Research Article

Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions

Table 3

Max-EWMA results considering shift in the shape1 parameter of beta distribution when , ,  = 0.20, , and .


Case 1
0.052.7180.180 026 60.009 312 01.001.00370.293357.63051.00114.00260.00507.00839.002.913500.901484.01866.90155.00352.00683.251127.00
0.052.7180.180 026 60.009 312 01.101.0020.4979.97510.0013.0018.0025.0034.002.91322.01210.68111.0014.0020.0027.0036.00
0.052.7180.180 026 60.009 312 01.201.008.8242.8026.007.008.0010.0013.002.9139.2752.8806.007.009.0011.0013.00
0.052.7180.180 026 60.009 312 01.301.005.7411.4594.005.006.007.008.002.9135.9961.5114.005.006.007.008.00
0.052.7180.180 026 60.009 312 01.401.004.3540.9553.004.004.005.006.002.9134.5260.9843.004.004.005.006.00
0.052.7180.180 026 60.009 312 00.901.0019.5249.01210.0013.0018.0024.0031.002.91320.6389.38711.0014.0019.0025.0033.00
0.052.7180.180 026 60.009 312 00.801.008.0242.2475.006.008.009.0011.002.9138.3652.3176.007.008.0010.0011.00
0.052.7180.180 026 60.009 312 00.701.005.0411.0604.004.005.006.006.002.9135.2571.1024.004.005.006.007.00
0.052.7180.180 026 60.009 312 00.601.003.7030.6633.003.004.004.004.002.9133.8510.6743.003.004.004.005.00
0.052.7180.180 026 60.009 312 00.501.002.9750.4212.003.003.003.003.002.9133.0760.4023.003.003.003.004.00
0.103.0400.258 086 10.019 059 31.001.00370.458362.65147.00114.00259.00503.25852.003.210499.010483.87260.00151.00350.00694.001139.00
0.103.0400.258 086 10.019 059 31.101.0020.87812.8948.0012.0018.0027.0038.003.21022.21013.7089.0012.0019.0028.0040.00
0.103.0400.258 086 10.019 059 31.201.007.7032.9764.006.007.009.0012.003.2107.9663.0945.006.007.0010.0012.00
0.103.0400.258 086 10.019 059 31.301.004.8051.4523.004.005.006.007.003.2105.0021.4993.004.005.006.007.00
0.103.0400.258 086 10.019 059 31.401.003.5880.9343.003.003.004.005.003.2103.7070.9513.003.004.004.005.00
0.103.0400.258 086 10.019 059 30.901.0019.66811.4818.0012.0017.0025.0035.003.21021.26012.7509.0012.0018.0026.0038.00
0.103.0400.258 086 10.019 059 30.801.006.8832.3294.005.006.008.0010.003.2107.1922.4435.005.007.008.0010.00
0.103.0400.258 086 10.019 059 30.701.004.1751.0543.003.004.005.006.003.2104.3061.0803.004.004.005.006.00
0.103.0400.258 086 10.019 059 30.601.003.0250.6262.003.003.003.004.003.2103.1270.6302.003.003.003.004.00
0.103.0400.258 086 10.019 059 30.501.002.3480.4862.002.002.003.003.003.2102.4310.5102.002.002.003.003.00
0.153.1950.320 219 40.029 386 71.001.00370.843362.01046.00115.00260.00505.00841.103.352500.784497.61659.00149.00349.00706.001140.10
0.153.1950.320 219 40.029 386 71.101.0022.76116.3397.0011.0018.0030.0044.003.35225.13218.3988.0012.0020.0033.0049.00
0.153.1950.320 219 40.029 386 71.201.007.3263.3224.005.007.009.0012.003.3527.7513.5104.005.007.009.0012.00
