Research Article
Exponentially Generated Modified Chen Distribution with Applications to Lifetime Dataset
Table 2
Simulation study for EGMC distribution.
| Sample size | Parameters | Estimates | Biasness | Variance | MSE |
| 5 | β | 0.1713 | −0.0287 | 0.012 | 0.013 | K | 0.6237 | 0.3237 | 0.141 | 0.246 | λ | 1.1954 | 0.7954 | 1.992 | 2.625 | S | 12.5394 | 12.0394 | 533.144 | 678.092 |
| 10 | β | 0.280894 | 0.0808945 | 0.0007150 | 0.0072589 | K | 0.068114 | −0.2318858 | 0.0017425 | 0.0555135 | λ | 0.522747 | 0.1227474 | 0.1423641 | 0.1574310 | S | 0.362870 | −0.1371298 | 0.0219349 | 0.0407395 |
| 15 | β | 0.214346 | 0.0143457 | 0.0021792 | 0.0023850 | K | 0.287914 | −0.0120858 | 0.0390955 | 0.0392416 | λ | 0.672829 | 0.2728287 | 0.1852556 | 0.2596911 | S | 0.679318 | 0.1793182 | 0.0864240 | 0.1185790 |
| 20 | β | 0.214598 | 0.0145978 | 0.0019183 | 0.0021314 | K | 0.268409 | −0.0315908 | 0.0184668 | 0.0194647 | λ | 0.460113 | 0.0601127 | 0.0239420 | 0.0275556 | S | 0.611566 | 0.1115664 | 0.0374533 | 0.0499004 |
| 25 | β | 0.199559 | −0.0004415 | 0.0007246 | 0.0007248 | K | 0.304595 | 0.0045946 | 0.0269611 | 0.0269822 | λ | 0.547158 | 0.1471579 | 0.0126824 | 0.0343378 | S | 0.599002 | 0.0990020 | 0.0208870 | 0.0306884 |
| 30 | β | 0.199638 | −0.0003624 | 0.0016594 | 0.0016596 | K | 0.354166 | 0.0541655 | 0.0365586 | 0.0394925 | λ | 0.450366 | 0.0503662 | 0.0071476 | 0.0096844 | S | 0.611024 | 0.1110236 | 0.0281597 | 0.0404859 |
| 35 | β | 0.203445 | 0.0034447 | 0.0002338 | 0.0002456 | K | 0.285176 | −0.0148241 | 0.0141166 | 0.0143364 | λ | 0.487202 | 0.0872016 | 0.0151478 | 0.0227519 | S | 0.531373 | 0.0313731 | 0.0046727 | 0.0056570 |
| 40 | β | 0.201502 | 0.0015015 | 0.0001629 | 0.0001651 | K | 0.335847 | 0.0358470 | 0.0187665 | 0.0200515 | λ | 0.444857 | 0.0448573 | 0.0103847 | 0.0123969 | S | 0.541332 | 0.0413316 | 0.0028457 | 0.0045540 |
| 45 | β | 0.205167 | 0.0051670 | 0.0000495 | 0.0000762 | K | 0.312382 | 0.0123821 | 0.0127784 | 0.0129317 | λ | 0.428793 | 0.0287925 | 0.0068836 | 0.0077126 | S | 0.538143 | 0.0381428 | 0.0041191 | 0.0055740 |
| 50 | β | 0.214585 | 0.0145849 | 0.0000446 | 0.0002573 | K | 0.274680 | −0.0253198 | 0.0207559 | 0.0213970 | λ | 0.431196 | 0.0311963 | 0.0091943 | 0.0101675 | S | 0.495276 | −0.0047244 | 0.0019541 | 0.0019764 |
| 55 | β | 0.211972 | 0.0119724 | 0.0005555 | 0.0006988 | K | 0.242762 | −0.0572375 | 0.0197700 | 0.0230462 | λ | 0.457445 | 0.0574451 | 0.0110922 | 0.0143921 | S | 0.508782 | 0.0087824 | 0.0181023 | 0.0181794 |
