Summary (JMSL Numerical Library (jmsl) 2021.0.0 API)

java.lang.Object
- com.imsl.stat.Summary

All Implemented Interfaces:

Serializable, Cloneable
```
public class Summary
extends Object
implements Serializable, Cloneable
```
Computes basic univariate statistics.
For the data in x. Summary computes the sample mean, variance, minimum, maximum, and ther basic statistics. It also computes confidence intervals for the mean and variance if the sample is assumed to be from a normal population.

Missing values, that is, values equal to NaN (not a number), are excluded from the computations. The sum of the weights is used only in computing the mean (of course, then the weighted mean is used in computing the central moments). The definitions of some of the statistics are given below in terms of a single variable x. The i-th datum is $x_i$, with corresponding weight $w_i$. If weights are not specified, the $w_i$ are identically one. The summation in each case is over the set of valid observations, based on the presence of missing values in the data.

Number of nonmissing observations,

$$n = \sum {f_i } $$

Mean,

$$\bar x_w = \frac{{\sum {f_i w_i x_i } }}{{\sum {f_i w_i } }} $$

Variance,

$$s_w^2 = \frac{{\sum {f_i w_i \left( {x_i - \bar x_w } \right)^2 } }}{{n - 1}} $$

Skewness,

$$\frac{{\sum {f_i w_i \left( {x_i - \bar x_w } \right)^3 /n} }}{{[\sum {f_i w_i \left( {x_i - \bar x_w } \right)^2 /n]^{3/2} } }} $$

Excess or Kurtosis,

$$\frac{{\sum {f_i w_i \left( {x_i - \bar x_w } \right)^4 /n} }}{{[\sum {f_i w_i \left( {x_i - \bar x_w } \right)^2 /n]^2 } }} - 3 $$

Minimum,

$$x_{\rm min} = \min (x_i ) $$

Maximum,

$$x_{\rm max} = \max (x_i ) $$)

See Also:

Example, Serialized Form

Constructor Summary

Constructors
Constructor and Description

Summary()
Constructs a new summary statistics object.

Constructors
Constructor and Description
`Summary()` Constructs a new summary statistics object.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double[]`	`confidenceMean(double p)` Returns the confidence interval for the mean (assuming normality).
`double[]`	`confidenceVariance(double p)` Returns the confidence interval for the variance (assuming normality).
`double`	`getKurtosis()` Returns the kurtosis.
`double`	`getMaximum()` Returns the maximum.
`double`	`getMean()` Returns the population mean.
`double`	`getMinimum()` Returns the minimum.
`int`	`getNumberOfObservations()` Returns the number of non-missing observations.
`double`	`getSampleStandardDeviation()` Returns the sample standard deviation.
`double`	`getSampleVariance()` Returns the sample variance.
`double`	`getSkewness()` Returns the skewness.
`double`	`getStandardDeviation()` Returns the population standard deviation.
`double`	`getVariance()` Returns the population variance.
`static double`	`kurtosis(double[] x)` Returns the kurtosis of the given data set.
`static double`	`kurtosis(double[] x, double[] weight)` Returns the kurtosis of the given data set and associated weights.
`static double`	`maximum(double[] x)` Returns the maximum of the given data set.
`protected static int`	`maximum(int[] x)` Returns the maximum of the given data set.
`static double`	`mean(double[] x)` Returns the mean of the given data set.
`static double`	`mean(double[] x, double[] weight)` Returns the mean of the given data set with associated weights.
`static double`	`median(double[] x)` Returns the median of the given data set.
`static double`	`median(double[] x, double[] weight)` Returns the weighted median of the given data set and associated weights.
`static double`	`minimum(double[] x)` Returns the minimum of the given data set.
`protected static int`	`minimum(int[] x)` Returns the minimum of the given data set.
`static double`	`mode(double[] x)` Returns the mode of the given data set.
`static int`	`numberOfObservations(double[] x)` Returns the number of non-missing observations in the given data set.
`static double`	`quantile(double[] x, double[] weight, double alpha)`
`static double`	`sampleStandardDeviation(double[] x)` Returns the sample standard deviation of the given data set.
`static double`	`sampleStandardDeviation(double[] x, double[] weight)` Returns the sample standard deviation of the given data set and associated weights.
`static double`	`sampleVariance(double[] x)` Returns the sample variance of the given data set.
`static double`	`sampleVariance(double[] x, double[] weight)` Returns the sample variance of the given data set and associated weights.
`static double`	`skewness(double[] x)` Returns the skewness of the given data set.
`static double`	`skewness(double[] x, double[] weight)` Returns the skewness of the given data set and associated weights.
`static double`	`standardDeviation(double[] x)` Returns the population standard deviation of the given data set.
`static double`	`standardDeviation(double[] x, double[] weight)` Returns the population standard deviation of the given data set and associated weights.
`void`	`update(double x)` Adds an observation to the `Summary` object.
`void`	`update(double[] x)` Adds a set of observations to the `Summary` object.
`void`	`update(double[] x, double[] weight)` Adds a set of observations and associated weights to the `Summary` object.
`void`	`update(double x, double weight)` Adds an observation and associated weight to the `Summary` object.
`static double`	`variance(double[] x)` Returns the population variance of the given data set.
`static double`	`variance(double[] x, double[] weight)` Returns the population variance of the given data set and associated weights.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - Summary
```
public Summary()
```
    Constructs a new summary statistics object.
- Method Detail
  - update
```
public void update(double x)
```
    Adds an observation to the Summary object.
    
