... """Joint distribution of two order statistics. Distribution of sample range.""" from pylab import figure, legend, title from pacal import *
		.

Using compiled interpolation routine
Compiled sparse grid routine not available

... X = NormalDistr(0, 1, sym="X") CIJ = IJthOrderStatsNDDistr(X, n=5, i=1, j=5) X1, X5 = CIJ.marginals X1.setSym("X1") X5.setSym("X5") M = TwoVarsModel(CIJ, X5 - X1) R = M.eval() R.plot(color="k", linewidth=2.0, linestyle="-", label=r'$X_{(5)} - X_{(1)}$'+'\n(sample range)') X1.plot(color="k", linewidth=2.0, linestyle="--", label=r'$X_{(1)}$') X5.plot(color="k", linewidth=2.0, linestyle=":", label=r'$X_{(5)}$') legend() figure() CIJ.plot() title("Joint distribution of min and max of 5 normals")
		.

Compare with values given in SAS/QC manual (functions: d2, d3)

... print repr(R.mean())
		.

2.3259289472810405

... print repr(R.var()), repr(R.std())
		.

0.74663760093428744 0.86408194109950442

... R.summary()
		.

============= summary =============
  PDISTR(-inf,inf)
                mean  =  2.3259289472810405
                 var  =  0.74663760093428744
            skewness  =  0.46551383286460202
            kurtosis  =  3.1691477882127366
             entropy  =  1.2509739123829031
              median  =  2.256882493026221
                mode  =  1.9999999697581552
            medianad  =  0.5844916749951602
      iqrange(0.025)  =  3.3473546743420313
            ci(0.05)  =  (0.8496716716531508, 4.197026345995182)
               range  =  (-inf, inf)
             tailexp  =  (0, -117.85789031893026)
             int_err  =  -4.4408920985006262e-16

... show()
		.