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stat_dispersion

Computes a number of robust statistics.

Prototype

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"  ; This library is automatically loaded
                                                             ; from NCL V6.2.0 onward.
                                                             ; No need for user to explicitly load.

	function stat_dispersion (
		x    : numeric,  
		opt  : logical   
	)

	return_val  :  [30]

Arguments

x

An array of any numeric type.

opt

Setting opt=True and opt@PrintStat=True means that the function will print the calculated statistics.

Return value

The results are returned in a one dimensional array of size [30]. Double if x is type "double"; otherwise, "float".

Description

This function is intended for large dataset sizes. It sorts the non-missing data values and uses the index values to extract the dectile, octile, sextile, quartile, tritile values. It does not do anything special with replicated values. It does not perform linear interpolation like "Minitab".

Currently the returned statistics (here, STATX) include:

               Mean="+STATX(0)      ; average of all values
             StdDev="+STATX(1)      ; standard deviation
                Min="+STATX(2)      ; minimum
             LowDec="+STATX(3)      ; lower dectile  
             LowOct="+STATX(4)      ; lower octile
             LowSex="+STATX(5)      ; lower sextile
        LowQuartile="+STATX(6)      ; lower quartile
             LowTri="+STATX(7)      ; lower tritile
             Median="+STATX(8)      ; median
            HighTri="+STATX(9)      ; upper tritile
       HighQuartile="+STATX(10)     ; upper quartile
            HighSex="+STATX(11)     ; upper sextile
            HighOct="+STATX(12)     ; upper octile
            HighDec="+STATX(13)     ; upper dectile
                Max="+STATX(14)     ; maximum
              Range="+STATX(15)     ; Max(x) - Min(x)
         Dispersion="+STATX(16)     ; Range/STATX(1)
        RMS Anomaly="+STATX(17)     ; sqrt( (x-xAvg)^2/N ) where N=# non-missing values
          #   Total="+STATX(18)     ; Total number of input values
          #    Used="+STATX(19)     ; Number of input values used for statistics
          # Missing="+STATX(20)     ; Number of missing values
          % Missing="+STATX(21)     ; percent of missing values

                                    ; STATX(22 to 29) added for v6.1.0
                                    ; STATX(22 to 27) require more than 1000 observations
                                    ; Otherwise, they are set to _FillValue

         Lower 0.1%="+STATX(22)     ; lower 0.1%   => 0.1th percentile
         Lower 1.0%="+STATX(23)     ; lower 1.0%   => 1th
         Lower 5.0%="+STATX(24)     ; lower 5.0%   => 5th
         Upper 5.0%="+STATX(25)     ; upper 5.0%   => 95th percentile
         Upper 1.0%="+STATX(26)     ; upper 1.0%   => 99th 
         Upper 0.1%="+STATX(27)     ; Upper 0.1%   => 99.9th 

           Skewness="+STATX(28)     ; Skewness    
           Kurtosis="+STATX(29)     ; Kurtosis    

See Also

avg, stddev, dim_stat4, dim_stat4_n, dim_avg, dim_avg_n, dim_stddev, dim_stddev_n, dim_median, dim_median_n

Examples

The following require that contributed.ncl be loaded prior to invoking the function.

 load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"

Example 1

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"

  b   = random_chi    (2   , (/1000/))