0.153.1950.320 219 40.029 386 71.301.004.3771.4953.003.004.005.006.003.3524.5811.5423.003.004.005.007.00
0.153.1950.320 219 40.029 386 71.401.003.2130.9172.003.003.004.004.003.3523.3070.9322.003.003.004.004.00
0.153.1950.320 219 40.029 386 70.901.0021.76614.9878.0011.0018.0028.0041.003.35223.88016.7228.0012.0019.0031.0046.00
0.153.1950.320 219 40.029 386 70.801.006.4902.5824.005.006.008.0010.003.3526.8382.7064.005.006.008.0010.00
0.153.1950.320 219 40.029 386 70.701.003.7651.0583.003.004.004.005.003.3523.8841.0803.003.004.004.005.00
0.153.1950.320 219 40.029 386 70.601.002.6790.6382.002.003.003.003.003.3522.7730.6472.002.003.003.004.00
0.153.1950.320 219 40.029 386 70.501.002.1290.3482.002.002.002.003.003.3522.1730.3862.002.002.002.003.00
Case 2
0.052.7130.180 650 10.009 289 11.001.00370.559360.57851.00116.00259.50511.00835.102.906500.162485.59971.00156.00353.00683.001112.00
0.052.7130.180 650 10.009 289 11.101.0033.48420.28414.0019.0028.0042.0060.002.90636.01221.60615.0021.0031.0045.0064.00
0.052.7130.180 650 10.009 289 11.201.0013.1555.0778.009.0012.0016.0020.002.90614.0095.5118.0010.0013.0017.0021.00
0.052.7130.180 650 10.009 289 11.301.008.2802.5865.006.008.0010.0012.002.9068.7162.6796.007.008.0010.0012.00
0.052.7130.180 650 10.009 289 11.401.006.1411.6244.005.006.007.008.002.9066.4341.6684.005.006.007.009.00
0.052.7130.180 650 10.009 289 10.901.0031.50218.05114.0019.0027.0039.0055.002.90634.11619.49315.0020.0029.0043.0060.00
0.052.7130.180 650 10.009 289 10.801.0011.8204.1167.009.0011.0014.0017.002.90612.5374.3188.009.0012.0015.0018.00
0.052.7130.180 650 10.009 289 10.701.007.1671.8395.006.007.008.0010.002.9067.4971.8885.006.007.009.0010.00
0.052.7130.180 650 10.009 289 10.601.005.1531.0634.004.005.006.007.002.9065.3441.0754.005.005.006.007.00
0.052.7130.180 650 10.009 289 10.501.004.0180.7073.004.004.004.005.002.9064.1910.7193.004.004.005.005.00
0.103.0260.259 390 10.019 083 31.001.00370.123360.81147.00112.00260.00508.00845.003.207500.490494.33061.00151.00350.00691.251142.20
0.103.0260.259 390 10.019 083 31.101.0036.56727.53311.0017.0029.0048.0072.003.20741.29731.51912.0019.0032.5054.0081.00
0.103.0260.259 390 10.019 083 31.201.0012.2356.1206.008.0011.0015.0020.003.20712.8546.4566.008.0011.0016.0021.00
0.103.0260.259 390 10.019 083 31.301.007.1812.7294.005.007.009.0011.003.2077.5402.8914.005.007.009.0011.00
0.103.0260.259 390 10.019 083 31.401.005.1891.6503.004.005.006.007.003.2075.3901.7103.004.005.006.008.00
0.103.0260.259 390 10.019 083 30.901.0035.67325.67112.0018.0028.0046.0069.003.20740.48730.12413.0019.0032.0052.0080.00
0.103.0260.259 390 10.019 083 30.801.0010.7894.7246.007.0010.0013.0017.003.20711.4055.0256.008.0010.0014.0018.00
0.103.0260.259 390 10.019 083 30.701.006.0771.8774.005.006.007.009.003.2076.3851.9844.005.006.007.009.00
