Table 5 Comparison of Bias, MSE, MRE for parameter estimateswhen \(\alpha = 0.20\); \(\beta = 0.95\); \(\gamma = 1.15\);\(\delta = 0.25\); and \(\lambda = 1.05\).

From: A novel extension of the power lindley distribution with statistical properties and application to COVID-19 data

Sample size	Value	Parameter	Methods of estimation
Sample size	Value	Parameter	\(\kappa_{1}\)	\(\kappa_{2}\)	\(\kappa_{3}\)	\(\kappa_{4}\)	\(\kappa_{5}\)	\(\kappa_{6}\)	\(\kappa_{7}\)	\(\kappa_{8}\)	\(\kappa_{9}\)	\(\kappa_{10}\)
20	Bias [ranks]	\(\alpha\)	0.9067 [7]	0.9267 [8]	0.7723 [5]	0.8021 [6]	1.0964 [9]	0.5963 [4]	1.1732 [10]	0.2400 [3]	0.0682 [1]	0.0740 [2]
		\(\beta\)	2.6788 [4]	5.0875 [9]	4.0345 [6]	2.4698 [3]	4.7464 [7]	5.0196 [8]	6.2200 [10]	3.3221 [5]	0.3904 [1]	0.9405 [2]
		\(\gamma\)	0.5789 [8]	0.5244 [7]	0.6380 [10]	0.5034 [5]	0.5827 [9]	0.4773 [3]	0.4992 [4]	0.5143 [6]	0.2215 [2]	0.1866 [1]
		\(\delta\)	0.1661 [3]	0.2332 [8]	0.2150 [5]	0.2228 [6]	0.2518 [9]	0.3477 [10]	0.1923 [4]	0.2287 [7]	0.0976 [1]	0.1162 [2]
		\(\lambda\)	2.3726 [8]	1.2387 [4]	3.2135 [10]	2.3487 [7]	3.1940 [9]	1.6740 [5]	1.6799 [6]	1.0958 [3]	0.4464 [1]	0.5556 [2]
	MSE [ranks]	\(\alpha\)	66.247 [7]	84.528 [8]	65.827 [6]	53.761 [5]	89.890 [9]	39.366 [4]	117.20 [10]	1.2769 [3]	0.0226 [2]	0.0184 [1]
		\(\beta\)	176.33 [5]	669.87 [9]	551.33 [8]	163.75 [4]	517.84 [7]	261.36 [6]	1724.1 [10]	113.75 [3]	3.9492 [1]	18.110 [2]
		\(\gamma\)	0.7300 [10]	0.5157 [5]	0.6310 [9]	0.5558 [7]	0.5527 [6]	0.3835 [3]	0.4846 [4]	0.6075 [8]	0.0972 [2]	0.0696 [1]
		\(\delta\)	0.0534 [2]	0.1720 [8]	0.0917 [5]	0.2204 [9]	0.1603 [7]	0.4399 [10]	0.0877 [4]	0.1009 [6]	0.0176 [1]	0.0581 [3]
		\(\lambda\)	122.02 [8]	26.433 [5]	192.63 [10]	150.39 [9]	120.75 [7]	21.831 [3]	24.656 [4]	38.396 [6]	0.5691 [1]	1.5900 [2]
	MRE [ranks]	\(\alpha\)	4.5337 [7]	4.6335 [8]	3.8613 [5]	4.0106 [6]	5.4821 [9]	2.9816 [4]	5.8661 [10]	1.2002 [3]	0.3409 [1]	0.3701 [2]
		\(\beta\)	2.8198 [4]	5.3552 [9]	4.2468 [6]	2.5998 [3]	4.9962 [7]	5.2838 [8]	6.5474 [10]	3.4970 [5]	0.4109 [1]	0.9900 [2]
		\(\gamma\)	0.5034 [8]	0.4560 [7]	0.5548 [10]	0.4377 [5]	0.5067 [9]	0.4151 [3]	0.4341 [4]	0.4472 [6]	0.1926 [2]	0.1623 [1]
