Table 3 Comparison of Bias, MSE, MRE for parameter estimateswhen \(\alpha = 0.40\); \(\beta = 0.10\); \(\gamma = 0.35\);\(\delta = 0.25\); and \(\lambda = 0.70\).

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]	\(\alpha\)	0.2650 [3]	0.6063 [7]	0.6133 [8]	0.6376 [9]	0.5681 [6]	0.5497 [5]	1.3031 [10]	0.2758 [4]	0.1867 [2]	0.1591 [1]
		\(\beta\)	0.1160 [3]	0.8323 [7]	0.5445 [5]	0.5925 [6]	1.0266 [9]	0.9584 [8]	1.2145 [10]	0.2464 [4]	0.0699 [1]	0.1049 [2]
		\(\gamma\)	0.2487 [8]	0.2089 [5]	0.2411 [7]	0.2494 [9]	0.2368 [6]	0.1872 [4]	0.2533 [10]	0.1818 [3]	0.0746 [2]	0.0668 [1]
		\(\delta\)	0.3783 [4]	0.3985 [6]	0.4954 [7]	0.5704 [10]	0.5139 [8]	0.3911 [5]	0.3587 [3]	0.5639 [9]	0.1319 [1]	0.1593 [2]
		\(\lambda\)	3.0810 [9]	1.0813 [7]	1.7593 [8]	7.1189 [10]	0.9999 [6]	0.6869 [3]	0.9065 [5]	0.7675 [4]	0.4054 [2]	0.3732 [1]
	MSE [ranks]	\(\alpha\)	0.2986 [4]	35.169 [8]	39.556 [9]	0.6512 [5]	30.098 [6]	32.203 [7]	125.01 [10]	0.1662 [3]	0.0379 [1]	0.0429 [2]
		\(\beta\)	0.1355 [2]	98.112 [9]	49.549 [6]	0.7846 [4]	68.654 [8]	51.025 [7]	115.23 [10]	1.8078 [5]	0.0172 [1]	0.1358 [3]
		\(\gamma\)	0.1095 [9]	0.0747 [5]	0.0956 [7]	0.1103 [10]	0.0933 [6]	0.0642 [4]	0.1039 [8]	0.0625 [3]	0.0150 [2]	0.0100 [1]
		\(\delta\)	0.4326 [4]	0.4515 [5]	0.6365 [8]	0.6467 [9]	0.6154 [7]	0.4846 [6]	0.2995 [3]	0.8427 [10]	0.0474 [1]	0.0798 [2]
		\(\lambda\)	17.345 [8]	10.827 [6]	22.643 [9]	59.833 [10]	15.815 [7]	3.4907 [4]	8.6605 [5]	1.9472 [3]	0.2487 [1]	0.3489 [2]
	MRE [ranks]	\(\alpha\)	0.6627 [3]	1.5158 [8]	1.5334 [9]	1.2940 [5]	1.4204 [7]	1.3743 [6]	3.2578 [10]	0.6894 [4]	0.4666 [2]	0.3978 [1]
		\(\beta\)	1.1605 [3]	8.3231 [7]	5.4447 [6]	1.9249 [4]	10.266 [9]	9.5843 [8]	12.145 [10]	2.4637 [5]	0.7982 [1]	1.0491 [2]
		\(\gamma\)	0.7106 [[8]	0.5968 [5]	0.6889 [7]	0.7127 [9]	0.6767 [6]	0.5349 [4]	0.7237 [10]	0.5196 [3]	0.2132 [2]	0.1909 [1]
		\(\delta\)	1.5134 [4]	1.5940 [6]	1.9614 [8]	1.9707 [9]	1.9001 [7]	1.5642 [5]	1.4347 [3]	2.2556 [10]	0.5276 [1]	0.6373 [2]
		\(\lambda\)	4.4142 [9]	1.5447 [7]	2.5133 [8]	10.170 [10]	1.4285 [6]	0.9814 [3]	1.2950 [5]	1.0965 [4]	0.5791 [2]	0.5330 [1]
