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

β = 0.5; K = 0.5; λ = 0.5; S = 0.5.