		\(\delta\)	0.6642 [3]	0.9330 [8]	0.8601 [5]	0.8913 [6]	1.0070 [9]	1.3908 [10]	0.7691 [4]	0.9147 [7]	0.3904 [1]	0.4648 [2]
		\(\lambda\)	2.2596 [8]	1.1797 [4]	3.0605 [10]	2.2369 [7]	3.0419 [9]	1.5943 [5]	1.600 [6]	1.0436 [3]	0.4252 [1]	0.5291 [2]
	Sum ranks [ranks]		92 [6]	107 [8]	110 [9]	88 [5]	122 [10]	86 [4]	100 [7]	74 [3]	19 [1]	27 [2]
50	Bias [ranks]	\(\alpha\)	0.1621 [4]	0.1536 [3]	0.1940 [9]	0.6141 [10]	0.1923 [8]	0.1674 [6]	0.1662 [5]	0.1727 [7]	0.0532 [1]	0.0557 [2]
		\(\beta\)	0.6640 [3]	3.5193 [10]	3.0219 [8]	1.4609 [4]	2.2103 [7]	3.3611 [9]	1.6007 [5]	1.9478 [6]	0.3815 [1]	0.4558 [2]
		\(\gamma\)	0.3102 [5]	0.3230 [6]	0.5007 [10]	0.2880 [3]	0.4508 [9]	0.3059 [4]	0.3552 [7]	0.4028 [8]	0.1549 [2]	0.1202 [1]
		\(\delta\)	0.0984 [3]	0.2146 [9]	0.2056 [6]	0.1408 [4]	0.2227 [10]	0.2134 [8]	0.1650 [5]	0.2099 [7]	0.0802 [2]	0.0791 [1]
		\(\lambda\)	0.3844 [3]	0.4118 [4]	0.9404 [10]	0.8949 [8]	0.9305 [9]	0.5114 [6]	0.5316 [7]	0.4187 [5]	0.2872 [2]	0.2641 [1]
	MSE [ranks]	\(\alpha\)	0.3619 [9]	0.1204 [6]	0.1283 [7]	15.960 [10]	0.1140 [5]	0.1090 [4]	0.0921 [3]	0.2392 [8]	0.0078 [1]	0.0103 [2]
		\(\beta\)	9.3527 [3]	188.91 [9]	263.41 [10]	22.420 [4]	90.345 [7]	148.94 [8]	25.912 [5]	27.090 [6]	1.0500 [1]	2.8342 [2]
		\(\gamma\)	0.3504 [8]	0.2279 [5]	0.4191 [10]	0.2134 [4]	0.3401 [7]	0.1859 [3]	0.2710 [6]	0.3918 [9]	0.0479 [2]	0.0359 [1]
		\(\delta\)	0.0277 [3]	0.1491 [9]	0.0986 [7]	0.0614 [4]	0.1439 [8]	0.1646 [10]	0.0840 [6]	0.0795 [5]	0.0139 [1]	0.0225 [2]
		\(\lambda\)	0.7126 [4]	0.9342 [6]	11.279 [9]	11.685 [10]	7.4979 [8]	0.8416 [5]	1.2365 [7]	0.4416 [3]	0.2101 [1]	0.2160 [2]
	MRE [ranks]	\(\alpha\)	0.8108 [4]	0.7683 [3]	0.9702 [9]	3.0704 [10]	0.9613 [8]	0.8368 [6]	0.8311 [5]	0.8635 [7]	0.2656 [1]	0.2787 [2]
		\(\beta\)	0.6990 [3]	3.7046 [10]	3.1810 [8]	1.5377 [4]	2.8877 [7]	3.5380 [9]	1.6849 [5]	2.0503 [6]	0.4016 [1]	0.4797 [2]
		\(\gamma\)	0.2698[5]	0.2809 [6]	0.4354 [10]	0.2504 [3]	0.3920 [9]	0.2660 [4]	0.3088 [7]	0.3503 [8]	0.1347 [2]	0.1045 [1]
		\(\delta\)	0.3936 [3]	0.8584 [9]	0.8225 [6]	0.5632 [4]	0.8907 [10]	0.8537 [8]	0.6599 [5]	0.8398 [7]	0.3208 [2]	0.3165 [1]
