Research Article
Exponentially Generated Modified Chen Distribution with Applications to Lifetime Dataset
Table 1
Simulation study for the EGMC distribution.
| Sample size | Parameters | Estimates | Biasness | Variance | MSE |
| 5 | β | 0.6767 | 0.1767 | 0.20 | 0.23 | K | 1.1759 | 0.6759 | 2.89 | 3.35 | λ | 0.4292 | −0.0708 | 0.17 | 0.18 | S | 26.6930 | 26.1930 | 2734.96 | 3421.03 |
| 10 | β | 0.860023 | 0.360023 | 0.0134272 | 0.143043 | K | 0.215724 | −0.284276 | 0.0222105 | 0.103024 | λ | 0.298949 | −0.201051 | 0.0783470 | 0.118769 | S | 0.298392 | −0.201608 | 0.0182780 | 0.058924 |
| 15 | β | 0.592134 | 0.0921336 | 0.0319309 | 0.0404195 | K | 0.480335 | −0.0196649 | 0.0771938 | 0.0775805 | λ | 0.593313 | 0.0933125 | 0.0331190 | 0.0418262 | S | 0.640158 | 0.1401576 | 0.1001277 | 0.1197719 |
| 20 | β | 0.583264 | 0.0832640 | 0.0218930 | 0.0288259 | K | 0.467710 | −0.0322904 | 0.0108118 | 0.0118545 | λ | 0.513104 | 0.0131039 | 0.0712279 | 0.0713996 | S | 0.560411 | 0.0604114 | 0.0334183 | 0.0370678 |
| 25 | β | 0.536804 | 0.0368039 | 0.0077052 | 0.0090597 | K | 0.501933 | 0.0019330 | 0.0044649 | 0.0044686 | λ | 0.489043 | −0.0109572 | 0.0130077 | 0.0131277 | S | 0.538829 | 0.0388294 | 0.0164299 | 0.0179376 |
| 30 | β | 0.529510 | 0.0295101 | 0.0177079 | 0.0185787 | K | 0.475855 | −0.0241445 | 0.0244566 | 0.0250395 | λ | 0.542904 | 0.0429037 | 0.0115442 | 0.0133849 | S | 0.566043 | 0.0660429 | 0.0234503 | 0.0278120 |
| 35 | β | 0.537156 | 0.0371558 | 0.0034353 | 0.0048159 | K | 0.520556 | 0.0205564 | 0.0108832 | 0.0113058 | λ | 0.460324 | −0.0396758 | 0.0072226 | 0.0087968 | S | 0.501010 | 0.0010104 | 0.0091000 | 0.0091010 |
| 40 | β | 0.520807 | 0.0208066 | 0.0023282 | 0.0027611 | K | 0.475722 | −0.0242781 | 0.0087483 | 0.0093377 | λ | 0.550854 | 0.0508535 | 0.0045059 | 0.0070920 | S | 0.519870 | 0.0198697 | 0.0035521 | 0.0039469 |
| 45 | β | 0.538171 | 0.0381715 | 0.0005072 | 0.0019643 | K | 0.491005 | −0.0089945 | 0.0115582 | 0.0116391 | λ | 0.481646 | −0.0183539 | 0.0035376 | 0.0038744 | S | 0.506524 | 0.0065238 | 0.0052825 | 0.0053251 |
| 50 | β | 0.567139 | 0.0671389 | 0.0003978 | 0.0049055 | K | 0.431462 | −0.0685376 | 0.0067192 | 0.0114167 | λ | 0.471225 | −0.0287750 | 0.0049601 | 0.0057881 | S | 0.465457 | −0.0345433 | 0.0023555 | 0.0035487 |
| 55 | β | 0.551303 | 0.0513027 | 0.0065554 | 0.0091874 | K | 0.449172 | −0.0508282 | 0.0166361 | 0.0192196 | λ | 0.456964 | −0.0430357 | 0.0335600 | 0.0354120 | S | 0.496700 | −0.0033005 | 0.0229119 | 0.0229228 |