0.103.0260.259 390 10.019 083 30.601.004.2371.0333.004.004.005.006.003.2074.4241.0803.004.004.005.006.00
0.103.0260.259 390 10.019 083 30.501.003.2910.6543.003.003.004.004.003.2073.4060.6773.003.003.004.004.00
0.153.1820.320 924 50.029 420 41.001.00369.737360.04944.00112.00256.50512.00850.003.365500.976496.84856.00148.00347.00691.001145.00
0.153.1820.320 924 50.029 420 41.101.0042.33835.52310.0017.0032.0056.0087.003.36548.99741.60411.0020.0037.0065.00103.00
0.153.1820.320 924 50.029 420 41.201.0012.2607.3065.007.0010.0015.0022.003.36513.2397.8716.008.0011.0017.0023.00
0.153.1820.320 924 50.029 420 41.301.006.8042.9954.005.006.008.0011.003.3657.1513.1374.005.007.009.0011.00
0.153.1820.320 924 50.029 420 41.401.004.7611.7073.004.004.006.007.003.3654.9521.7753.004.005.006.007.00
0.153.1820.320 924 50.029 420 40.901.0044.03936.56411.0018.0033.0058.0091.003.36551.92743.70713.0021.0039.0069.00109.00
0.153.1820.320 924 50.029 420 40.801.0010.7785.4945.007.0010.0013.0018.003.36511.5606.0466.007.0010.0014.0019.00
0.153.1820.320 924 50.029 420 40.701.005.6752.0334.004.005.007.008.003.3655.9432.0934.004.006.007.009.00
0.153.1820.320 924 50.029 420 40.601.003.8671.0663.003.004.004.005.003.3654.0171.1143.003.004.005.005.00
0.153.1820.320 924 50.029 420 40.501.002.9350.6962.002.003.003.004.003.3653.0390.6962.003.003.003.004.00
Case 3
0.052.7110.180 491 70.009 324 51.001.00370.786357.29751.00117.00262.00506.00831.102.909500.195484.82167.00155.00346.00683.001136.10
0.052.7110.180 491 70.009 324 51.101.0053.00537.11118.0027.0043.0069.00102.102.90857.89541.61619.0028.0046.0075.00112.00
0.052.7110.180 491 70.009 324 51.201.0019.6829.47410.0013.0018.0024.0032.002.90821.01410.09710.0014.0019.0026.0034.00
0.052.7110.180 491 70.009 324 51.301.0011.9744.5657.009.0011.0014.0018.002.90812.5134.7237.009.0012.0015.0019.00
0.052.7110.180 491 70.009 324 51.401.008.6592.7926.007.008.0010.0012.002.9089.0652.8866.007.009.0011.0013.00
0.052.7110.180 491 70.009 324 50.901.0050.71634.34018.0027.0041.0065.0096.002.90857.80039.62820.0030.0047.0075.00110.00
0.052.7110.180 491 70.009 324 50.801.0017.5517.44210.0012.0016.0021.0027.002.90818.8138.13510.0013.0017.0023.0029.00
0.052.7110.180 491 70.009 324 50.701.0010.2923.1797.008.0010.0012.0014.002.90810.7083.3077.008.0010.0012.0015.00
0.052.7110.180 491 70.009 324 50.601.007.1071.7395.006.007.008.009.002.9087.4871.8215.006.007.008.0010.00
0.052.7110.180 491 70.009 324 50.501.005.4551.1044.005.005.006.007.002.9085.7051.1334.005.006.006.007.00
0.103.0340.259 294 40.019 150 01.001.00370.837354.19749.00115.00267.00513.00842.003.210500.029484.46759.00149.00355.00695.251123.00
0.103.0340.259 294 40.019 150 01.101.0061.76751.60615.0025.0047.0081.25130.103.21072.34561.31817.0029.0054.0097.00152.00