		\(\lambda\)	0.3661 [3]	0.3922 [4]	0.8956 [10]	0.8523 [8]	0.8862 [9]	0.4870 [6]	0.5063 [7]	0.3988 [5]	0.2736 [2]	0.2516 [1]
	Sum ranks [ranks]		63 [3]	99 [8]	129 [10]	90 [5]	121 [9]	96 [6]	85 [4]	97 [7]	22 [1]	23 [2]
100	Bias [ranks]	\(\alpha\)	0.1186 [3]	0.1526 [5]	0.1911 [10]	0.1546 [6]	0.1766 [9]	0.1264 [4]	0.1623 [8]	0.1570 [7]	0.0460 [2]	0.0446 [1]
		\(\beta\)	0.3498 [3]	2.9456 [10]	2.1138 [7]	0.5568 [4]	2.6356 [9]	2.1743 [8]	1.4263 [5]	1.5507 [6]	0.2629 [1]	0.2973 [2]
		\(\gamma\)	0.1790 [4]	0.2210 [6]	0.4083 [10]	0.1439 [3]	0.3662 [9]	0.2119 [5]	0.2642 [7]	0.2861 [8]	0.0927 [2]	0.0795 [1]
		\(\delta\)	0.0599 [3]	0.1669 [7]	0.2012 [9]	0.0711 [4]	0.2193 [10]	0.1544 [6]	0.1403 [5]	0.1838 [8]	0.0544 [2]	0.0495 [1]
		\(\lambda\)	0.1736 [1]	0.2564 [5]	0.4928 [10]	0.2514 [4]	0.4635 [9]	0.3205 [8]	0.3068 [7]	0.2884 [6]	0.1896 [3]	0.1737 [2]
	MSE [ranks]	\(\alpha\)	0.2017 [9]	0.1193 [7]	0.1192 [6]	0.5305 [10]	0.0984 [5]	0.0661 [3]	0.0866 [4]	0.1541 [8]	0.0074 [1]	0.0090 [2]
		\(\beta\)	1.2720 [3]	180.38 [10]	56.025 [7]	3.4094 [4]	58.570 [8]	127.70 [9]	20.122 [6]	15.038 [5]	0.4684 [1]	1.0769 [2]
		\(\gamma\)	0.1779 [7]	0.1077 [5]	0.2741 [10]	0.0850 [3]	0.2151 [8]	0.0913 [4]	0.1681 [6]	0.2171 [9]	0.0211 [1]	0.0239 [2]
		\(\delta\)	0.0107 [3]	0.1120 [9]	0.0963 [8]	0.0184 [4]	0.1280 [10]	0.0808 [7]	0.0583 [5]	0.0696 [6]	0.0096 [2]	0.0092 [1]
		\(\lambda\)	0.0785 [1]	0.1487 [4]	0.6591 [10]	0.2410 [6]	0.4775 [9]	0.3326 [8]	0.3042 [7]	0.1690 [5]	0.1082 [3]	0.0808 [2]
	MRE [ranks]	\(\alpha\)	0.5931 [3]	0.7429 [5]	0.9556 [10]	0.7728 [6]	0.8830 [9]	0.6318 [4]	0.8114 [7]	0.8563 [8]	0.2300 [2]	0.2229 [1]
		\(\beta\)	0.3682 [3]	3.1006 [10]	2.2251 [8]	0.5861 [4]	2.0743 [7]	2.2888 [9]	1.5014 [5]	1.6323 [6]	0.2768 [1]	0.3129 [2]
		\(\gamma\)	0.1556 [4]	0.1922 [6]	0.3550 [10]	0.1251 [3]	0.3184 [9]	0.1842 [5]	0.2298 [7]	0.2487 [8]	0.0806 [2]	0.0691 [1]
		\(\delta\)	0.2395 [3]	0.6677 [7]	0.8049 [9]	0.2843 [4]	0.8173 [10]	0.6176 [6]	0.5614 [5]	0.7351 [8]	0.2174 [2]	0.1982 [1]
