umontreal.iro.lecuyer.stat

## Class Tally

- java.lang.Object
- umontreal.iro.lecuyer.stat.StatProbe
- umontreal.iro.lecuyer.stat.Tally

- All Implemented Interfaces:
- Cloneable

- Direct Known Subclasses:
- TallyStore

public class Tallyextends StatProbeimplements Cloneable

This type of statistical collector takes a sequence of real-valued observations and can return the average, the variance, a confidence interval for the theoretical mean, etc. Each call to`add`

provides a new observation. When the broadcasting to observers is activated, the method`add`

will also pass this new information to its registered observers. This type of collector does not memorize the individual observations, but only their number, sum, sum of squares, maximum, and minimum. The subclass`TallyStore`

offers a collector that memorizes the observations.

### Constructor Summary

Constructors Constructor and Description **Tally**()Constructs a new unnamed`Tally`statistical probe.**Tally**(String name)Constructs a new`Tally`statistical probe with name`name`.

### Method Summary

Methods Modifier and Type Method and Description `void`

**add**(double x)Gives a new observation`x`to the statistical collector.`double`

**average**()Returns the average for this collector.`Tally`

**clone**()Clones this object.`void`

**confidenceIntervalNormal**(double level, double[] centerAndRadius)Computes a confidence interval on the mean.`void`

**confidenceIntervalStudent**(double level, double[] centerAndRadius)Computes a confidence interval on the mean.`void`

**confidenceIntervalVarianceChi2**(double level, double[] interval)Computes a confidence interval on the variance.`String`

**formatCINormal**(double level)Equivalent to`formatCINormal (level, 3)`.`String`

**formatCINormal**(double level, int d).`String`

**formatCIStudent**(double level)Equivalent to`formatCIStudent (level, 3)`.`String`

**formatCIStudent**(double level, int d).`String`

**formatCIVarianceChi2**(double level, int d).`String`

**formatConfidenceIntervalNormal**(double level)**Deprecated.**`String`

**formatConfidenceIntervalNormal**(double level, int d)**Deprecated.**`String`

**formatConfidenceIntervalStudent**(double level)**Deprecated.**`String`

**formatConfidenceIntervalStudent**(double level, int d)**Deprecated.**`double`

**getConfidenceLevel**()Returns the level of confidence for the intervals on the mean displayed in reports.`void`

**init**()Initializes the statistical collector.`int`

**numberObs**()Returns the number of observations given to this probe since its last initialization.`String`

**report**()Returns a formatted string that contains a report on this probe.`String`

**report**(double level, int d)Returns a formatted string that contains a report on this probe with a confidence interval level`level`using*d*fractional decimal digits.`String`

**reportAndCIStudent**(double level)Same as`reportAndCIStudent`

`(level, 3)`.`String`

**reportAndCIStudent**(double level, int d)Returns a formatted string that contains a report on this probe (as in`report`

), followed by a confidence interval (as in`formatCIStudent`

), using*d*fractional decimal digits.`String`

**reportAndConfidenceIntervalStudent**(double level)**Deprecated.**`String`

**reportAndConfidenceIntervalStudent**(double level, int d)**Deprecated.**`void`

**setConfidenceIntervalNone**()Indicates that no confidence interval needs to be printed in reports formatted by`report`

, and`shortReport`

.`void`

**setConfidenceIntervalNormal**()Indicates that a confidence interval on the true mean, based on the central limit theorem, needs to be included in reports formatted by`report`

and`shortReport`

.`void`

**setConfidenceIntervalStudent**()Indicates that a confidence interval on the true mean, based on the normality assumption, needs to be included in reports formatted by`report`

and`shortReport`

.`void`

**setConfidenceLevel**(double level)Sets the level of confidence for the intervals on the mean displayed in reports.`void`

**setShowNumberObs**(boolean showNumObs)Determines if the number of observations must be displayed in reports.`String`

**shortReport**()Formats and returns a short statistical report for this tally.`String`

**shortReportHeader**()Returns a string containing the name of the values returned in the report strings.`double`

**standardDeviation**()Returns the sample standard deviation of the observations since the last initialization.`double`

**variance**()Returns the sample variance of the observations since the last initialization.### Methods inherited from class umontreal.iro.lecuyer.stat.StatProbe

`addObservationListener, clearObservationListeners, getName, isBroadcasting, isCollecting, max, min, notifyListeners, removeObservationListener, report, report, setBroadcasting, setCollecting, setName, sum`

### Constructor Detail

#### Tally

public Tally()

Constructs a new unnamed`Tally`statistical probe.

#### Tally

public Tally(String name)

Constructs a new`Tally`statistical probe with name`name`.- Parameters:
`name`

- name of the tally

### Method Detail

#### init

public void init()

**Description copied from class:**`StatProbe`

Initializes the statistical collector.

#### add

public void add(double x)

Gives a new observation`x`to the statistical collector. If broadcasting to observers is activated for this object, this method also transmits the new information to the registered observers by invoking the method`notifyListeners`

.- Parameters:
`x`

- observation being added to this tally

#### numberObs

public int numberObs()

Returns the number of observations given to this probe since its last initialization.

