Research Article

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

Table 4

Max-EWMA results considering shift in the shape parameter of unit gamma distribution when , , , , and .


Case 1
0.052.7180.180 026 60.009 312 01.001.00370.028354.6651.00115.00262.00515.00827.002.913500.31485.3669.00158.00352.00689.001133.00
0.052.7180.180 026 60.009 312 01.001.1010.223 43.083 27.008.0010.0012.0014.002.91310.7083.231 97.008.0010.0012.0015.00
0.052.7180.180 026 60.009 312 01.001.205.119 30.978 84.004.005.006.006.002.9135.349 80.996 74.005.005.006.007.00
0.052.7180.180 026 60.009 312 01.001.303.675 30.573 73.003.004.004.004.002.9133.836 20.573 23.003.004.004.004.00
0.052.7180.180 026 60.009 312 01.001.403.046 40.282 93.003.003.003.003.002.9133.108 40.327 23.003.003.003.004.00
0.052.7180.180 026 60.009 312 01.000.908.477 42.834 65.006.008.0010.0012.002.9138.938 12.956 86.007.008.0011.0013.00
0.052.7180.180 026 60.009 312 01.000.803.784 70.888 73.003.004.004.005.002.9133.9360.905 83.003.004.004.005.00
0.052.7180.180 026 60.009 312 01.000.702.4060.523 32.002.002.003.003.002.9132.498 90.541 12.002.002.003.003.00
0.052.7180.180 026 60.009 312 01.000.601.899 10.326 41.002.002.002.002.002.9131.945 50.284 52.002.002.002.002.00
0.052.7180.180 026 60.009 312 01.000.501.3340.471 71.001.001.002.002.002.9131.423 50.494 11.001.001.002.002.00
0.103.040.258 086 10.019 059 31.001.00370.286 8360.7645.00109.00259.00516.00852.003.210499.25484.1663.00153.00354.00682.001138.00
0.103.040.258 086 10.019 059 31.001.109.092 13.394 55.007.008.0011.0014.003.2109.491 43.5426.007.009.0011.0014.00
0.103.040.258 086 10.019 059 31.001.204.236 80.958 33.004.004.005.005.003.2104.411 40.989 73.004.004.005.006.00
0.103.040.258 086 10.019 059 31.001.303.0210.499 22.003.003.003.004.003.2103.115 10.501 53.003.003.003.004.00
0.103.040.258 086 10.019 059 31.001.402.386 30.489 62.002.002.003.003.003.2102.503 70.505 82.002.003.003.003.00
0.103.040.258 086 10.019 059 31.000.907.408 32.994.005.007.009.0011.003.2107.744 63.1584.005.007.009.0012.00
0.103.040.258 086 10.019 059 31.000.803.085 70.837 42.003.003.004.004.003.2103.191 90.858 82.003.003.004.004.00
0.103.040.258 086 10.019 059 31.000.702.017 70.414 32.002.002.002.002.003.2102.060 90.411 62.002.002.002.003.00
0.103.040.258 086 10.019 059 31.000.601.4380.496 41.001.001.002.002.003.2101.507 90.500 81.001.002.002.002.00
0.103.040.258 086 10.019 059 31.000.501.037 20.189 31.001.001.001.001.003.2101.048 80.215 51.001.001.001.001.00
0.153.1950.320 924 50.029 386 71.001.00370.842 9362.0146.00115.00260.00505.00841.103.352500.784495.6858.00152.00351.50689.251133.10
0.153.1950.320 924 50.029 386 71.001.108.952 24.052 85.006.008.0011.0014.003.3539.361 14.185 65.006.008.0011.0015.00
0.153.1950.320 924 50.029 386 71.001.203.819 40.954 73.003.004.004.005.003.3533.956 10.983 13.003.004.004.005.00
0.153.1950.320 924 50.029 386 71.001.302.6660.562 72.002.003.003.003.003.3532.763 10.556 42.002.003.003.003.00
0.153.1950.320 924 50.029 386 71.001.402.112 90.316 82.002.002.002.003.003.3532.159 90.367 12.002.002.002.003.00
0.153.1950.320 924 50.029 386 71.000.907.045 33.283 64.005.006.009.0011.003.3537.359 83.486 54.005.007.009.0012.00
0.153.1950.320 924 50.029 386 71.000.802.769 40.823 82.002.003.003.004.003.3532.866 60.852 72.002.003.003.004.00
0.153.1950.320 924 50.029 386 71.000.701.799 90.485 31.002.002.002.002.003.3531.853 10.467 31.002.002.002.002.00