	Sum ranks [ranks]		81 [5]	98 [6]	112 [8.5]	119 [10]	104 [7]	79 [4]	112 [8.5]	74 [3]	22 [1]	24 [2]
50	Bias [ranks]	\(\alpha\)	0.2167 [3]	0.2679 [6]	0.2948 [8]	0.2896 [7]	0.3160 [10]	0.2206 [4]	0.2986 [9]	0.2576 [5]	0.1810 [2]	0.1553 [1]
		\(\beta\)	0.0853 [3]	0.1545 [6]	0.1846 [8]	0.1360 [4]	0.1920 [9]	0.1540 [5]	0.1999 [10]	0.1740 [7]	0.0706 [1]	0.0723 [2]
		\(\gamma\)	0.1477 [7]	0.1256 [4]	0.1677 [9]	0.1533 [8]	0.1727 [10]	0.1096 [3]	0.1439 [6]	0.1394 [5]	0.0638 [1]	0.0639 [2]
		\(\delta\)	0.2655 [3]	0.3708 [6]	0.4759 [8]	0.4927 [9]	0.4972 [10]	0.3207 [5]	0.3009 [4]	0.4464 [7]	0.1261 [1]	0.1473 [2]
		\(\lambda\)	0.7997 [8]	0.7349 [5]	0.9720 [9]	0.9962 [10]	0.7948 [7]	0.4951 [3]	0.5133 [4]	0.7440 [6]	0.4002 [2]	0.3453 [1]
	MSE [ranks]	\(\alpha\)	0.0590 [3]	0.1668 [7]	0.1639 [6]	0.1728 [8]	0.2698 [9]	0.1088 [5]	0.2718 [10]	0.0980 [4]	0.0372 [1]	0.0413 [2]
		\(\beta\)	0.0138 [3]	0.1984 [5]	0.2373 [7]	0.1326 [4]	0.2096 [6]	0.2674 [9]	0.2402 [8]	0.4282 [10]	0.0110 [2]	0.0092 [1]
		\(\gamma\)	0.0418 [7]	0.0290 [4]	0.0475 [9]	0.0424 [8]	0.0518 [10]	0.0216 [3]	0.0379 [6]	0.0347 [5]	0.0092 [2]	0.0085 [1]
		\(\delta\)	0.1817 [3]	0.4196 [6]	0.5407 [9]	0.4967 [7]	0.5111 [8]	0.3305 [5]	0.2567 [4]	0.5636 [10]	0.0458 [1]	0.0709 [2]
		\(\lambda\)	11.059 [10]	1.8545 [7]	2.2696 [8]	6.3703 [9]	1.6360 [6]	0.7984 [3]	0.8064 [4]	1.5743 [5]	0.2454 [1]	0.3019 [2]
	MRE [ranks]	\(\alpha\)	0.5418 [3]	0.6697 [6]	0.7371 [8]	0.7240 [7]	0.7901 [10]	0.5516 [4]	0.7464 [9]	0.6440 [5]	0.4525 [2]	0.3882 [1]
		\(\beta\)	0.8531 [3]	1.5449 [6]	1.8461 [8]	1.3602 [4]	1.9208 [9]	1.5401 [5]	1.9993 [10]	1.7400 [7]	0.7588 [2]	0.7228 [1]
		\(\gamma\)	0.4221 [7]	0.3589 [4]	0.4792 [9]	0.4381 [8]	0.4934 [10]	0.3131 [3]	0.4110 [6]	0.3983 [5]	0.1824 [1]	0.1827 [2]
		\(\delta\)	1.0622 [3]	1.4833 [6]	1.8235 [10]	1.7707 [8]	1.7362 [7]	1.2828 [5]	1.2039 [4]	1.7858 [9]	0.5044 [1]	0.5891 [2]
		\(\lambda\)	1.1424 [8]	1.0499 [5]	1.2457 [9]	1.4232 [10]	1.1355 [7]	0.7073 [3]	0.7333 [4]	1.0629 [6]	0.5717 [2]	0.4933 [1]
