Package hec.lang

Class Statistics

java.lang.Object
hec.lang.Statistics
public class Statistics extends Object
Title: Statistics - supplies static statistical results. Description: This includes returning the normal standard deviate for an exceedance probability, getting Log Pearson Type III deviates, computing confidence limits using the incomplete beta function, as well as simple utilities such as ordering an array of numbers and computing the mean and standard deviation of a series of numbers. Company:

  • Constructor Summary

    Constructors
    Constructor
    Description
    Statistics()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    protected static double
    betacf(double a, double b, double pn)
    This is the continued fraction portion of the incomplete beta function evaluation routine as described in "Numerical Recipes (fortran) " by W.
    protected static double
    betai(double a, double b, double pn)
    Computes the incomplete beta function routine as described in "Numerical Recipes (fortran) " by W.
    protected static int
    btclmt(int nsyst, double pe, double[] pc)
    Compute confidence limits for a given exceedance probability given an ordered set derived from observations of an idependent random variable pc is computed to be the probability tha the quantile (discharge) associated with exceedance probability exceeds a given value Convert exceedance probability to non-exceedance pe is the exceedance probability associated with a quantile xe
    static int
    computeConfidenceLimits(int nyr, double probFlow, double[] probFlowExceeds)
    Computes confidence limits for a given exceedance probability given an ordered set derived from observations of an idependent random variable.
    static int
    computeCurveMoments(int nuOrds, double[] prob, double[] flow, double[] results)
    Calculates the mean and standard deviation for the specified frequency curve by approximating the integral definition.
    protected static double
    gammln(double y)
    Computes the natural of the gamma function routine as described in "Numerical Recipes (fortran) " by W H Press, Brian P Flannery, Saul A Teukolsky, W T Vetterling, cambridge press, 1989, pg 166.
    static double
    getLP3Deviate(double stdNormDev, double skew)
    Return the Log Pearson Type III deviate for the input standard normal deviate and skew.
    static double
    getNormalStandardDeviate(double lp3Dev, double skew)
    Return the Standard Normal deviate for the input Log Pearson Type III deviate and skew.
    static double
    getNormalStdDeviate(double prob)
    getNormalStdDeviate returns the normal standard deviate for an input probability.
    static boolean
    isMonotonicallyDecreasing(int nval, double[] x)
    Returns boolean indicating if x array is monotonically decreasing.
    static boolean
    isMonotonicallyIncreasing(int nval, double[] x)
    Returns boolean indicating if x array is monotonically increasing.
    static void
    main(String[] args)
     
    static boolean
    orderArray(int nval, char direction, double[] x, double[] y)
    Orders a paired array so that the x array is monotonically increasing or decreasing.
    static void
    printResult(String s, double devIn, double devOut)
    Print Current Deviate Values
    static double
    roundIt2(float sp, int nsig)
    Rounds single precision floating point number to nsig digits and stores in double.
    static double
    roundIt3(float sp, int nsig)
    Rounds single precision floating point number to nsig digits and stores in double.
    static double
    roundRealToDouble(float sp)
    Rounds single precision floating point number to 7 digits and stores in double
    static double
    roundRealToDouble(float sp, int numSignificantDigits)
    Rounds single precision floating point number and stores in double
    protected static int
    search(int medpos, int npt, double[] sd, int[] compPos, int[] ipos)
    Finds the minimum in the exceedance probability Uncertainty relationship

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Statistics

      public Statistics()

  • Method Details

    • getNormalStdDeviate

      public static double getNormalStdDeviate(double prob)
      getNormalStdDeviate returns the normal standard deviate for an input probability. prob is exceedance probability between 0 and 1;

    • orderArray

      public static boolean orderArray(int nval, char direction, double[] x, double[] y)
      Orders a paired array so that the x array is monotonically increasing or decreasing. nval Number of ordinates (rows) in the paired array. direction Direction that the x array is ordered: d or D Array will decrease. i or I Array will increase. x Array that will be ordered. y Array whose ordiantes correspond to the x array.

    • isMonotonicallyDecreasing

      public static boolean isMonotonicallyDecreasing(int nval, double[] x)
      Returns boolean indicating if x array is monotonically decreasing.

    • isMonotonicallyIncreasing

      public static boolean isMonotonicallyIncreasing(int nval, double[] x)
      Returns boolean indicating if x array is monotonically increasing.