0.153.1950.320 924 50.029 386 71.000.601.203 70.402 81.001.001.001.002.003.3531.242 70.428 71.001.001.001.002.00
0.153.1950.320 924 50.029 386 71.000.501.005 90.076 61.001.001.001.001.003.3531.008 80.093 41.001.001.001.001.00
Case 2
0.052.7130.180 650 10.009 289 11.001.00370.559358.57852.00115.00259.50511.00835.102.906500.162485.59971.00156.00353.00683.001112.00
0.052.7130.180 650 10.009 289 11.001.1013.6824.8618.0010.0013.0016.0020.002.90614.4625.0299.0011.0014.0017.0021.00
0.052.7130.180 650 10.009 289 11.001.206.5911.4285.006.006.007.008.002.9066.8691.4695.006.007.008.009.00
0.052.7130.180 650 10.009 289 11.001.304.6490.7624.004.005.005.006.002.9064.8290.7734.004.005.005.006.00
0.052.7130.180 650 10.009 289 11.001.403.7610.5523.003.004.004.004.002.9063.9180.5183.004.004.004.004.00
0.052.7130.180 650 10.009 289 11.000.9011.3824.4956.008.0011.0014.0017.002.90611.8894.5917.009.0011.0014.0018.00
0.052.7130.180 650 10.009 289 11.000.804.8031.2793.004.005.006.006.002.9064.9981.3263.004.005.006.007.00
0.052.7130.180 650 10.009 289 11.000.702.9960.6782.003.003.003.004.002.9063.1110.6942.003.003.003.004.00
0.052.7130.180 650 10.009 289 11.000.602.1580.4102.002.002.002.003.002.9062.2150.4352.002.002.002.003.00
0.052.7130.180 650 10.009 289 11.000.501.8010.4071.002.002.002.002.002.9061.8670.3581.002.002.002.002.00
0.103.0260.259 390 10.019 083 31.001.00370.864361.68648.00111.00260.00519.00847.003.207499.903488.66061.00154.00354.00678.251133.00
0.103.0260.259 390 10.019 083 31.001.1012.8415.8847.009.0012.0016.0020.003.20713.6206.2367.009.0012.0016.0022.00
0.103.0260.259 390 10.019 083 31.001.205.5371.4354.005.005.006.007.003.2075.7741.4824.005.006.007.008.00
0.103.0260.259 390 10.019 083 31.001.303.8030.7373.003.004.004.005.003.2073.9670.7563.003.004.004.005.00
0.103.0260.259 390 10.019 083 31.001.403.0810.4413.003.003.003.004.003.2073.1750.4503.003.003.003.004.00
0.103.0260.259 390 10.019 083 31.000.9010.1494.8845.007.009.0013.0017.003.20710.5515.0775.007.009.0013.0017.00
0.103.0260.259 390 10.019 083 31.000.803.9351.2353.003.004.005.006.003.2074.1121.2533.003.004.005.006.00
0.103.0260.259 390 10.019 083 31.000.702.4490.6182.002.002.003.003.003.2072.5240.6332.002.002.003.003.00
0.103.0260.259 390 10.019 083 31.000.601.8330.4381.002.002.002.002.003.2071.8890.4271.002.002.002.002.00
0.103.0260.259 390 10.019 083 31.000.501.3120.4631.001.001.002.002.003.2071.3770.4861.001.001.002.002.00
0.153.1820.321 317 50.029 420 41.001.00369.685365.81343.00111.00256.00511.00845.003.365500.280484.31057.00150.00351.00698.001136.00
0.153.1820.321 317 50.029 420 41.001.1013.4377.3826.008.0012.0017.0023.003.36214.6648.3557.009.0012.0018.0025.00
0.153.1820.321 317 50.029 420 41.001.205.1161.5243.004.005.006.007.003.3625.3721.6014.004.005.006.007.00
0.153.1820.321 317 50.029 420 41.001.303.4170.7233.003.003.004.004.003.3623.5710.7463.003.003.004.005.00
0.153.1820.321 317 50.029 420 41.001.402.7180.5392.002.003.003.003.003.3622.8420.5192.003.003.003.003.00
0.153.1820.321 317 50.029 420 41.000.909.8535.3944.006.009.0012.0017.003.36210.5325.9065.006.009.0013.0018.00
0.153.1820.321 317 50.029 420 41.000.803.5761.2412.003.003.004.005.003.3623.7161.2802.003.004.004.005.00
0.153.1820.321 317 50.029 420 41.000.702.1940.5942.002.002.003.003.003.3622.2560.6032.002.002.003.003.00
0.153.1820.321 317 50.029 420 41.000.601.5890.5101.001.002.002.002.003.3621.6480.5021.001.002.002.002.00
