Journal of Probability and Statistics / 2013 / Article / Tab 2

Research Article

Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean

Table 2

The estimated coverage probabilities and expected lengths of 90% confidence intervals for the coefficient of variation in a normal distribution with a known population mean.

Coverage probabilitiesExpected lengths
MillerMcKayVangelApprox.ShortestEqual-tailedMillerMcKayVangelApprox.ShortestEqual-tailed

50.050.84990.90660.88580.90160.90230.89790.05550.06070.05820.07410.05870.0675
0.100.85180.90690.88660.90240.90080.89880.11200.12370.11770.14820.11740.1349
0.200.85240.91300.89600.90360.89900.90060.23150.26890.24570.29630.23470.2696
0.330.85720.92580.91360.90380.89990.90010.40990.58720.45280.48950.38780.4453
0.500.86640.94300.93210.90360.89940.90010.69591.21230.93600.74090.58690.6741
0.670.87730.95780.94280.90310.90000.89921.06031.57641.63940.99470.78800.9050

100.050.87470.90310.88700.90200.89960.90060.03790.03960.03820.04310.03880.0416
0.100.87920.90520.88990.90240.90010.90140.07650.08040.07730.08640.07780.0833
0.200.88020.91350.90020.90130.89930.90010.15760.16860.16030.17260.15530.1664
0.330.88990.93040.92020.90170.90210.90150.27780.31400.28930.28530.25660.2750
0.500.89990.95270.94510.90070.90040.89950.47090.65750.53230.43290.38950.4174
0.670.91290.96940.96000.90180.89990.89920.71281.42051.02570.58010.52180.5593

150.050.88460.90100.88700.90000.89890.89880.03070.03160.03060.03330.03110.0326
0.100.88660.90650.89250.90110.90130.90010.06180.06380.06170.06660.06220.0652
0.200.89130.91270.90070.90060.89930.89870.12710.13280.12750.13300.12420.1301
0.330.90460.93080.92180.90120.90220.90130.22390.24180.22860.22000.20540.2151
0.500.91500.95440.94770.90000.90040.89910.37870.45220.40870.33380.31160.3264
0.670.92800.97250.96610.90100.90020.89990.57130.89000.70100.44660.41700.4367

250.050.89330.90560.89320.90290.90350.90210.02360.02400.02330.02470.02380.0244
0.100.89480.90540.89390.90100.90140.90040.04750.04850.04710.04950.04750.0489
0.200.90220.91460.90420.90280.90080.90210.09770.10030.09710.09880.09490.0976
0.330.91440.93180.92380.90050.90160.90040.17160.17960.17270.16300.15660.1610
0.500.92850.95480.94910.89760.89770.89780.28930.32070.30270.24710.23740.2440
0.670.94300.97680.97220.90180.89990.90080.43630.54180.49300.33100.31790.3268

500.050.89410.89920.89050.89930.89770.89890.01660.01670.01640.01700.01660.0168
0.100.89960.90430.89490.90040.90070.89970.03340.03370.03300.03390.03330.0337
0.200.90610.91180.90410.89940.89890.89960.06880.06970.06800.06780.06650.0674
0.330.92200.93140.92530.89970.89960.89940.12060.12360.12040.11180.10960.1112
0.500.94360.95830.95390.90090.90220.90100.20310.21530.20840.16950.16620.1685
0.670.95880.98010.97700.90100.90090.90080.30620.34600.33090.22710.22260.2257

1000.050.89980.90260.89610.90190.89020.90170.01170.01170.01150.01180.01130.0118
0.100.90000.90310.89590.89950.88780.89920.02360.02370.02330.02360.02270.0236
0.200.91100.91310.90720.90110.89010.90080.04850.04880.04800.04720.04530.0471
0.330.92770.93290.92820.90150.89000.90120.08500.08630.08470.07790.07480.0777
0.500.94850.95890.95610.90010.88850.89980.14290.14860.14550.11800.11330.1177
0.670.96780.98100.97900.90200.89100.90210.21570.23470.22890.15820.15190.1578

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