    • computeCurveMoments

      public static int computeCurveMoments(int nuOrds, double[] prob, double[] flow, double[] results)
      Calculates the mean and standard deviation for the specified frequency curve by approximating the integral definition. results is an array of 2 that returns the (1) mean, (2) standard deviation.

    • computeConfidenceLimits

      public static int computeConfidenceLimits(int nyr, double probFlow, double[] probFlowExceeds)
      Computes confidence limits for a given exceedance probability given an ordered set derived from observations of an idependent random variable. probFlowExceeds is computed to be the probability that the quantile (discharge) associated with exceedance probability exceed a given value Convert exeedance probability to non-exceedance probFlow is the exceedance probabibility associated with a quantile flow the array is ordered from smallest to largest betai returns the probability that the ith ordered variable is less than the quantile flow associated with non-exeedance probability pn in other words betai returns the probability that the quantile xe exceeds the ith ordered statistic

    • betai

      protected static double betai(double a, double b, double pn)
      Computes the incomplete beta function routine as described in "Numerical Recipes (fortran) " by W. H. Press, Brian P. Flannery, Saul A. Teukolsky, W. T. Vetterling, cambridge press, 1989, pg.166

    • betacf

      protected static double betacf(double a, double b, double pn)
      This is the continued fraction portion of the incomplete beta function evaluation routine as described in "Numerical Recipes (fortran) " by W. H. Press, Brian P. Flannery, Saul A. Teukolsky, W. T. Vetterling, Cambridge press, 1989, pg.168 Continued fraction being evaluated is frac = 1/(1 + d1/(1 + d2/(1 + d3 ..... where d2m+1 = -(a+m)(a+b+m)x/((a+2m)(a+2m+1)) d2m = m(b-m)x/((a+2m-1)(a+2m))

    • btclmt

      protected static int btclmt(int nsyst, double pe, double[] pc)
      Compute confidence limits for a given exceedance probability given an ordered set derived from observations of an idependent random variable pc is computed to be the probability tha the quantile (discharge) associated with exceedance probability exceeds a given value Convert exceedance probability to non-exceedance pe is the exceedance probability associated with a quantile xe

    • gammln

      protected static double gammln(double y)
      Computes the natural of the gamma function routine as described in "Numerical Recipes (fortran) " by W H Press, Brian P Flannery, Saul A Teukolsky, W T Vetterling, cambridge press, 1989, pg 166. The routine is based on an algorithm by Lanczos who somehow came up with a way of improving the sterling formula. Full accuracy is obtained for y > 1 for y <= 1 the reflection formula is used

    • search

      protected static int search(int medpos, int npt, double[] sd, int[] compPos, int[] ipos)
      Finds the minimum in the exceedance probability Uncertainty relationship

    • getLP3Deviate

      public static double getLP3Deviate(double stdNormDev, double skew)
      Return the Log Pearson Type III deviate for the input standard normal deviate and skew.

    • getNormalStandardDeviate

      public static double getNormalStandardDeviate(double lp3Dev, double skew)
      Return the Standard Normal deviate for the input Log Pearson Type III deviate and skew.

    • printResult

      public static void printResult(String s, double devIn, double devOut)
      Print Current Deviate Values

    • roundRealToDouble

      public static double roundRealToDouble(float sp, int numSignificantDigits)
      Rounds single precision floating point number and stores in double
      Parameters:
      sp - Single Precision Number
      numSignificantDigits - Integer Number
      Returns:
      Double precision number

    • roundRealToDouble

      public static double roundRealToDouble(float sp)
      Rounds single precision floating point number to 7 digits and stores in double
      Parameters:
      sp - Single Precision Number
      Returns:
      Double precision number

    • roundIt2

      public static double roundIt2(float sp, int nsig)
      Rounds single precision floating point number to nsig digits and stores in double. It does it by processing characters rather than a numeric calculation.
      Parameters:
      sp - Input single precision number.
      nsig - Number of significant digits desired in output result.
      Returns:
      RESULT contains the double value of sp rounded to nsig digits.

    • roundIt3

      public static double roundIt3(float sp, int nsig)
      Rounds single precision floating point number to nsig digits and stores in double. It does it by processing characters rather than a numeric calculation.
      Parameters:
      sp - Input single precision number.
      nsig - Number of significant digits desired in output result.
      Returns:
      RESULT contains the double value of sp rounded to nsig digits.

    • main

      public static void main(String[] args)