0.153.1820.321 317 50.029 420 41.000.501.1380.3451.001.001.001.002.003.3621.1670.3731.001.001.001.002.00
Case 3
0.052.7110.180 491 70.009 324 51.001.00370.377350.69752.00115.75262.00519.00835.002.909500.460483.26267.00155.00353.00688.001125.00
0.052.7110.180 491 70.009 324 51.001.1020.9239.19611.0014.0019.0025.0033.002.90922.4819.84812.0016.0020.0027.0035.00
0.052.7110.180 491 70.009 324 51.001.209.4112.4577.008.009.0011.0013.002.9099.8732.5867.008.009.0011.0013.00
0.052.7110.180 491 70.009 324 51.001.306.4651.2375.006.006.007.008.002.9096.7571.2625.006.007.007.008.00
0.052.7110.180 491 70.009 324 51.001.405.1370.7914.005.005.006.006.002.9095.3620.8144.005.005.006.006.00
0.052.7110.180 491 70.009 324 51.000.9016.8328.0048.0011.0015.0021.0027.002.90917.9528.4929.0012.0016.0022.0029.00
0.052.7110.180 491 70.009 324 51.000.806.7222.1644.005.006.008.0010.002.9096.9962.2084.005.007.008.0010.00
0.052.7110.180 491 70.009 324 51.000.704.0471.0603.003.004.005.005.002.9094.1951.0783.003.004.005.006.00
0.052.7110.180 491 70.009 324 51.000.602.8480.6812.002.003.003.004.002.9092.9530.6982.003.003.003.004.00
0.052.7110.180 491 70.009 324 51.000.502.1800.4312.002.002.002.003.002.9092.2470.4672.002.002.003.003.00
0.103.0340.259 294 40.019 150 01.001.00370.080361.08047.00115.00258.00509.00833.003.210500.197486.35061.00152.00352.50686.001124.00
0.103.0340.259 294 40.019 150 01.001.1022.25212.83710.0013.0019.0028.0039.003.21124.23914.51910.0014.0020.0030.0043.00
0.103.0340.259 294 40.019 150 01.001.208.2932.7055.006.008.0010.0012.003.2118.7952.8906.007.008.0010.0013.00
0.103.0340.259 294 40.019 150 01.001.305.4401.2564.005.005.006.007.003.2115.6691.3084.005.005.006.007.00
0.103.0340.259 294 40.019 150 01.001.404.2450.7743.004.004.005.005.003.2114.4010.8034.004.004.005.005.00
0.103.0340.259 294 40.019 150 01.000.9016.0179.4407.009.0014.0020.0028.003.21117.15310.1427.0010.0015.0021.0030.00
0.103.0340.259 294 40.019 150 01.000.805.6602.1393.004.005.007.009.003.2115.9672.2823.004.006.007.009.00
0.103.0340.259 294 40.019 150 01.000.703.3301.0122.003.003.004.005.003.2113.4471.0422.003.003.004.005.00
0.103.0340.259 294 40.019 150 01.000.602.3460.6132.002.002.003.003.003.2112.4030.6182.002.002.003.003.00
0.103.0340.259 294 40.019 150 01.000.501.8270.4761.002.002.002.002.003.2111.8880.4581.002.002.002.002.00
0.153.1910.321 317 50.029 541 01.001.00370.863359.73946.00114.75261.00512.00841.003.368500.139487.50058.00148.00353.00699.251155.00
0.153.1910.321 317 50.029 541 01.001.1026.12318.5859.0013.0021.0033.0050.003.36929.99321.88610.0015.0024.0039.0058.00
0.153.1910.321 317 50.029 541 01.001.208.1273.1875.006.007.0010.0012.003.3698.6333.3595.006.008.0010.0013.00
0.153.1910.321 317 50.029 541 01.001.305.0221.3554.004.005.006.007.003.3695.2651.3844.004.005.006.007.00
0.153.1910.321 317 50.029 541 01.001.403.8260.7873.003.004.004.005.003.3693.9940.8213.003.004.004.005.00
0.153.1910.321 317 50.029 541 01.000.9016.60211.4256.009.0014.0021.0031.003.36917.98912.4886.009.0015.0023.0034.00
0.153.1910.321 317 50.029 541 01.000.805.2352.2613.004.005.006.008.003.3695.4422.2953.004.005.007.008.00
0.153.1910.321 317 50.029 541 01.000.702.9941.0022.002.003.004.004.003.3693.1021.0232.002.003.004.004.00
0.153.1910.321 317 50.029 541 01.000.602.0910.5991.002.002.002.003.003.3692.1510.6032.002.002.002.003.00
0.153.1910.321 317 50.029 541 01.000.501.5920.5211.001.002.002.002.003.3691.6440.5211.001.002.002.002.00