| 60 | β | 0.526591 | 0.0265911 | 0.0065541 | 0.0072612 | K | 0.479260 | −0.0207400 | 0.0263108 | 0.0267409 | λ | 0.492259 | −0.0077412 | 0.0237598 | 0.0238197 | S | 0.532581 | 0.0325812 | 0.0256740 | 0.0267355 |
| 65 | β | 0.538517 | 0.0385171 | 0.0048136 | 0.0062972 | K | 0.516116 | 0.0161156 | 0.0215632 | 0.0218229 | λ | 0.447913 | −0.0520869 | 0.0285807 | 0.0312938 | S | 0.501517 | 0.0015166 | 0.0115791 | 0.0115814 |
| 70 | β | 0.548071 | 0.0480707 | 0.0038407 | 0.0061515 | K | 0.456693 | −0.0433071 | 0.0192083 | 0.0210838 | λ | 0.459096 | −0.0409037 | 0.0243834 | 0.0260565 | S | 0.487784 | −0.0122158 | 0.0117084 | 0.0118576 |
| 75 | β | 0.548961 | 0.0489606 | 0.0026224 | 0.0050195 | K | 0.426153 | −0.0738469 | 0.0131622 | 0.0186156 | λ | 0.475248 | −0.0247522 | 0.0139003 | 0.0145130 | S | 0.484497 | −0.0155032 | 0.0108139 | 0.0110542 |
| 80 | β | 0.551148 | 0.0511482 | 0.0018515 | 0.0044677 | K | 0.438722 | −0.0612779 | 0.0092576 | 0.0130126 | λ | 0.454927 | −0.0450735 | 0.0116320 | 0.0136636 | S | 0.482163 | −0.0178373 | 0.0079547 | 0.0082729 |
| 85 | β | 0.559469 | 0.0594688 | 0.0018985 | 0.0054351 | K | 0.396534 | −0.1034659 | 0.0155387 | 0.0262439 | λ | 0.483670 | −0.0163304 | 0.0039485 | 0.0042151 | S | 0.472042 | −0.0279576 | 0.0085035 | 0.0092851 |
| 90 | β | 0.565155 | 0.0651552 | 0.0020697 | 0.0063149 | K | 0.464896 | −0.0351035 | 0.0120228 | 0.0132550 | λ | 0.391887 | −0.1081130 | 0.0101104 | 0.0217988 | S | 0.458074 | −0.0419260 | 0.0084377 | 0.0101955 |
| 95 | β | 0.557711 | 0.0577108 | 0.0008321 | 0.0041626 | K | 0.463745 | −0.0362547 | 0.0125396 | 0.0138540 | λ | 0.403962 | −0.0960380 | 0.0011227 | 0.0103460 | S | 0.457842 | −0.0421576 | 0.0040510 | 0.0058283 |
| 100 | β | 0.545665 | 0.0456645 | 0.0009652 | 0.0030504 | K | 0.488159 | −0.0118409 | 0.0015978 | 0.0017381 | λ | 0.422859 | −0.0771412 | 0.0093100 | 0.0152607 | S | 0.474627 | −0.0253733 | 0.0039089 | 0.0045527 |
| 200 | β | 0.520441 | 0.0204407 | 0.0005537 | 0.0009716 | K | 0.504617 | 0.0046170 | 0.0019462 | 0.0019676 | λ | 0.487193 | −0.0128068 | 0.0041899 | 0.0043539 | S | 0.516876 | 0.0168757 | 0.0061796 | 0.0064644 |
| 500 | β | 0.499557 | −0.0004432 | 0.0009495 | 0.0009497 | K | 0.450622 | −0.0493783 | 0.0025090 | 0.0049472 | λ | 0.549669 | 0.0496685 | 0.0037656 | 0.0062326 | S | 0.503851 | 0.0038511 | 0.0057207 | 0.0057356 |
| 1000 | β | 0.506285 | 0.0062851 | 0.0008078 | 0.0008473 | K | 0.469542 | −0.0304584 | 0.0018271 | 0.0027548 | λ | 0.512220 | 0.0122200 | 0.0049380 | 0.0050874 | S | 0.486622 | −0.0133776 | 0.0022385 | 0.0024174 |
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β = 0.5; K = 0.5; λ = 0.5; S = 0.5.
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