    Parameters:
    
    x - a double, the data observation to be added
  - update
```
public void update(double x,
                   double weight)
```
    Adds an observation and associated weight to the Summary object.
    
    Parameters:
    
    x - a double, the data observation to be added
    
    weight - a double, the weight associated with the observation
  - update
```
public void update(double[] x)
```
    Adds a set of observations to the Summary object.
    
    Parameters:
    
    x - a double array of data observations to be added
  - update
```
public void update(double[] x,
                   double[] weight)
```
    Adds a set of observations and associated weights to the Summary object.
    
    Parameters:
    
    x - a double array of data observations to be added
    
    weight - a double array of weights associated with the observations
  - getNumberOfObservations
```
public int getNumberOfObservations()
```
    Returns the number of non-missing observations.
    
    Returns:
    
    an int, the number of non-missing observations in the Summary object.
  - getMinimum
```
public double getMinimum()
```
    Returns the minimum.
    
    Returns:
    
    a double representing the minimum
  - getMaximum
```
public double getMaximum()
```
    Returns the maximum.
    
    Returns:
    
    a double representing the maximum
  - getMean
```
public double getMean()
```
    Returns the population mean.
    
    Returns:
    
    a double representing the population mean
  - getVariance
```
public double getVariance()
```
    Returns the population variance.
    
    Returns:
    
    a double representing the population variance
  - getSampleVariance
```
public double getSampleVariance()
```
    Returns the sample variance.
    
    Returns:
    
    a double representing the sample variance
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Returns the population standard deviation.
    
    Returns:
    
    a double representing the population standard deviation
  - getSampleStandardDeviation
```
public double getSampleStandardDeviation()
```
    Returns the sample standard deviation.
    
    Returns:
    
    a double representing the sample standard deviation
  - getSkewness
```
public double getSkewness()
```
    Returns the skewness.
    
    Returns:
    
    a double representing the skewness
  - getKurtosis
```
public double getKurtosis()
```
    Returns the kurtosis.
    
    Returns:
    
    a double representing the kurtosis
  - confidenceMean
```
public double[] confidenceMean(double p)
```
    Returns the confidence interval for the mean (assuming normality).
    
    Parameters:
    
    p - a double, the confidence level desired, usually 0.90, 0.95 or 0.99.
    
    Returns:
    
    a double array of length 2 which contains the lower and upper confidence limits for the mean
  - confidenceVariance
```
public double[] confidenceVariance(double p)
```
    Returns the confidence interval for the variance (assuming normality).
    
    Parameters:
    
    p - a double, the confidence level desired, usually 0.90, 0.95 or 0.99.
    
    Returns:
    
    a double array of length 2 which contains the lower and upper confidence limits for the variance
  - minimum
```
public static double minimum(double[] x)
```
    Returns the minimum of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose minimum is to be found.
    
    Returns:
    
    a double, the minimum of the given data set.
  - numberOfObservations
```
public static int numberOfObservations(double[] x)
```
    Returns the number of non-missing observations in the given data set.
    
    Parameters:
    
    x - a double array containing the data set.
    
    Returns:
    
    an int, the number of non-missing observations in the given data set.
  - minimum
```
protected static int minimum(int[] x)
```
    Returns the minimum of the given data set.
    
    Parameters:
    
    x - an int array containing the data set whose minimum is to be found
    
    Returns:
    
    an int, the minimum of the given data set
  - maximum
```
public static double maximum(double[] x)
```
    Returns the maximum of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose maximum is to be found
    
    Returns:
    
    a double, the maximum of the given data set
  - maximum
```
protected static int maximum(int[] x)
```
    Returns the maximum of the given data set.
    
    Parameters:
    
    x - an int array containing the data set whose maximum is to be found
    
    Returns:
    
    an int, the maximum of the given data set
  - mean
```
public static double mean(double[] x)
```
    Returns the mean of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose mean is to be found
    
    Returns:
    
    a double, the mean of the given data set
  - mean
```
public static double mean(double[] x,
                          double[] weight)
```
    Returns the mean of the given data set with associated weights.
    