Case 4
0.052.7220.180 379 60.009 286 71.001.00370.678353.13354.90117.00263.00514.00826.202.913500.038488.98166.00156.00350.00685.251139.10
0.052.7220.180 379 60.009 286 71.001.1043.46126.10718.0025.0037.0054.0077.102.91348.07029.93919.9027.0040.0061.0087.00
0.052.7220.180 379 60.009 286 71.001.2017.0326.18111.0013.0016.0020.0025.002.91318.1866.62411.0013.0017.0022.0027.00
0.052.7220.180 379 60.009 286 71.001.3011.0342.8298.009.0011.0013.0015.002.91311.6092.9388.0010.0011.0013.0016.00
0.052.7220.180 379 60.009 286 71.001.408.5101.7067.007.008.009.0011.002.9138.9291.7667.008.009.0010.0011.00
0.052.7220.180 379 60.009 286 71.000.9031.71519.58812.0018.0027.0041.0058.002.91334.43421.68413.0019.0029.0044.0063.00
0.052.7220.180 379 60.009 286 71.000.8011.3424.7876.008.0010.0014.0018.002.91311.9425.0176.008.0011.0015.0018.00
0.052.7220.180 379 60.009 286 71.000.706.5612.2544.005.006.008.0010.002.9136.8332.2964.005.006.008.0010.00
0.052.7220.180 379 60.009 286 71.000.604.4381.2963.004.004.005.006.002.9134.6241.3153.004.004.005.006.00
0.052.7220.180 379 60.009 286 71.000.503.2880.8802.003.003.004.004.002.9133.4060.8892.003.003.004.005.00
0.103.0470.259 130 80.019 243 31.001.00370.285362.77348.00114.00262.00508.00839.003.233499.602493.30460.00150.00348.00683.251136.00
0.103.0470.259 130 80.019 243 31.001.1061.12247.89717.0028.0047.0080.00123.003.23374.41160.30819.0032.0056.0099.00152.00
0.103.0470.259 130 80.019 243 31.001.2017.4108.3409.0012.0015.0021.0028.003.23318.9379.40810.0012.0017.0023.0031.00
0.103.0470.259 130 80.019 243 31.001.3010.1343.3147.008.009.0012.0015.003.23310.7953.6037.008.0010.0013.0016.00
0.103.0470.259 130 80.019 243 31.001.407.4291.8275.006.007.008.0010.003.2337.8221.9386.006.008.009.0010.00
0.103.0470.259 130 80.019 243 31.000.9032.67125.01610.0015.0026.0043.0065.003.23337.04728.01511.0017.0029.0049.0074.00
0.103.0470.259 130 80.019 243 31.000.8010.1395.2105.006.009.0013.0017.003.23310.7425.5075.007.0010.0013.0018.00
0.103.0470.259 130 80.019 243 31.000.705.5522.2473.004.005.007.008.003.2335.7862.2773.004.005.007.009.00
0.103.0470.259 130 80.019 243 31.000.603.6931.2662.003.003.004.005.003.2333.8091.2982.003.004.005.005.00
0.103.0470.259 130 80.019 243 31.000.502.6980.8122.002.003.003.004.003.2332.8010.8342.002.003.003.004.00
0.153.2360.321 317 50.029 541 01.001.00370.094366.48743.00110.00257.00502.00850.003.428501.415493.98061.00149.00350.00693.001155.00
0.153.2360.321 317 50.029 541 01.001.10102.11092.38320.0037.0075.00137.00220.003.428136.543127.62824.0047.0099.00183.00300.10
0.153.2360.321 317 50.029 541 01.001.2020.58112.4819.0012.0017.0026.0037.003.42823.19014.50910.0013.0019.0029.0042.00
0.153.2360.321 317 50.029 541 01.001.3010.4294.2206.007.009.0012.0016.003.42811.2634.6907.008.0010.0013.0017.00
0.153.2360.321 317 50.029 541 01.001.407.2422.1675.006.007.008.0010.003.4287.6922.3295.006.007.009.0011.00
0.153.2360.321 317 50.029 541 01.000.9036.26730.3549.0015.0027.0048.0076.003.42841.06934.2609.0017.0031.0055.0086.00
0.153.2360.321 317 50.029 541 01.000.809.9865.8774.006.009.0013.0018.003.42810.6406.3024.006.009.0013.0019.00
0.153.2360.321 317 50.029 541 01.000.705.1482.3213.003.005.006.008.003.4285.3992.4423.004.005.007.009.00
0.153.2360.321 317 50.029 541 01.000.603.3511.2612.002.003.004.005.003.4283.4801.2772.003.003.004.005.00
0.153.2360.321 317 50.029 541 01.000.502.4270.7932.002.002.003.003.003.4282.5200.8162.002.002.003.004.00