Tally
umontreal.iro.lecuyer.stat

Class 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 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.
        Specified by:
        init in class StatProbe
      • 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.
        Specified by:
        average in class StatProbe
        Returns:
        the average value of the collected observations
      • 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/(Sn, x/(n)1/2)

        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, Sn, 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/(Sn, x/(n)1/2)

        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, Sn, 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
        ``95% confidence interval for mean (normal): (32.431, 32.487)'',
        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
      • 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
        ``95% confidence interval for mean (student): (32.431, 32.487)'',
        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
      • 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 [I1, I2] of a confidence interval on the true variance σ2 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 χ2n-1 = (n - 1)S2n/σ2 where n is the number of observations given to this collector since its last initialization, and S2n = variance() is the empirical variance of these observations. Under the assumption that the observations of X are i.i.d. and normally distributed, χ2n-1 has the chi-square distribution with n - 1 degrees of freedom. Given the level = 1 - α, one has P[χ2n-1 < x1] = P[χ2n-1 > x2] = α/2 and [I1, I2] = [(n - 1)S2n/x2,  (n - 1)S2n/x1].
        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
        ``95.0% confidence interval for variance (chi2): ( 510.642, 519.673 )'',
        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
      • report

        public String report()
        Returns a formatted string that contains a report on this probe.
        Specified by:
        report in class StatProbe
        Returns:
        a statistical report formatted as a string
      • 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.

SCaVis 2.0 © jWork.ORG