#### average

public double average()

**Description copied from class:**`StatProbe`

Returns the average for this collector. This returns`Double.NaN`if the probe was not updated since the last initialization.

#### variance

public double variance()

Returns the sample variance of the observations since the last initialization. This returns`Double.NaN`if the tally contains less than two observations.- Returns:
- the variance of the observations

#### standardDeviation

public double standardDeviation()

Returns the sample standard deviation of the observations since the last initialization. This returns`Double.NaN`if the tally contains less than two observations.- Returns:
- the standard deviation of the observations

#### confidenceIntervalNormal

public void confidenceIntervalNormal(double level, double[] centerAndRadius)

Computes a confidence interval on the mean. Returns, in elements 0 and 1 of the array object`centerAndRadius[]`, the center and half-length (radius) of a confidence interval on the true mean of the random variable*X*, with confidence level`level`, assuming that the*n*observations given to this collector are independent and identically distributed (i.i.d.) copies of*X*, and that*n*is large enough for the central limit theorem to hold. This confidence interval is computed based on the statistic*Z*= bar(X)_{n}-*μ*/(*S*_{n, x}/(n)^{1/2})*n*is the number of observations given to this collector since its last initialization, bar(X)_{n}=`average()`is the average of these observations,*S*_{n, x}=`standardDeviation()`is the empirical standard deviation. Under the assumption that the observations of*X*are i.i.d. and*n*is large,*Z*has the standard normal distribution. The confidence interval given by this method is valid only if this assumption is approximately verified.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)`centerAndRadius`

- array of size 2 in which are returned the center and radius of the confidence interval, respectively

#### confidenceIntervalStudent

public void confidenceIntervalStudent(double level, double[] centerAndRadius)

Computes a confidence interval on the mean. Returns, in elements 0 and 1 of the array object`centerAndRadius[]`, the center and half-length (radius) of a confidence interval on the true mean of the random variable*X*, with confidence level`level`, assuming that the observations given to this collector are independent and identically distributed (i.i.d.) copies of*X*, and that*X*has the normal distribution. This confidence interval is computed based on the statistic*T*= bar(X)_{n}-*μ*/(*S*_{n, x}/(n)^{1/2})*n*is the number of observations given to this collector since its last initialization, bar(X)_{n}=`average()`is the average of these observations,*S*_{n, x}=`standardDeviation()`is the empirical standard deviation. Under the assumption that the observations of*X*are i.i.d. and normally distributed,*T*has the Student distribution with*n*- 1 degrees of freedom. The confidence interval given by this method is valid only if this assumption is approximately verified, or if*n*is large enough so that bar(X)_{n}is approximately normally distributed.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)`centerAndRadius`

- array of size 2 in which are returned the center and radius of the confidence interval, respectively

#### formatConfidenceIntervalNormal

@Deprecatedpublic String formatConfidenceIntervalNormal(double level, int d)

Deprecated.

#### formatConfidenceIntervalNormal

@Deprecatedpublic String formatConfidenceIntervalNormal(double level)

Deprecated.

#### formatCINormal

public String formatCINormal(double level, int d)

. Similar to`confidenceIntervalNormal`

, but returns the confidence interval in a formatted string of the form

``using`95% confidence interval for mean (normal): (32.431, 32.487)`'',*d*fractional decimal digits.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)`d`

- number of fractional decimal digits- Returns:
- a confidence interval formatted as a string

#### formatCINormal

public String formatCINormal(double level)

Equivalent to`formatCINormal (level, 3)`.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)- Returns:
- a confidence interval formatted as a string

#### formatConfidenceIntervalStudent

@Deprecatedpublic String formatConfidenceIntervalStudent(double level, int d)

Deprecated.

#### formatConfidenceIntervalStudent

@Deprecatedpublic String formatConfidenceIntervalStudent(double level)

Deprecated.

#### formatCIStudent

public String formatCIStudent(double level, int d)

. Similar to`confidenceIntervalStudent`

, but returns the confidence interval in a formatted string of the form

``using`95% confidence interval for mean (student): (32.431, 32.487)`'',*d*fractional decimal digits.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)`d`

- number of fractional decimal digits- Returns:
- a confidence interval formatted as a string

#### formatCIStudent

public String formatCIStudent(double level)

Equivalent to`formatCIStudent (level, 3)`.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)- Returns:
- a confidence interval formatted as a string

#### confidenceIntervalVarianceChi2

public void confidenceIntervalVarianceChi2(double level, double[] interval)