	Sum ranks [ranks]		74 [4]	83 [5]	125 [9]	111 [8]	128 [10]	65 [3]	98 [7]	96 [6]	22 [1]	23 [2]
100	Bias [ranks]	\(\alpha\)	0.2038 [4]	0.2108 [5]	0.2280 [8]	0.2228 [6]	0.2371 [9]	0.1667 [3]	0.2257 [7]	0.2408 [10]	0.1590 [2]	0.1522 [1]
		\(\beta\)	0.0795 [3]	0.0953 [6]	0.1158 [8]	0.0944 [5]	0.1169 [9]	0.0816 [4]	0.1235 [10]	0.1138 [7]	0.0715 [2]	0.0705 [1]
		\(\gamma\)	0.0901 [4]	0.0933 [5]	0.1312 [10]	0.0981 [6]	0.1301 [8]	0.0756 [3]	0.0990 [7]	0.1311 [9]	0.0585 [1]	0.0608 [2]
		\(\delta\)	0.2563 [4]	0.3542 [6]	0.4429 [9]	0.4109 [7]	0.4750 [10]	0.2864 [5]	0.2453 [3]	0.4204 [8]	0.1214 [1]	0.1356 [2]
		\(\lambda\)	0.5222 [5]	0.6163 [6]	0.7284 [10]	0.6623 [7]	0.7110 [9]	0.4228 [4]	0.4155 [3]	0.7074 [8]	0.3585 [2]	0.3401 [1]
	MSE [ranks]	\(\alpha\)	0.0480 [4]	0.0661 [5]	0.0984 [9]	0.0771 [7]	0.0920 [8]	0.0371 [3]	0.1304 [10]	0.0699 [6]	0.0369 [2]	0.0368 [1]
		\(\beta\)	0.0077 [3]	0.0260 [5]	0.0542 [9]	0.0248 [4]	0.0416 [7]	0.0344 [6]	0.0928 [10]	0.0434 [8]	0.0074 [1]	0.0076 [2]
		\(\gamma\)	0.0153 [5]	0.0151 [4]	0.0292 [9]	0.0171 [6]	0.0301 [10]	0.0097 [3]	0.0188 [7]	0.0286 [8]	0.0067 [1]	0.0078 [2]
		\(\delta\)	0.1780 [4]	0.3512 [6]	0.4277 [8]	0.3921 [7]	0.4670 [9]	0.2849 [5]	0.1614 [3]	0.5471 [10]	0.0433 [1]	0.0700 [2]
		\(\lambda\)	0.9423 [6]	1.0387 [7]	1.0821 [8]	0.9096 [5]	1.3220 [9]	0.5160 [4]	0.3898 [3]	1.4512 [10]	0.2453 [1]	0.2841 [2]
	MRE [ranks]	\(\alpha\)	0.5095 [4]	0.5269 [5]	0.5700 [8]	0.5571 [6]	0.5929 [9]	0.4168 [3]	0.5643 [7]	0.6019 [10]	0.3975 [2]	0.3806 [1]
		\(\beta\)	0.7952 [3]	0.9532 [6]	1.1583 [8]	0.9444 [5]	1.1692 [9]	0.8165 [4]	1.2355 [10]	1.1086 [7]	0.7556 [2]	0.7046 [1]
		\(\gamma\)	0.2573 [4]	0.2665 [5]	0.3750 [10]	0.2803 [6]	0.3716 [8]	0.2161 [3]	0.2828 [7]	0.3746 [9]	0.1672 [1]	0.1738 [2]
		\(\delta\)	1.0250 [4]	1.4166 [6]	1.7815 [10]	1.6436 [8]	1.6289 [7]	1.1455 [5]	0.9810 [3]	1.6817 [9]	0.4857 [1]	0.5424 [2]
		\(\lambda\)	0.7459 [5]	0.8805 [6]	1.0277 [10]	0.9461 [7]	1.0157 [9]	0.6041 [4]	0.5935 [3]	1.0106 [8]	0.5122 [2]	0.4859 [1]
	Sum ranks [ranks]		62 [4]	83 [5]	134 [10]	92 [6]	130 [9]	59 [3]	93 [7]	127 [8]	22 [1]	23 [2]