    Parameters:
    
    x - a double array containing the data set whose mean is to be found
    
    weight - a double array containing the weights associated with the data points x
    
    Returns:
    
    a double, the mean of the given data set
  - variance
```
public static double variance(double[] x)
```
    Returns the population variance of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose population variance is to be found
    
    Returns:
    
    a double, the population variance of the given data set
  - variance
```
public static double variance(double[] x,
                              double[] weight)
```
    Returns the population variance of the given data set and associated weights.
    
    Parameters:
    
    x - a double array containing the data set whose population variance is to be found
    
    weight - a double array containing the weights associated with the data points x
    
    Returns:
    
    a double, the population variance of the given data set
  - sampleVariance
```
public static double sampleVariance(double[] x)
```
    Returns the sample variance of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose sample variance is to be found
    
    Returns:
    
    a double, the sample variance of the given data set
  - sampleVariance
```
public static double sampleVariance(double[] x,
                                    double[] weight)
```
    Returns the sample variance of the given data set and associated weights.
    
    Parameters:
    
    x - a double array containing the data set whose sample variance is to be found
    
    weight - a double array containing the weights associated with the data points x
    
    Returns:
    
    a double, the sample variance of the given data set
  - standardDeviation
```
public static double standardDeviation(double[] x)
```
    Returns the population standard deviation of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose standard deviation is to be found
    
    Returns:
    
    a double, the population standard deviation of the given data set
  - standardDeviation
```
public static double standardDeviation(double[] x,
                                       double[] weight)
```
    Returns the population standard deviation of the given data set and associated weights.
    
    Parameters:
    
    x - a double array containing the data set whose standard deviation is to be found
    
    weight - a double array containing the weights associated with the data points x
    
    Returns:
    
    a double, the population standard deviation of the given data set
  - sampleStandardDeviation
```
public static double sampleStandardDeviation(double[] x)
```
    Returns the sample standard deviation of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose sample standard deviation is to be found
    
    Returns:
    
    a double, the sample standard deviation of the given data set
  - sampleStandardDeviation
```
public static double sampleStandardDeviation(double[] x,
                                             double[] weight)
```
    Returns the sample standard deviation of the given data set and associated weights.
    
    Parameters:
    
    x - a double array containing the data set whose sample standard deviation is to be found
    
    weight - a double array containing the weights associated with the data points x.
    
    Returns:
    
    a double, the sample standard deviation of the given data set
  - skewness
```
public static double skewness(double[] x)
```
    Returns the skewness of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose skewness is to be found
    
    Returns:
    
    a double, the skewness of the given data set
  - skewness
```
public static double skewness(double[] x,
                              double[] weight)
```
    Returns the skewness of the given data set and associated weights.
    
    Parameters:
    
    x - a double array containing the data set whose skewness is to be found
    
    weight - a double array containing the weights associated with the data points x
    
    Returns:
    
    a double, the skewness of the given data set
  - kurtosis
```
public static double kurtosis(double[] x)
```
    Returns the kurtosis of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose kurtosis is to be found
    
    Returns:
    
    a double, the kurtosis of the given data set
  - kurtosis
```
public static double kurtosis(double[] x,
                              double[] weight)
```
    Returns the kurtosis of the given data set and associated weights.
    
    Parameters:
    
    x - a double array containing the data set whose kurtosis is to be found
    
    weight - a double array containing the weights associated with the data points x
    
    Returns:
    
    a double, the kurtosis of the given data set
  - median
```
public static double median(double[] x,
                            double[] weight)
```
    Returns the weighted median of the given data set and associated weights.
    
    Parameters:
    
    x - a double array containing the data set whose median is to be found
    
    weight - a double array containing the weights associated with the data
    
    Returns:
    
    a double, the weighted median of the given data set
  - quantile
```
public static double quantile(double[] x,
                              double[] weight,
                              double alpha)
```
  - median
```
public static double median(double[] x)
```
    Returns the median of the given data set.
    
    Parameters:
    
    x - a double array containing the data set whose median is to be found
    
    Returns:
    
    a double, the median of the given data set
  - mode
```
public static double mode(double[] x)
```
    Returns the mode of the given data set. Ties are broken at random.
    
    Parameters:
    
    x - a double array containing the data set whose mode is to be found
    
    Returns:
    
    a double, the mode of the given data set

Class Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Summary

Method Detail

update

update

update

update

getNumberOfObservations

getMinimum

getMaximum

getMean

getVariance

getSampleVariance

getStandardDeviation

getSampleStandardDeviation

getSkewness

getKurtosis

confidenceMean

confidenceVariance

minimum

numberOfObservations

minimum

maximum

maximum

mean

mean

variance

variance

sampleVariance

sampleVariance

standardDeviation

standardDeviation

sampleStandardDeviation

sampleStandardDeviation

skewness

skewness

kurtosis

kurtosis

median

quantile

median

mode