value, or null if numbers is empty

max

public static int max(int[] numbers)

Returns the maximum of an array of integers (assume array length > 0).

Parameters:

numbers - array of integers, assumed non-empty

Returns:

maximum

range

public static java.lang.Double range(java.util.Vector<java.lang.Double> numbers)

Returns the range of a vector of numbers.

Parameters:

numbers - vector of doubles

Returns:

range, or null if the vector is empty

median

public static java.lang.Double median(java.util.Vector<java.lang.Double> numbers)

Returns the median of a vector of numbers.

Parameters:

numbers - vector of doubles

Returns:

median, or null if the vector is empty

sumOfSquares

public static double sumOfSquares(java.util.Vector<java.lang.Double> numbers)

Returns the sum of squares of a vector of numbers.

Parameters:

numbers - vector of number

Returns:

sum of squares

SEmean

public static java.lang.Double SEmean(java.util.Vector<java.lang.Double> numbers)

Return the standard error of the mean (s/sqrt(n)) of a vector of numbers.

Parameters:

numbers - vector of doubles

Returns:

standard error of the mean, or null if the vector has less than two numbers

coefficientOfVariance

public static java.lang.Double coefficientOfVariance(java.util.Vector<java.lang.Double> numbers)

Returns the coefficient of variance (standard deviation / mean * 100).

Parameters:

numbers - vector of number

Returns:

coefficient of variance, or null if the vector has less than two numbers

firstQuartile

public static java.lang.Double firstQuartile(java.util.Vector<java.lang.Double> numbers)

Returns the first quartile of a vector of numbers as a Double object. Returns null if the first quartile is undefined

Parameters:

numbers - vector of numbers

Returns:

first quartile, or null if it is undefined

thirdQuartile

public static java.lang.Double thirdQuartile(java.util.Vector<java.lang.Double> numbers)

Returns the third quartile of a vector of numbers as a Double object. Returns null if the third quartile is undefined

Parameters:

numbers - vector of numbers

Returns:

third quartile, or null if it is undefined

percentile

public static java.lang.Double percentile(java.util.Vector<java.lang.Double> numbers,
                                          double i)

Returns the i'th percentile of a vector of numbers as a Double object. Returns null if the i'th percentile is undefined

Parameters:

numbers - vector of numbers

Returns:

i'th percentile, or null if it is undefined

interquartileRange

public static java.lang.Double interquartileRange(java.util.Vector<java.lang.Double> numbers)

Returns the interquartile range (third quartile - first quartile).

Parameters:

numbers - vector of numbers

Returns:

interquartile range, or null if it is undefined

mode

public static java.lang.Object[] mode(java.util.Vector<java.lang.Double> numbers)

Finds the mode of a vector of numbers and returns a vector of the mode(s) along with the number of occurences for the mode(s).

Parameters:

numbers - vector of double values

Returns:

an array of Object, where the first element is a vector of double values representing the mode(s) and the second element is an Integer representing the number of occurences of the mode(s)

trimmedMean

public static java.lang.Double trimmedMean(java.util.Vector<java.lang.Double> numbers,
                                           double percent)

Returns the trimmed mean of a vector doubles. The trimmed mean is found by removing the smallest and largest given percent of the values and then computing the mean of the remaining values.

Parameters:

numbers - vector of double values

percent - percent of smallest and largest values to remove

Returns:

trimmed mean, or null is undefined

skewness

public static java.lang.Double skewness(java.util.Vector<java.lang.Double> numbers)

Returns the unbiased skewness of a vector of numbers.

Parameters:

numbers - vector of double values

Returns:

skewness, or null if the vector has less than three elements

skewnessBiased

public static java.lang.Double skewnessBiased(java.util.Vector<java.lang.Double> numbers)

Returns the biased skewness of a vector of numbers.

Parameters:

numbers - vector of double values

Returns:

skewness, or null if the vector has less than two elements

kurtosis

public static java.lang.Double kurtosis(java.util.Vector<java.lang.Double> numbers)

Returns the unbiased kurtosis of a vector of numbers (centered at 0).

Parameters:

numbers - vector of double values

Returns:

kurtosis, or null if the vector has less than four elements

kurtosisCentered3

public static java.lang.Double kurtosisCentered3(java.util.Vector<java.lang.Double> numbers)

Returns the kurtosis of a vector of numbers (centered at 3)

Parameters:

numbers - vector of double values

Returns:

kurtosis, or null if the vector has less than four elements

kurtosisBiased

public static java.lang.Double kurtosisBiased(java.util.Vector<java.lang.Double> numbers)

Returns the biased kurtosis of a vector of numbers (centered at 0).

Parameters:

numbers - vector of double values

Returns:

kurtosis, or null if the vector has less than four elements

kurtosisBiasedCentered3

public static java.lang.Double kurtosisBiasedCentered3(java.util.Vector<java.lang.Double> numbers)

Returns the biased kurtosis of a vector of numbers (centered at 3).

Parameters:

numbers - vector of double values

Returns:

kurtosis, or null if the vector has less than four elements

MSSD

public static java.lang.Double MSSD(java.util.Vector<java.lang.Double> numbers)

Returns the mean of successive squared differences (MSSD).

Parameters:

numbers - vector of double values

Returns:

MSSD, or null if the vector has less than two numbers

RyanJoinerNormalityCV

public static double RyanJoinerNormalityCV(int n,
                                           double significance)

Returns the critical value used in the Ryan-Joiner normality test.

Parameters:

n - sample size

significance - significance level

Returns:

critical value

removeOutliers

public static java.util.Vector<java.lang.Double> removeOutliers(java.util.Vector<java.lang.Double> values)

Removes the outliers from a vector of double values and returns a vector of the outliers.

Parameters:

values - a vector of double values

Returns:

a vector of outliers

numberOfNegativeSigns

public static int numberOfNegativeSigns(java.util.Vector<java.lang.Double> values,
                                        double k)

Returns the number of the values in the given vector that are less than the given median.

Parameters:

values - vector of double values

k - median

Returns:

number of negative signs

numberOfPositiveSigns

public static int numberOfPositiveSigns(java.util.Vector<java.lang.Double> values,
                                        double k)

Returns the number of the values in the given vector that are greater than the given median.

Parameters:

values - vector of double values

k - median

Returns:

number of positive signs