150	Bias [ranks]	\(\alpha\)	0.1939 [4]	0.1966 [5]	0.2197 [9]	0.2152 [8]	0.2060 [7]	0.1619 [3]	0.1995 [6]	0.2391 [10]	0.1486 [1]	0.1501 [2]
		\(\beta\)	0.0761 [3]	0.0855 [6]	0.1060 [8]	0.0819 [5]	0.1082 [9]	0.0810 [4]	0.1028 [7]	0.1109 [10]	0.0748 [2]	0.0695 [1]
		\(\gamma\)	0.0664 [4]	0.0692 [5]	0.1110 [9]	0.0738 [6]	0.1072 [8]	0.0609 [3]	0.0759 [7]	0.1117 [10]	0.0535 [2]	0.0525 [1]
		\(\delta\)	0.2304 [5]	0.3475 [6]	0.3953 [9]	0.3658 [7]	0.4341 [10]	0.2290 [4]	0.2269 [3]	0.3774 [8]	0.1159 [1]	0.1331 [2]
		\(\lambda\)	0.4727 [5]	0.5549 [6]	0.5907 [7]	0.6523 [9]	0.6117 [8]	0.3792 [4]	0.3563 [3]	0.6840 [10]	0.3169 [1]	0.3301 [2]
	MSE [ranks]	\(\alpha\)	0.0436 [4]	0.0471 [5]	0.0701 [9]	0.0539 [7]	0.0520 [6]	0.0352 [2]	0.1495 [10]	0.0658 [8]	0.0351 [1]	0.0358 [3]
		\(\beta\)	0.0074 [3]	0.0165 [6]	0.0439 [9]	0.0135 [4]	0.0379 [7]	0.0146 [5]	0.1190 [10]	0.0405 [8]	0.0070 [1]	0.0070 [2]
		\(\gamma\)	0.0072 [4]	0.0074 [5]	0.0204 [10]	0.0086 [6]	0.0194 [9]	0.0060 [3]	0.0101 [7]	0.0186 [8]	0.0059 [2]	0.0055 [1]
		\(\delta\)	0.1533 [4]	0.3630 [8]	0.3560 [7]	0.3115 [6]	0.4566 [10]	0.1950 [5]	0.1394 [3]	0.4469 [9]	0.0407 [1]	0.0475 [2]
		\(\lambda\)	0.4846 [5]	0.6637 [6]	0.8797 [8]	0.8033 [7]	0.8918 [9]	0.3549 [4]	0.2964 [3]	1.2183 [10]	0.2397 [2]	0.2325 [1]
	MRE [ranks]	\(\alpha\)	0.4847 [4]	0.4915 [5]	0.5493 [9]	0.5384 [8]	0.5151 [7]	0.4048 [3]	0.4987 [6]	0.5978 [10]	0.3715 [1]	0.3803 [2]
		\(\beta\)	0.7613 [3]	0.8555 [6]	1.0600 [8]	0.8187 [5]	1.0824 [9]	0.8100 [4]	1.0285 [7]	1.1384 [10]	0.7479 [2]	0.6956 [1]
		\(\gamma\)	0.1898 [4]	0.1977 [5]	0.3174 [9]	0.2110 [6]	0.3064 [8]	0.1740 [3]	0.2171 [7]	0.3191 [10]	0.1528 [2]	0.1501 [1]
		\(\delta\)	0.9218 [5]	1.3899 [6]	1.6113 [9]	1.4632 [7]	1.6210 [10]	0.9159 [4]	0.9077 [3]	1.5095 [8]	0.4637 [1]	0.5324 [2]
		\(\lambda\)	0.6753 [5]	0.7927 [6]	0.9010 [8]	0.9319 [9]	0.8739 [7]	0.5417 [4]	0.5091 [3]	0.9771 [10]	0.4527 [1]	0.4716 [2]
	Sum ranks [ranks]		62 [4]	86 [6]	128 [9]	100 [7]	124 [8]	55 [3]	85 [5]	139 [10]	21 [1]	25 [2]
250	Bias [ranks]	\(\alpha\)	0.1750 [5]	0.1872 [6]	0.2022 [8]	0.2124 [10]	0.1938 [7]	0.1612 [4]	0.1499 [3]	0.2102 [9]	0.1483 [2]	0.1482 [1]
