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SSJ: Tally Class Reference

A subclass of StatProbe. More...

A subclass of StatProbe.

This type of statistical collector takes a sequence of real-valued observations \(X_1,X_2,X_3,…\) 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.

Constructs a new Tally statistical probe with name name.

Parameters

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 object

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

\[ Z = {\bar{X}_n - \mu\over{S_{n,x}/\sqrt{n}}} \]

where \(n\) 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

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

\[ T = {\bar{X}_n - \mu\over{S_{n,x}/\sqrt{n}}} \]

where \(n\) 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

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 \(\sigma^2\) 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 \( \chi^2_{n-1} = (n-1)S^2_n/\sigma^2 \) 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, \(\chi^2_{n-1}\) has the chi-square distribution with \(n-1\) degrees of freedom. Given the level \( = 1 - \alpha\), one has \(P[\chi^2_{n-1} < x_1] = P[\chi^2_{n-1} > x_2] = \alpha/2\) 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

Similar to confidenceIntervalNormal.

Returns the confidence interval in a formatted string of the form

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 confidence interval formatted as a string

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

Similar to confidenceIntervalStudent.

Returns the confidence interval in a formatted string of the form

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 confidence interval formatted as a string

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

Similar to confidenceIntervalVarianceChi2.

Returns the confidence interval in a formatted string of the form

using \(d\) 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

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)

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

Returns

the number of collected observations

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

Returns

a statistical report formatted as a string

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

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

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

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.

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.

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.

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)

Set the name of this Tally to name.

Parameters

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.

Formats and returns a short statistical report for this tally.

The returned single-line report contains the minimum value, the maximum value, the average, the variance, 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.

Returns

the string containing the report.

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

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

The documentation for this class was generated from the following file:

• Tally.java

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