  opt = True
  opt@PrintStat = True
  statb = stat_dispersion(b, opt )
will yield
See http://www.ncl.ucar.edu/ for more details.
(0)      
(0)        ===> Robust Dispersion Statistics <===
(0)      [0]            Mean=1.96763
(0)      [1]          StdDev=1.94921
(0)      [2]             Min=0.00386701
(0)      [3]          LowDec=0.217212
(0)      [4]          LowOct=0.284452
(0)      [5]          LowSex=0.383918
(0)      [6]     LowQuartile=0.592704
(0)      [7]          LowTri=0.783372
(0)      [8]          Median=1.34768
(0)      [9]         HighTri=2.21197
(0)      [10]   HighQuartile=2.75091
(0)      [11]        HighSex=3.55215
(0)      [12]        HighOct=4.0649
(0)      [13]        HighDec=4.39585
(0)      [14]            Max=12.4941
(0)      [15]          Range=12.4903
(0)      [16]     Dispersion=6.40786
(0)      [17]    RMS Anomaly=1.94824
(0)      [18]      #   Total=1000
(0)      [19]      #    Used=1000
(0)      [20]      # Missing=0
(0)      [21]      % Missing=0
(0)	 [22]     Lower 0.1%=0.00386701
(0)	 [23]     Lower 1.0%=0.0306022
(0)	 [24]     Lower 5.0%=0.112683
(0)	 [25]     Upper 5.0%=5.76009
(0)	 [26]     Upper 1.0%=9.32739
(0)	 [27]     Upper 0.1%=12.0497
(0)      [28]       Skewness=1.85963
(0)      [29]       Kurtosis=4.42162


Example 2: Very similar but the user prints the values.

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"


  a   = random_normal (0,50, (/64,128/))
  b   = random_chi    (2   , (/1000/))
  c   = random_gamma  (75,2, (/50,100/))

  opt   = False
  stata = stat_dispersion(a, opt )
  statb = stat_dispersion(b, opt )
  statc = stat_dispersion(c, opt )

  nStat = num(.not.ismissing(stata))
  statLabel = new ( nStat, "string")

  statLabel = (/ "    mean", "  stddev", "     min" \
               , "  lowDec", "  LowOct", "  LowSex" \
               , "LowQuart", "  LowTri" \
               , "  Median" \
               , "   HiTri", " HiQuart","   HiSex","   HiOct", "   HiDec" \
               , "     Max", "   Range","  Disper","     RMS" \
               , "    nTot", "    nUse","    nMsg","    %Msg" /)

  print(statLabel+"   " \
       +sprintf("%9.5f", stata(0:nStat-1))+"   " \
       +sprintf("%9.5f", statb(0:nStat-1))+"   " \
       +sprintf("%9.5f", statc(0:nStat-1)) )
The print yields (titles added):
                      Normal         Chi      Gamma
(0)	    mean    -0.50953     2.06056     0.02719
(1)	  stddev    49.86744     2.01248     0.01904
(2)	     min  -202.86754     0.00221     0.00012
(3)	  lowDec   -64.91030     0.24242     0.00730
(4)	  LowOct   -58.03373     0.29952     0.00834
(5)	  LowSex   -48.72330     0.39296     0.01013
(6)	LowQuart   -33.34077     0.61729     0.01310
(7)	  LowTri   -21.46025     0.87286     0.01633
(8)	  Median    -0.80563     1.39053     0.02284
(9)	   HiTri    21.11183     2.31731     0.03127
(10)	 HiQuart    33.43311     2.90952     0.03675
(11)	   HiSex    47.70136     3.63185     0.04362
(12)	   HiOct    56.36256     4.26664     0.04851
(13)	   HiDec    62.17917     4.70950     0.05222
(14)	     Max   182.83937    15.80180     0.16530
(15)	   Range   385.70691    15.79958     0.16518
(16)	  Disper     7.73464     7.85079     8.67700
(17)	     RMS    49.86436     2.01148     0.01903
(18)	    nTot  8192.00000  1000.00000  5000.00000
(19)	    nUse  8192.00000  1000.00000  5000.00000
(20)	    nMsg     0.00000     0.00000     0.00000
(21)	    %Msg     0.00000     0.00000     0.00000
(22)        0.1%   -153.01517    0.00189     0.00061
(23)        1.0%   -117.51499    0.01804     0.00195
(24)        5.0%   -84.37138     0.08294     0.00486
(25)       95.0%    82.00737     5.87699     0.06296
(26)       99.0%   116.81857     7.92976     0.08951
(27)       99.9%   155.62813    13.01617     0.12813
(28)    Skewness    -0.00585     1.64650     1.46050
(29)    Kurtosis     0.02865     3.99830     3.46480