		\(\lambda\)	0.1654 [2]	0.2442 [5]	0.4694 [10]	0.2395 [4]	0.4415 [9]	0.3053 [8]	0.2922 [7]	0.2747 [6]	0.1806 [3]	0.1653 [1]
	Sum ranks [ranks]		52 [3]	101 [7]	134 [10]	69 [4]	130 [9]	94 [6]	91 [5]	104 [8]	28 [2]	22 [1]
150	Bias [ranks]	\(\alpha\)	0.0919 [4]	0.1337 [7]	0.1875 [10]	0.0885 [3]	0.1709 [9]	0.1001 [5]	0.1302 [6]	0.1460 [8]	0.0429 [2]	0.0281 [1]
		\(\beta\)	0.2743 [3]	2.0731 [9]	2.0613 [8]	0.3782 [4]	2.4960 [10]	2.0018 [7]	0.8144 [5]	1.0518 [6]	0.1574 [1]	0.1966 [2]
		\(\gamma\)	0.1079 [4]	0.1892 [7]	0.3496 [10]	0.0949 [3]	0.3174 [9]	0.1619 [5]	0.1757 [6]	0.2562 [8]	0.0792 [2]	0.0532 [1]
		\(\delta\)	0.0470 [3]	0.1463 [7]	0.1975 [9]	0.0479 [4]	0.2025 [10]	0.1317 [6]	0.0936 [5]	0.1510 [8]	0.0415 [2]	0.0350 [1]
		\(\lambda\)	0.1213 [2]	0.2380 [7]	0.3640 [10]	0.1523 [4]	0.3516 [9]	0.2112 [5]	0.2208 [6]	0.2579 [8]	0.1384 [3]	0.0978 [1]
	MSE [ranks]	\(\alpha\)	0.1034 [8]	0.1064 [9]	0.0972 [7]	0.0814 [6]	0.0785 [5]	0.0455 [3]	0.0702 [4]	0.1267 [10]	0.0065 [2]	0.0028 [1]
		\(\beta\)	0.6117 [3]	60.483 [9]	31.124 [7]	2.2144 [4]	56.049 [8]	114.19 [10]	12.026 [6]	5.9491 [5]	0.2361 [1]	0.3846 [2]
		\(\gamma\)	0.0843 [5]	0.0865 [7]	0.2011 [10]	0.0387 [3]	0.1637 [8]	0.0625 [4]	0.0857 [6]	0.1694 [9]	0.0174 [2]	0.0151 [1]
		\(\delta\)	0.0083 [3]	0.0903 [8]	0.0952 [9]	0.0088 [4]	0.0979 [10]	0.0742 [7]	0.0240 [5]	0.0431 [6]	0.0039 [1]	0.0046 [2]
		\(\lambda\)	0.0460 [2]	0.2277 [8]	0.2621 [9]	0.0626 [4]	0.2761 [10]	0.0965 [5]	0.1487 [6]	0.1647 [7]	0.0537 [3]	0.0290 [1]
	MRE [ranks]	\(\alpha\)	0.4595 [4]	0.6686 [7]	0.9374 [10]	0.4427 [3]	0.8656 [9]	0.5004 [5]	0.6512 [6]	0.7849 [8]	0.2147 [2]	0.1407 [1]
		\(\beta\)	0.2887 [3]	2.1822 [10]	2.1698 [9]	0.3981 [4]	1.6273 [7]	2.1072 [8]	0.8573 [5]	1.1071 [6]	0.1657 [1]	0.2070 [2]
		\(\gamma\)	0.0939 [4]	0.1645 [7]	0.3040 [10]	0.0825 [3]	0.2760 [9]	0.1408 [5]	0.1527[6]	0.2228 [8]	0.0689 [2]	0.0463 [1]
		\(\delta\)	0.1881 [3]	0.5852 [7]	0.7901 [10]	0.1918 [4]	0.7882 [9]	0.5266 [6]	0.3746 [5]	0.6041 [8]	0.1660 [2]	0.1401 [1]
		\(\lambda\)	0.1156 [2]	0.2266 [7]	0.3467 [10]	0.1450 [4]	0.3349 [9]	0.2011 [5]	0.2103 [6]	0.2456 [8]	0.1318 [3]	0.0932 [1]