		\(\beta\)	0.0726 [4]	0.0786 [7]	0.0965 [9]	0.0774 [6]	0.0851 [8]	0.0699 [3]	0.0639 [1]	0.0966 [10]	0.0756 [5]	0.0642 [2]
		\(\gamma\)	0.0552 [4]	0.0592 [6]	0.0881 [9]	0.0585 [5]	0.0811 [8]	0.0482 [3]	0.0603 [7]	0.1054 [10]	0.0450 [2]	0.0429 [1]
		\(\delta\)	0.1578 [3]	0.3078 [7]	0.3746 [9]	0.2770 [6]	0.4052 [10]	0.1816 [4]	0.1945 [5]	0.3636 [8]	0.1004 [1]	0.1098 [2]
		\(\lambda\)	0.3720 [6]	0.5303 [7]	0.5182 [5]	0.5916 [9]	0.5458 [8]	0.3457 [4]	0.3200 [3]	0.6530 [10]	0.2858 [1]	0.3143 [2]
	MSE [ranks]	\(\alpha\)	0.0360 [5]	0.0456 [7]	0.0501 [8]	0.0505 [9]	0.0460 [6]	0.0333 [3]	0.0309 [2]	0.0519 [10]	0.0334 [4]	0.0302 [1]
		\(\beta\)	0.0058 [2]	0.0111 [7]	0.0236 [9]	0.0071 [5]	0.0178 [8]	0.0083 [6]	0.0063 [3]	0.0384 [10]	0.0068 [4]	0.0050 [1]
		\(\gamma\)	0.0050 [4]	0.0055 [6]	0.0118 [9]	0.0051 [5]	0.0107 [8]	0.0037 [2.5]	0.0061 [7]	0.0159 [10]	0.0037 [2.5]	0.0032 [1]
		\(\delta\)	0.0726 [3]	0.2673 [7]	0.3392 [8]	0.1973 [6]	0.4121 [9]	0.1164 [5]	0.0938 [4]	0.4250 [10]	0.0224 [1]	0.0351 [2]
		\(\lambda\)	0.2929 [5]	0.4881 [6]	0.7627 [9]	0.5982 [8]	0.5919 [7]	0.2428 [4]	0.2159 [3]	1.1676 [10]	0.1762 [1]	0.1832 [2]
	MRE [ranks]	\(\alpha\)	0.4376 [5]	0.4831 [6]	0.5056 [8]	0.5311 [9]	0.4844 [7]	0.4030 [4]	0.3748 [3]	0.5570 [10]	0.3709 [2]	0.3705 [1]
		\(\beta\)	0.7256 [5]	0.7861 [7]	0.9651 [9]	0.7739 [6]	0.8513 [8]	0.6994 [3]	0.6386 [1]	1.0792 [10]	0.7151 [4]	0.6422 [2]
		\(\gamma\)	0.1578 [4]	0.1693 [6]	0.2517 [9]	0.1670 [5]	0.2317 [8]	0.1378 [3]	0.1723 [7]	0.2677 [10]	0.1287 [2]	0.1225 [1]
		\(\delta\)	0.6310 [3]	1.2312 [7]	1.5287 [9]	1.1080 [6]	1.6157 [10]	0.7266 [4]	0.7781 [5]	1.4513 [8]	0.4016 [1]	0.4392 [2]
		\(\lambda\)	0.5314 [5]	0.7576 [6]	0.8132 [8]	0.8451 [9]	0.7798 [7]	0.4938 [4]	0.4571 [3]	0.8935 [10]	0.4083 [1]	0.4490 [2]
	Sum ranks [ranks]		63 [5]	98 [6]	126 [9]	104 [7]	119 [8]	56.5 [3]	57 [4]	145 [10]	33.5 [2]	23 [1]
400	Bias [ranks]	\(\alpha\)	0.1728 [5]	0.1942 [9]	0.1845 [6]	0.2102 [10]	0.1854 [7]	0.1609 [4]	0.1437 [3]	0.1870 [8]	0.1337 [1]	0.1403 [2]
