Package org.djutils.stats.summarizers

Interface TallyInterface

    • Method Detail

      • ingest

        double ingest​(double value)
        Process one observed value.
        Parameters:
        value - double; the value to process
        Returns:
        double; the value

      • getSum

        double getSum()
        Return the sum of the values of the observations.
        Returns:
        double; sum

      • getSampleMean

        double getSampleMean()
        Returns the sample mean of all observations since the initialization.
        Returns:
        double; the sample mean

      • getPopulationMean

        default double getPopulationMean()
        Returns the population mean of all observations since the initialization.
        Returns:
        double; the population mean

      • getSampleStDev

        double getSampleStDev()
        Returns the current (unbiased) sample standard deviation of all observations since the initialization. The sample standard deviation is defined as the square root of the sample variance.
        Returns:
        double; the sample standard deviation

      • getPopulationStDev

        double getPopulationStDev()
        Returns the current (biased) population standard deviation of all observations since the initialization. The population standard deviation is defined as the square root of the population variance.
        Returns:
        double; the population standard deviation

      • getSampleVariance

        double getSampleVariance()
        Returns the current (unbiased) sample variance of all observations since the initialization. The calculation of the sample variance in relation to the population variance is undisputed. The formula is:
          S2 = (1 / (n - 1)) * [ Σx2 - (Σx)2 / n ]
        which can be calculated on the basis of the calculated population variance σ2 as follows:
          S2 = σ2 * n / (n - 1)
        Returns:
        double; the current sample variance of this tally

      • getPopulationVariance

        double getPopulationVariance()
        Returns the current (biased) population variance of all observations since the initialization. The population variance is defined as:
        σ2 = (1 / n) * [ Σx2 - (Σx)2 / n ]
        Returns:
        double; the current population variance of this tally

      • getSampleSkewness

        double getSampleSkewness()
        Return the (unbiased) sample skewness of the ingested data. There are different formulas to calculate the unbiased (sample) skewness from the biased (population) skewness. Minitab, for instance calculates unbiased skewness as:
          Skewunbiased = Skewbiased [ ( n - 1) / n ] 3/2
        whereas SAS, SPSS and Excel calculate it as:
          Skewunbiased = Skewbiased √[ n ( n - 1)] / (n - 2)
        Here we follow the last mentioned formula. All formulas converge to the same value with larger n.
        Returns:
        double; the sample skewness of the ingested data

      • getPopulationSkewness

        double getPopulationSkewness()
        Return the (biased) population skewness of the ingested data. The population skewness is defined as:
          Skewbiased = [ Σ ( x - μ ) 3 ] / [ n . S3 ]
        where S2 is the sample variance. So the denominator is equal to [ n . sample_var3/2 ] .
        Returns:
        double; the skewness of the ingested data

      • getSampleKurtosis

        double getSampleKurtosis()
        Return the sample kurtosis of the ingested data. The sample kurtosis can be defined in multiple ways. Here, we choose the following formula:
          Kurtunbiased = [ Σ ( x - μ ) 4 ] / [ ( n - 1 ) . S4 ]
        where S2 is the sample variance. So the denominator is equal to [ ( n - 1 ) . sample_var2 ] .
        Returns:
        double; the sample kurtosis of the ingested data

      • getPopulationKurtosis

        double getPopulationKurtosis()
        Return the (biased) population kurtosis of the ingested data. The population kurtosis is defined as:
          Kurtbiased = [ Σ ( x - μ ) 4 ] / [ n . σ4 ]
        where σ2 is the population variance. So the denominator is equal to [ n . pop_var2 ] .
        Returns:
        double; the population kurtosis of the ingested data

      • getSampleExcessKurtosis

        double getSampleExcessKurtosis()
        Return the sample excess kurtosis of the ingested data. The sample excess kurtosis is the sample-corrected value of the excess kurtosis. Several formulas exist to calculate the sample excess kurtosis from the population kurtosis. Here we use:
          ExcessKurtunbiased = ( n - 1 ) / [( n - 2 ) * ( n - 3 )] [ ( n + 1 ) * ExcessKurtbiased + 6]
        This is the excess kurtosis that is calculated by, for instance, SAS, SPSS and Excel.
        Returns:
        double; the sample excess kurtosis of the ingested data

      • getPopulationExcessKurtosis

        double getPopulationExcessKurtosis()
        Return the population excess kurtosis of the ingested data. The kurtosis value of the normal distribution is 3. The excess kurtosis is the kurtosis value shifted by -3 to be 0 for the normal distribution.
        Returns:
        double; the population excess kurtosis of the ingested data

      • getQuantile

        double getQuantile​(double probability)
        Compute the quantile for the given probability.
        Parameters:
        probability - double; the probability for which the quantile is to be computed. The value should be between 0 and 1, inclusive.
        Returns:
        double; the quantile for the probability
        Throws:
        IllegalArgumentException - when the probability is less than 0 or larger than 1

      • getCumulativeProbability

        double getCumulativeProbability​(double quantile)
                         throws IllegalArgumentException
        Get, or estimate fraction of ingested values between -infinity up to and including a given quantile.
        Parameters:
        quantile - double; the given quantile
        Returns:
        double; the estimated or observed fraction of ingested values between -infinity up to and including the given quantile. When this TallyInterface has ingested zero values; this method shall return NaN.
        Throws:
        IllegalArgumentException - when quantile is NaN

      • getConfidenceInterval

        double[] getConfidenceInterval​(double alpha)
        returns the confidence interval on either side of the mean.
        Parameters:
        alpha - double; Alpha is the significance level used to compute the confidence level. The confidence level equals 100*(1 - alpha)%, or in other words, an alpha of 0.05 indicates a 95 percent confidence level.
        Returns:
        double[]; the confidence interval of this tally
        Throws:
        IllegalArgumentException - when alpha is less than 0 or larger than 1

      • getConfidenceInterval

        double[] getConfidenceInterval​(double alpha,
                               ConfidenceInterval side)
        returns the confidence interval based of the mean.
        Parameters:
        alpha - double; Alpha is the significance level used to compute the confidence level. The confidence level equals 100*(1 - alpha)%, or in other words, an alpha of 0.05 indicates a 95 percent confidence level.
        side - ConfidenceInterval; the side of the confidence interval with respect to the mean
        Returns:
        double[]; the confidence interval of this tally
        Throws:
        IllegalArgumentException - when alpha is less than 0 or larger than 1
        NullPointerException - when side is null