	Sum ranks [ranks]		53 [3]	116 [8]	138 [10]	57 [4]	131 [9]	86 [6]	83 [5]	113 [7]	29 [2]	19 [1]
250	Bias [ranks]	\(\alpha\)	0.0558 [4]	0.1080 [6]	0.1782 [10]	0.0488 [3]	0.1553 [9]	0.0781 [5]	0.1188 [7]	0.1399 [8]	0.0272 [2]	0.0213 [1]
		\(\beta\)	0.1429 [3]	0.7168 [6]	1.8060 [9]	0.1498 [4]	2.1433 [10]	1.0549 [8]	0.6786 [5]	0.9317 [7]	0.1274 [2]	0.1263 [1]
		\(\gamma\)	0.0523 [4]	0.1310 [6]	0.2886 [10]	0.0486 [3]	0.2698 [9]	0.1230 [5]	0.1339 [7]	0.1959 [8]	0.0403 [2]	0.0271 [1]
		\(\delta\)	0.0262 [3]	0.0844 [5]	0.1794 [10]	0.0252 [2]	0.1608 [9]	0.0845 [6]	0.0856 [7]	0.1355 [8]	0.0269 [4]	0.0202 [1]
		\(\lambda\)	0.0760 [2]	0.1595 [5]	0.2562 [9]	0.0880 [4]	0.2766 [10]	0.1659 [7]	0.1627 [6]	0.2113 [8]	0.0815 [3]	0.0615 [1]
	MSE [ranks]	\(\alpha\)	0.0533 [5]	0.0656 [7]	0.0961 [10]	0.0329 [4]	0.0620 [6]	0.0279 [3]	0.0810 [8]	0.0933 [9]	0.0034 [1]	0.0047 [2]
		\(\beta\)	0.1882 [2]	7.1560 [7]	25.892 [8]	0.4895 [4]	50.015 [10]	38.730 [9]	5.1819 [5]	5.5347 [6]	0.1416 [1]	0.1925 [3]
		\(\gamma\)	0.0284 [4]	0.0485 [6]	0.1312 [10]	0.0123 [3]	0.1191 [9]	0.0372 [5]	0.0522 [7]	0.0989 [8]	0.0062 [2]	0.0039 [1]
		\(\delta\)	0.0036 [3]	0.0259 [6]	0.0702 [9]	0.0037 [4]	0.0809 [10]	0.0324 [7]	0.0225 [5]	0.0360 [8]	0.0023 [1.5]	0.0023 [1.5]
		\(\lambda\)	0.0207 [2]	0.0683 [6]	0.1171 [9]	0.0372 [4]	0.1793 [10]	0.0759 [7]	0.0636 [5]	0.1006 [8]	0.0213 [3]	0.0120 [1]
	MRE [ranks]	\(\alpha\)	0.2792 [4]	0.5402 [6]	0.8910 [10]	0.2439 [3]	0.8352 [9]	0.3906 [5]	0.5939 [7]	0.7300 [8]	0.1359 [2]	0.1064 [1]
		\(\beta\)	0.1505 [3]	0.7545 [6]	1.9011 [10]	0.1577 [4]	1.2655 [9]	1.1104 [8]	0.7144 [5]	0.9807 [7]	0.1341 [2]	0.1329 [1]
		\(\gamma\)	0.0455 [4]	0.1139 [6]	0.2509 [10]	0.0423 [3]	0.2346 [9]	0.1070 [5]	0.1164 [7]	0.1703 [8]	0.0350 [2]	0.0236 [1]
		\(\delta\)	0.1047 [3]	0.3376 [5]	0.7176 [10]	0.1007 [2]	0.6950 [9]	0.3381 [6]	0.3424 [7]	0.5419 [8]	0.1075 [4]	0.0810 [1]
		\(\lambda\)	0.0724 [2]	0.1519 [5]	0.2440 [9]	0.0838 [4]	0.2635 [10]	0.1580 [7]	0.1550 [6]	0.2012 [8]	0.0776 [3]	0.0586 [1]
	Sum ranks [ranks]		48 [3]	88 [5]	143 [10]	51 [4]	138 [9]	93 [6]	94 [7]	117 [8]	34.5 [2]	18.5 [1]