		\(\beta\)	0.0715 [4]	0.0716 [5]	0.0780 [9]	0.0764 [8]	0.0758 [6]	0.0683 [3]	0.0559 [1]	0.0837 [10]	0.0759 [7]	0.0625 [2]
		\(\gamma\)	0.0436 [3]	0.0487 [5]	0.0692 [9]	0.0497 [7]	0.0685 [8]	0.0440 [4]	0.0496 [6]	0.0943 [10]	0.0426 [2]	0.0350 [1]
		\(\delta\)	0.1398 [3]	0.2441 [7]	0.3658 [9]	0.2336 [6]	0.3813 [10]	0.1564 [5]	0.1549 [4]	0.3549 [8]	0.0923 [1]	0.0988 [2]
		\(\lambda\)	0.3671 [5]	0.4912 [7]	0.4540 [6]	0.5488 [9]	0.5186 [8]	0.3468 [4]	0.2849 [3]	0.6147 [10]	0.2144 [1]	0.2821 [2]
	MSE [ranks]	\(\alpha\)	0.0348 [6]	0.0425 [8]	0.0423 [7]	0.0488 [10]	0.0427 [9]	0.0312 [4]	0.0272 [2]	0.0215 [1]	0.0316 [5]	0.0278 [3]
		\(\beta\)	0.0056 [4]	0.0068 [7]	0.0137 [10]	0.0063 [6]	0.0110 [8]	0.0052 [3]	0.0040 [1]	0.0118 [9]	0.0061 [5]	0.0047 [2]
		\(\gamma\)	0.0029 [3]	0.0038 [6.5]	0.0073 [9]	0.0035 [5]	0.0071 [8]	0.0029 [3]	0.0038 [6.5]	0.0094 [10]	0.0029 [3]	0.0022 [1]
		\(\delta\)	0.0588 [4]	0.1577 [7]	0.3066 [9]	0.1305 [6]	0.3648 [10]	0.0824 [5]	0.0516 [3]	0.3036 [8]	0.0174 [1]	0.0337 [2]
		\(\lambda\)	0.2551 [5]	0.3945 [6]	0.5162 [8]	0.4681 [7]	0.5360 [9]	0.2326 [4]	0.1497 [2]	1.0330 [10]	0.1066 [1]	0.1516 [3]
	MRE [ranks]	\(\alpha\)	0.4320 [5]	0.4781 [8]	0.4612 [6]	0.5256 [10]	0.4635 [7]	0.4022 [4]	0.3591 [3]	0.5194 [9]	0.3344 [1]	0.3508 [2]
		\(\beta\)	0.7150 [5]	0.7157 [6]	0.7799 [9]	0.7636 [8]	0.7570 [7]	0.6821 [3]	0.5594 [1]	0.9802 [10]	0.7062 [4]	0.6255 [2]
		\(\gamma\)	0.1247 [3]	0.1391 [5]	0.1976 [9]	0.1421 [7]	0.1956 [8]	0.1257 [4]	0.1418 [6]	0.2168 [10]	0.1216 [2]	0.0999 [1]
		\(\delta\)	0.5592 [3]	0.9763 [7]	1.4631 [9]	0.9345 [6]	1.5251 [10]	0.6256 [5]	0.6195 [4]	1.3334 [8]	0.3695 [1]	0.3952 [2]
		\(\lambda\)	0.5244 [5]	0.7017 [6]	0.7486 [8]	0.7839 [9]	0.7408 [7]	0.4801 [4]	0.4069 [3]	0.8094 [10]	0.3064 [1]	0.4031 [2]
	Sum ranks [ranks]		63 [5]	99.5 [6]	123 [9]	114 [7]	122 [8]	56 [4]	48.5 [3]	131 [10]	36 [2]	29 [1]
600	Bias [ranks]	\(\alpha\)	0.1568 [5]	0.1920 [9]	0.1708 [7]	0.1957 [10]	0.1853 [8]	0.1583 [6]	0.1304 [2]	0.1513 [4]	0.1287 [1]	0.1315 [3]
		\(\beta\)	0.0702 [8]	0.0655 [4.5]	0.0674 [7]	0.0750 [9]	0.0655 [4.5]	0.0668 [6]	0.0524 [1]	0.0654 [3]	0.0798 [10]	0.0613 [2]
