Journal of Mathematics

Research Article

Statistical Analysis Based on Progressive Type-I Censored Scheme from Alpha Power Exponential Distribution with Engineering and Medical Applications

Table 11

The 95% asymptotic/credible intervals (first-line) with their lengths (second-line) of , , , and under head-neck cancer dataset.
SchemeParameterAsymptoticCredible
NALog-NABCIHPD
I(0.0000, 10.313) 10.313(0.1898, 41.160) 40.970(0.4257, 3.0318) 2.6061(0.5049, 3.0548) 2.5500
(0.0013, 0.0748) 0.0735(0.0145, 0.1000) 0.0855(0.0143, 0.0516) 0.0373(0.0130, 0.0501) 0.0371
(0.9611, 0.9953) 0.0342(0.9612, 0.9955) 0.0342(0.9633, 0.9864) 0.0231(0.9648, 0.9873) 0.0225
(0.0053, 0.0393) 0.0340(0.0104, 0.0477) 0.0373(0.0138, 0.0374) 0.0236(0.0128, 0.0358) 0.0230
II(0.0000, 9.9967) 9.9967(0.2848, 31.277) 30.993(1.1593, 2.5497) 1.3904(1.2420, 2.5824) 1.3404
(0.0046, 0.0688) 0.0642(0.0153, 0.0880) 0.0727(0.0189, 0.0484) 0.0295(0.0180, 0.0471) 0.0291
(0.9652, 0.9943) 0.0291(0.9653, 0.9944) 0.0291(0.9672, 0.9867) 0.0195(0.9678, 0.9871) 0.0193
(0.0062, 0.0352) 0.0290(0.0103, 0.0417) 0.0314(0.0134, 0.0336) 0.0202(0.0125, 0.0325) 0.0200
III(0.0000, 6.1691) 6.1691(0.0020, 387.15) 387.14(0.2360, 0.9267) 0.7267(0.2199, 0.9306) 0.7107
(0.0000, 0.0863) 0.0863(0.0023, 0.2817) 0.2794(0.0110, 0.0348) 0.0238(0.0094, 0.0327) 0.0233
(0.9533, 0.9932) 0.0399(0.9535, 0.9934) 0.0399(0.9580, 0.9844) 0.0265(0.9596, 0.9856) 0.0260
(0.0073, 0.0469) 0.0396(0.0131, 0.0562) 0.0431(0.0157, 0.0428) 0.0271(0.0145, 0.0411) 0.0266
IV(0.0000, 5.8077) 5.8077(0.1460, 19.456) 19.310(1.0969, 2.1573) 1.0604(1.1052, 2.1632) 1.0580
(0.0157, 0.1094) 0.0937(0.0296, 0.1323) 0.1027(0.0424, 0.0854) 0.0430(0.0415, 0.0844) 0.0429
(0.9223, 0.9838) 0.0614(0.9228, 0.9843) 0.0614(0.9353, 0.9665) 0.0312(0.9364, 0.9675) 0.0311
(0.0180, 0.0790) 0.0610(0.0259, 0.0909) 0.0651(0.0343, 0.0674) 0.0331(0.0337, 0.0667) 0.0330
V(0.0000, 0.0940) 0.0940(0.0001, 50.924) 50.924(0.0064, 0.0109) 0.0045(0.0068, 0.0112) 0.0043
(0.0000, 0.0386) 0.0386(0.0018, 0.0947) 0.0929(0.0105, 0.0143) 0.0038(0.0106, 0.0143) 0.0037
(0.9195, 0.9645) 0.0550(0.9197, 0.9647) 0.0450(0.9340, 0.9513) 0.0173(0.9344, 0.9516) 0.0172
(0.0361, 0.0827) 0.0467(0.0401, 0.0880) 0.0479(0.0497, 0.0678) 0.0182(0.0493, 0.0673) 0.0180