400	Bias [ranks]	\(\alpha\)	0.0329 [4]	0.0796 [6]	0.1760 [10]	0.0186 [2]	0.1314 [9]	0.0629 [5]	0.0804 [7]	0.1207 [8]	0.0192 [3]	0.0124 [1]
		\(\beta\)	0.0637 [3]	0.5235 [7]	1.2910 [10]	0.0620 [2]	1.2813 [9]	0.5061 [5]	0.5074 [6]	0.8577 [8]	0.0741 [4]	0.0447 [1]
		\(\gamma\)	0.0310 [4]	0.0926 [5]	0.2283 [10]	0.0193 [2]	0.2236 [9]	0.0931 [6]	0.0947 [7]	0.1464 [8]	0.0244 [3]	0.0134 [1]
		\(\delta\)	0.0148 [3]	0.0633 [6]	0.1421 [9]	0.0128 [2]	0.1459 [10]	0.0634 [7]	0.0612 [5]	0.1108 [8]	0.0171 [4]	0.0106 [1]
		\(\lambda\)	0.0502 [3]	0.1164 [6]	0.2009 [10]	0.0471 [2]	0.1997 [9]	0.1231 [7]	0.1159 [5]	0.1767 [8]	0.0548 [4]	0.0355 [1]
	MSE [ranks]	\(\alpha\)	0.0333 [5]	0.0424 [7]	0.0943 [10]	0.0066 [3]	0.0431 [8]	0.0182 [4]	0.0398 [6]	0.0736 [9]	0.0024 [2]	0.0008 [1]
		\(\beta\)	0.0319 [2]	2.8128 [6]	8.1959 [9]	0.0773 [3]	14.007 [10]	2.1052 [5]	3.5468 [7]	3.9855 [8]	0.1198 [4]	0.0178 [1]
		\(\gamma\)	0.0222 [5]	0.0257 [6]	0.0874 [10]	0.0021 [2]	0.0852 [9]	0.0201 [4]	0.0268 [7]	0.0631 [8]	0.0031 [3]	0.0012 [1]
		\(\delta\)	0.0015 [4]	0.0109 [5]	0.0392 [9]	0.0009 [2]	0.0495 [10]	0.0112 [6]	0.0120 [7]	0.0276 [8]	0.0010 [3]	0.0005 [1]
		\(\lambda\)	0.0135 [4]	0.0499 [7]	0.0778 [8]	0.0083 [2]	0.0848 [10]	0.0261 [5]	0.0294 [6]	0.0836 [9]	0.0127 [3]	0.0058 [1]
	MRE [ranks]	\(\alpha\)	0.1646 [4]	0.3981 [6]	0.8802 [10]	0.0931 [2]	0.8097 [9]	0.3145 [5]	0.4002 [7]	0.6581 [8]	0.0960 [3]	0.0622 [1]
		\(\beta\)	0.0671 [3]	0.5511 [7]	1.3589 [10]	0.0653 [2]	0.9834 [9]	0.5328 [5]	0.5341 [6]	0.8427 [8]	0.0780 [4]	0.0470 [1]
		\(\gamma\)	0.0269 [4]	0.0805 [5]	0.1985 [10]	0.0167 [2]	0.1944 [9]	0.0810 [6]	0.0824 [7]	0.1316 [8]	0.0212 [3]	0.0117 [1]
		\(\delta\)	0.0594 [3]	0.2533 [6]	0.5685 [9]	0.0513 [2]	0.5837 [10]	0.2538 [7]	0.2448 [5]	0.4319 [8]	0.0685 [4]	0.0425 [1]
		\(\lambda\)	0.0480 [3]	0.1109 [6]	0.1914 [10]	0.0448 [2]	0.1902 [9]	0.1172 [7]	0.1104 [5]	0.1463 [8]	0.0522 [4]	0.0338 [1]
	Sum ranks [ranks]		54 [4]	91 [6]	144 [10]	32 [2]	139 [9]	84 [5]	93 [7]	122 [8]	51 [3]	15 [1]
600	Bias [ranks]	\(\alpha\)	0.0178 [4]	0.0657 [7]	0.1620 [10]	0.0090 [2]	0.1027 [8]	0.0501 [5]	0.0609 [6]	0.1157 [9]	0.0122 [3]	0.0084 [1]