0.103.0340.259 294 40.019 150 01.201.0019.62211.8768.0011.0017.0025.0035.003.21020.93112.9558.0012.0018.0026.0038.00
0.103.0340.259 294 40.019 150 01.301.0010.8085.0725.007.0010.0013.0017.003.21011.4405.3606.008.0010.0014.0019.00
0.103.0340.259 294 40.019 150 01.401.007.5342.9744.005.007.009.0011.003.2107.8573.0255.006.007.009.0012.00
0.103.0340.259 294 40.019 150 00.901.0066.02753.78617.0028.0050.0088.00136.003.21078.14966.74019.0031.0058.00104.00165.00
0.103.0340.259 294 40.019 150 00.801.0017.4079.5498.0011.0015.0022.0030.003.21018.68810.3668.0011.0016.0023.0032.00
>0.103.0340.259 294 40.019 150 00.701.009.1373.5035.007.008.0011.0014.003.2109.5813.6946.007.009.0011.0015.00
0.103.0340.259 294 40.019 150 00.601.006.0881.8234.005.006.007.008.003.2106.3171.8584.005.006.007.009.00
0.103.0340.259 294 40.019 150 00.501.004.5451.1043.004.004.005.006.003.2104.7361.1244.004.005.005.006.00
0.153.1910.321 317 50.029 541 01.001.00369.015363.01645.00111.00255.00505.00850.003.368500.117491.44162.00150.00355.00687.001131.10
0.153.1910.321 317 50.029 541 01.101.0071.64264.78614.0026.0052.0095.00157.003.36885.58777.54316.0030.0062.00118.00188.00
0.153.1910.321 317 50.029 541 01.201.0020.94814.8447.0011.0017.0027.0040.003.36823.22016.9997.0011.0019.0030.0045.00
0.153.1910.321 317 50.029 541 01.301.0010.7655.9095.007.009.0013.0018.003.36811.4936.3845.007.0010.0014.0020.00
0.153.1910.321 317 50.029 541 01.401.007.1823.2744.005.007.009.0011.003.3687.5163.4254.005.007.009.0012.00
0.153.1910.321 317 50.029 541 00.901.0088.24580.19817.0032.0064.00119.00193.003.368110.05798.92620.0038.0080.00151.00241.00
0.153.1910.321 317 50.029 541 00.801.0019.15712.6987.0010.0016.0024.0036.003.36821.08414.0028.0011.0017.0027.0039.00
0.153.1910.321 317 50.029 541 00.701.008.8473.9915.006.008.0011.0014.003.3689.4194.1835.006.009.0011.0015.00
0.153.1910.321 317 50.029 541 00.601.005.6501.9214.004.005.007.008.003.3685.9191.9934.004.006.007.008.00
0.153.1910.321 317 50.029 541 00.501.004.1211.0963.003.004.005.006.003.3684.2991.1683.003.004.005.006.00
Case 4
0.052.7220.180 379 60.009 286 71.001.00371.624355.93652.00115.00264.00510.00839.002.913499.713475.50569.00157.00359.00678.001123.00
0.052.7220.180 379 60.009 286 71.101.00102.89087.21925.0042.0077.00134.00216.002.913118.797101.98026.9047.0088.00158.00254.00
0.052.7220.180 379 60.009 286 71.201.0038.21523.90015.0021.0032.0049.0069.102.91342.07227.10416.0023.0035.0054.0077.00
0.052.7220.180 379 60.009 286 71.301.0021.93911.43710.0014.0019.0027.0037.002.91323.34711.97311.0015.0021.0029.0039.00
0.052.7220.180 379 60.009 286 71.401.0015.2026.5318.0011.0014.0019.0024.002.91316.2647.1279.0011.0015.0020.0026.00
0.052.7220.180 379 60.009 286 70.901.00109.60888.08528.0046.0083.00147.00224.002.913128.305105.21032.0054.0097.00170.00266.10