Computes a confidence interval on the variance. Returns, in elements 0 and 1 of array`interval`, the left and right boundaries [*I*_{1},*I*_{2}] of a confidence interval on the true variance*σ*^{2}of the random variable*X*, with confidence level`level`, assuming that the observations given to this collector are independent and identically distributed (i.i.d.) copies of*X*, and that*X*has the normal distribution. This confidence interval is computed based on the statistic*χ*^{2}_{n-1}= (*n*- 1)*S*^{2}_{n}/*σ*^{2}where*n*is the number of observations given to this collector since its last initialization, and*S*^{2}_{n}=`variance()`is the empirical variance of these observations. Under the assumption that the observations of*X*are i.i.d. and normally distributed,*χ*^{2}_{n-1}has the chi-square distribution with*n*- 1 degrees of freedom. Given the`level`= 1 -*α*, one has*P*[*χ*^{2}_{n-1}<*x*_{1}] =*P*[*χ*^{2}_{n-1}>*x*_{2}] =*α*/2 and [*I*_{1},*I*_{2}] = [(*n*- 1)*S*^{2}_{n}/*x*_{2}, (*n*- 1)*S*^{2}_{n}/*x*_{1}].- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)`interval`

- array of size 2 in which are returned the left and right boundaries of the confidence interval, respectively

#### formatCIVarianceChi2

public String formatCIVarianceChi2(double level, int d)

. Similar to`confidenceIntervalVarianceChi2`

, but returns the confidence interval in a formatted string of the form

``using`95.0% confidence interval for variance (chi2): ( 510.642, 519.673 )`'',*d*fractional decimal digits.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true variance`d`

- number of fractional decimal digits- Returns:
- a confidence interval formatted as a string

#### report

public String report()

Returns a formatted string that contains a report on this probe.

#### report

public String report(double level, int d)

Returns a formatted string that contains a report on this probe with a confidence interval level`level`using*d*fractional decimal digits.- Parameters:
`level`

- desired probability that the confidence interval covers the true mean`d`

- number of fractional decimal digits- Returns:
- a statistical report formatted as a string

#### shortReportHeader

public String shortReportHeader()

**Description copied from class:**`StatProbe`

Returns a string containing the name of the values returned in the report strings. The returned string must depend on the type of probe and on the reporting options only. It must not depend on the observations received by the probe. This can be used as header when printing several reports. For example,System.out.println (probe1.shortReportHeader()); System.out.println (probe1.getName() + " " + probe1.shortReport()); System.out.println (probe2.getName() + " " + probe2.shortReport()); ...

Alternatively, one can use`report`

`(String,StatProbe[])`to get a report with aligned probe names.**Specified by:**`shortReportHeader`

in class`StatProbe`

- Returns:
- the header string for the short reports.

#### shortReport

public String shortReport()

Formats and returns a short statistical report for this tally. The returned single-line report contains the minimum value, the maximum value, the average, and the standard deviation, in that order, separated by three spaces. If the number of observations is shown in the short report, a column containing the number of observations in this tally is added.**Specified by:**`shortReport`

in class`StatProbe`

- Returns:
- the string containing the report.

#### reportAndConfidenceIntervalStudent

@Deprecatedpublic String reportAndConfidenceIntervalStudent(double level, int d)

Deprecated.

#### reportAndConfidenceIntervalStudent

@Deprecatedpublic String reportAndConfidenceIntervalStudent(double level)

Deprecated.

#### reportAndCIStudent

public String reportAndCIStudent(double level, int d)

Returns a formatted string that contains a report on this probe (as in`report`

), followed by a confidence interval (as in`formatCIStudent`

), using*d*fractional decimal digits.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)`d`

- number of fractional decimal digits- Returns:
- a statistical report with a confidence interval, formatted as a string

#### reportAndCIStudent

public String reportAndCIStudent(double level)

Same as`reportAndCIStudent`

`(level, 3)`.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)- Returns:
- a statistical report with a confidence interval, formatted as a string

#### getConfidenceLevel

public double getConfidenceLevel()

Returns the level of confidence for the intervals on the mean displayed in reports. The default confidence level is 0.95.- Returns:
- desired probability that the (random) confidence interval covers the true mean (a constant)

#### setConfidenceLevel

public void setConfidenceLevel(double level)

Sets the level of confidence for the intervals on the mean displayed in reports.- Parameters:
`level`

- desired probability that the (random) confidence interval covers the true mean (a constant)

#### setConfidenceIntervalNone

public void setConfidenceIntervalNone()

Indicates that no confidence interval needs to be printed in reports formatted by`report`

, and`shortReport`

. This restores the default behavior of the reporting system.

#### setConfidenceIntervalNormal

public void setConfidenceIntervalNormal()

Indicates that a confidence interval on the true mean, based on the central limit theorem, needs to be included in reports formatted by`report`

and`shortReport`

. The confidence interval is formatted using`formatCINormal`

.

#### setConfidenceIntervalStudent

public void setConfidenceIntervalStudent()

Indicates that a confidence interval on the true mean, based on the normality assumption, needs to be included in reports formatted by`report`

and`shortReport`

. The confidence interval is formatted using`formatCIStudent`

.

#### setShowNumberObs

public void setShowNumberObs(boolean showNumObs)

Determines if the number of observations must be displayed in reports. By default, the number of observations is displayed.- Parameters:
`showNumObs`

- the value of the indicator.

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