		\(\beta\)	0.0554 [4]	0.2769 [5]	0.9243 [9]	0.0308 [2]	0.9862 [10]	0.3051 [6]	0.3443 [7]	0.7024 [8]	0.0381 [3]	0.0253 [1]
		\(\gamma\)	0.0140 [4]	0.0662 [5]	0.1809 [9]	0.0101 [2]	0.1879 [10]	0.0715 [6]	0.0734 [7]	0.1081 [8]	0.0135 [3]	0.0088 [1]
		\(\delta\)	0.0094 [3]	0.0492 [7]	0.1255 [9]	0.0076 [2]	0.1323 [10]	0.0468 [5]	0.0472 [6]	0.0948 [8]	0.0098 [4]	0.0070 [1]
		\(\lambda\)	0.0339 [4]	0.0844 [5]	0.1582 [9]	0.0276 [2]	0.1638 [10]	0.0985 [7]	0.0902 [6]	0.1296 [8]	0.0338 [3]	0.0194 [1]
	MSE [ranks]	\(\alpha\)	0.0077 [4]	0.0301 [7]	0.0754 [9]	0.0007 [1.5]	0.0838 [10]	0.0132 [5]	0.0277 [6]	0.0511 [8]	0.0008 [3]	0.0007 [1.5]
		\(\beta\)	0.0477 [4]	0.3343 [5]	4.4609 [9]	0.0076 [2]	4.9907 [10]	0.4820 [6]	1.8023 [7]	2.7640 [8]	0.0169 [3]	0.0061 [1]
		\(\gamma\)	0.0037 [4]	0.0108 [5]	0.0553 [9]	0.0007 [2]	0.0599 [10]	0.0128 [6]	0.0193 [7]	0.0519 [8]	0.0009 [3]	0.0003 [1]
		\(\delta\)	0.0007 [4]	0.0067 [6]	0.0301 [9]	0.0003 [2.5]	0.0349 [10]	0.0060 [5]	0.0077 [7]	0.0208 [8]	0.0003 [2.5]	0.0002 [1]
		\(\lambda\)	0.0063 [4]	0.0137 [5]	0.0491 [8]	0.0038 [2]	0.0512 [9]	0.0160 [6]	0.0193 [7]	0.0551 [10]	0.0061 [3]	0.0023 [1]
	MRE [ranks]	\(\alpha\)	0.0889 [4]	0.3284 [7]	0.8101 [10]	0.0452 [2]	0.7985 [9]	0.2505 [5]	0.3044 [6]	0.5068 [8]	0.0612 [3]	0.0420 [1]
		\(\beta\)	0.0584 [4]	0.2915 [5]	0.9730 [10]	0.0324 [2]	0.9036 [9]	0.3212 [6]	0.3624 [7]	0.7592 [8]	0.0402 [3]	0.0267 [1]
		\(\gamma\)	0.0121 [4]	0.0576 [5]	0.1574 [9]	0.0088 [2]	0.1634 [10]	0.0622 [6]	0.0639 [7]	0.0964 [8]	0.0117 [3]	0.0076 [1]
		\(\delta\)	0.0374 [3]	0.1970 [7]	0.5018 [9]	0.0304 [2]	0.5293 [10]	0.1872 [5]	0.1889 [6]	0.3240 [8]	0.0393 [4]	0.0281 [1]
		\(\lambda\)	0.0323 [4]	0.0804 [5]	0.1507 [9]	0.0263 [2]	0.1560 [10]	0.0938 [7]	0.0859 [6]	0.1087 [8]	0.0322 [3]	0.0185 [1]
	Sum ranks [ranks]		58 [4]	86 [5.5]	137 [9]	30 [2]	145 [10]	86 [5.5]	98 [7]	123 [8]	46.5 [3]	15.5 [1]

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Table 5 Comparison of Bias, MSE, MRE for parameter estimateswhen \(\alpha = 0.20\); \(\beta = 0.95\); \(\gamma = 1.15\);\(\delta = 0.25\); and \(\lambda = 1.05\).

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