| 60 | β | 0.205369 | 0.0053689 | 0.0006813 | 0.0007101 | K | 0.291756 | −0.0082437 | 0.0228865 | 0.0229545 | λ | 0.449340 | 0.0493396 | 0.0180440 | 0.0204783 | S | 0.542706 | 0.0427059 | 0.0213443 | 0.0231681 |
| 65 | β | 0.209262 | 0.0092617 | 0.0005194 | 0.0006052 | K | 0.239025 | −0.0609746 | 0.0187766 | 0.0224945 | λ | 0.502227 | 0.1022273 | 0.0037510 | 0.0142015 | S | 0.514289 | 0.0142891 | 0.0109054 | 0.0111095 |
| 70 | β | 0.211547 | 0.0115467 | 0.0003807 | 0.0005140 | K | 0.227124 | −0.0728760 | 0.0209029 | 0.0262138 | λ | 0.507838 | 0.1078379 | 0.0063921 | 0.0180211 | S | 0.503045 | 0.0030448 | 0.0099347 | 0.0099439 |
| 75 | β | 0.211490 | 0.0114898 | 0.0002288 | 0.0003609 | K | 0.246249 | −0.0537507 | 0.0147249 | 0.0176140 | λ | 0.430925 | 0.0309247 | 0.0034540 | 0.0044104 | S | 0.501292 | 0.0012920 | 0.0089441 | 0.0089458 |
| 80 | β | 0.212430 | 0.0124304 | 0.0001578 | 0.0003123 | K | 0.229270 | −0.0707295 | 0.0124339 | 0.0174365 | λ | 0.464509 | 0.0645094 | 0.0071615 | 0.0113230 | S | 0.499626 | −0.0003744 | 0.0067773 | 0.0067774 |
| 85 | β | 0.214901 | 0.0149014 | 0.0001533 | 0.0003753 | K | 0.251061 | −0.0489395 | 0.0136089 | 0.0160040 | λ | 0.395856 | −0.0041445 | 0.0015089 | 0.0015261 | S | 0.489312 | −0.0106877 | 0.0067650 | 0.0068792 |
| 90 | β | 0.216428 | 0.0164283 | 0.0001707 | 0.0004406 | K | 0.227604 | −0.0723962 | 0.0148859 | 0.0201271 | λ | 0.431185 | 0.0311850 | 0.0062951 | 0.0072676 | S | 0.476394 | −0.0236059 | 0.0071911 | 0.0077483 |
| 95 | β | 0.213985 | 0.0139850 | 0.0000657 | 0.0002613 | K | 0.227602 | −0.0723978 | 0.0127325 | 0.0179739 | λ | 0.464126 | 0.0641258 | 0.0127330 | 0.0168452 | S | 0.478173 | −0.0218267 | 0.0031903 | 0.0036667 |
| 100 | β | 0.210518 | 0.0105181 | 0.0001064 | 0.0002170 | K | 0.282820 | −0.0171799 | 0.0179628 | 0.0182580 | λ | 0.418992 | 0.0189918 | 0.0127201 | 0.0130808 | S | 0.493453 | −0.0065473 | 0.0033437 | 0.0033865 |
| 200 | β | 0.202282 | 0.0022815 | 0.0000349 | 0.0000401 | K | 0.277753 | −0.0222475 | 0.0089753 | 0.0094703 | λ | 0.478029 | 0.0780293 | 0.0063246 | 0.0124131 | S | 0.535234 | 0.0352336 | 0.0044893 | 0.0057307 |
| 500 | β | 0.198131 | −0.0018686 | 0.0000873 | 0.0000908 | K | 0.344009 | 0.0440091 | 0.0025124 | 0.0044492 | λ | 0.368620 | −0.0313799 | 0.0091554 | 0.0101401 | S | 0.509545 | 0.0095452 | 0.0048733 | 0.0049645 |
| 1000 | β | 0.201294 | 0.0012945 | 0.0000722 | 0.0000739 | K | 0.330686 | 0.0306855 | 0.0055191 | 0.0064607 | λ | 0.360292 | −0.0397083 | 0.0027592 | 0.0043359 | S | 0.488960 | −0.0110397 | 0.0018084 | 0.0019302 |
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β = 0.2; K = 0.3; λ = 0.4; S = 0.5.
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