0.052.7220.180 379 60.009 286 70.801.0034.58919.80615.0021.0030.0043.0061.002.91337.45021.39116.0022.0032.0047.0065.00
0.052.7220.180 379 60.009 286 70.701.0018.4867.69610.0013.0017.0022.0029.002.91319.5498.11111.0014.0018.0024.0030.00
0.052.7220.180 379 60.009 286 70.601.0012.3234.0918.009.0012.0014.0018.002.91312.9094.2548.0010.0012.0015.0019.00
0.052.7220.180 379 60.009 286 70.501.009.0692.3996.007.009.0010.0012.002.9139.5912.4857.008.009.0011.0013.00
0.103.0480.259 130 80.019 243 31.001.00369.605360.08546.00113.00258.00510.25844.003.234501.045490.02659.00149.00349.00691.001144.10
0.103.0480.259 130 80.019 243 31.101.00121.821111.48522.0043.0088.00165.00267.003.234145.184135.10124.0049.00104.00195.00324.00
0.103.0480.259 130 80.019 243 31.201.0042.27633.25612.0019.0033.0055.0086.003.23449.54839.63613.0022.0038.0065.00101.00
0.103.0480.259 130 80.019 243 31.301.0022.33714.4788.0012.0019.0028.0041.003.23424.73416.2729.0013.0020.0032.0046.00
0.103.0480.259 130 80.019 243 31.401.0014.7168.0826.909.0013.0019.0025.003.23415.5988.5867.009.0014.0020.0027.00
0.103.0480.259 130 80.019 243 30.901.00166.689156.86628.0056.00118.00225.00373.003.234220.609204.47536.0074.00160.00302.00483.00
0.103.0480.259 130 80.019 243 30.801.0042.61331.08414.0020.0033.0056.0082.003.23449.08036.58215.0023.0039.0063.0097.00
0.103.0480.259 130 80.019 243 30.701.0018.70910.1809.0011.0016.0023.0032.003.23420.35311.2159.0012.0018.0025.0035.00
0.103.0480.259 130 80.019 243 30.601.0011.4854.7457.008.0010.0014.0018.003.23412.1314.9417.009.0011.0015.0019.00
0.103.0480.259 130 80.019 243 30.501.008.0592.6765.006.008.009.0012.003.2348.4282.7556.006.008.0010.0012.00
0.153.2360.321 317 50.029 5411.001.00370.007363.04246.00113.75258.00506.00843.103.428501.583494.73657.00152.00351.00702.001139.10
0.153.2360.321 317 50.029 5411.101.00132.713127.20020.0042.0094.00181.00300.003.428167.453159.60324.0054.00120.00230.00372.00
0.153.2360.321 317 50.029 5411.201.0049.44342.18311.0020.0037.0066.00105.003.42857.58649.86412.0022.0043.0077.00123.00
0.153.2360.321 317 50.029 5411.301.0024.50318.4028.0012.0019.0032.0048.003.42827.29921.3308.0013.0021.0035.0054.00
0.153.2360.321 317 50.029 5411.401.0015.21510.0336.008.0013.0019.0028.003.42816.46110.7096.009.0014.0021.0030.00
0.153.2360.321 317 50.029 5410.901.00248.646240.20833.0077.00174.00345.25563.003.428345.015338.70344.00104.00244.00475.00774.10
0.153.2360.321 317 50.029 5410.801.0058.91449.93414.0024.0044.0078.00123.003.42874.06664.87217.0029.0054.0098.00158.00
0.153.2360.321 317 50.029 5410.701.0021.71614.3598.0012.0018.0028.0041.003.42824.74616.6619.0013.0020.0032.0046.00
0.153.2360.321 317 50.029 5410.601.0011.8335.8706.008.0010.0014.0020.003.42812.6756.3726.008.0011.0015.0021.00
0.153.2360.321 317 50.029 5410.501.007.8242.9985.006.007.009.0012.003.4288.3033.2265.006.008.0010.0013.00