		\(\gamma\)	0.0384 [2]	0.0450 [7]	0.0629 [8]	0.0414 [6]	0.0641 [9]	0.0399 [4]	0.0408 [5]	0.0759 [10]	0.0394 [3]	0.0313 [1]
		\(\delta\)	0.1101 [3]	0.2164 [7]	0.3470 [9]	0.1609 [6]	0.3631 [10]	0.1543 [5]	0.1390 [4]	0.3320 [8]	0.0848 [1]	0.0920 [2]
		\(\lambda\)	0.3088 [4]	0.4527 [8]	0.3271 [5]	0.4503 [7]	0.5176 [9]	0.3339 [6]	0.2659 [3]	0.5865 [10]	0.1967 [1]	0.2233 [2]
	MSE [ranks]	\(\alpha\)	0.0290 [4]	0.04192 [9]	0.0419 [8]	0.0422 [10]	0.0417 [7]	0.0310 [6]	0.0223 [2]	0.0136 [1]	0.0307 [5]	0.0250 [3]
		\(\beta\)	0.0054 [5]	0.0048 [3]	0.0076 [9]	0.0061 [7]	0.0073 [8]	0.0049 [4]	0.0034 [1]	0.0086 [10]	0.0057 [6]	0.0046 [2]
		\(\gamma\)	0.0022 [2]	0.0031 [7]	0.0060 [8]	0.0025 [5]	0.0061 [9]	0.0023 [3.5]	0.0026 [6]	0.0079 [10]	0.0023 [3.5]	0.0017 [1]
		\(\delta\)	0.0397 [3]	0.1494 [7]	0.2796 [9]	0.0792 [6]	0.3571 [10]	0.0747 [5]	0.0428 [4]	0.2625 [8]	0.0130 [1]	0.0287 [2]
		\(\lambda\)	0.1846 [4]	0.3672 [7]	0.4674 [9]	0.3136 [6]	0.4527 [8]	0.2149 [5]	0.1247 [2]	1.0123 [10]	0.0971 [1]	0.1289 [3]
	MRE [ranks]	\(\alpha\)	0.3922 [4]	0.4610 [7]	0.4495 [6]	0.4892 [10]	0.4632 [8]	0.3958 [5]	0.3260 [2]	0.4817 [9]	0.3218 [1]	0.3289 [3]
		\(\beta\)	0.7025 [8]	0.6550 [4]	0.6744 [6]	0.7504 [9]	0.6545 [3]	0.6683 [5]	0.5240 [1]	0.9054 [10]	0.6994 [7]	0.6129 [2]
		\(\gamma\)	0.1098 [2]	0.1287 [7]	0.1798 [9]	0.1183 [6]	0.1831 [10]	0.1139 [4]	0.1167 [5]	0.1609 [8]	0.1126 [3]	0.0895 [1]
		\(\delta\)	0.4404 [3]	0.9320 [7]	1.3581 [9]	0.6436 [6]	1.4525 [10]	0.6171 [5]	0.5559 [4]	1.2067 [8]	0.3393 [1]	0.3683 [2]
		\(\lambda\)	0.4412 [4]	0.6732 [8]	0.6130 [6]	0.6434 [7]	0.7394 [9]	0.4769 [5]	0.3799 [3]	0.7584 [10]	0.2810 [1]	0.3191 [2]
	Sum ranks [ranks]		61 [4]	101.5 [6]	115 [8]	110 [7]	122.5 [10]	74.5 [5]	45 [2]	119 [9]	45.5 [3]	31 [1]

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Table 3 Comparison of Bias, MSE, MRE for parameter estimateswhen \(\alpha = 0.40\); \(\beta = 0.10\); \(\gamma = 0.35\);\(\delta = 0.25\); and \(\lambda = 0.70\).

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