Research Article
[Retracted] The Power XLindley Distribution: Statistical Inference, Fuzzy Reliability, and COVID-19 Application
Table 4
Simulation values of BIAS, MSE, and MRE for
and
.
| | Est. | Est. Par. | MLE | ADE | CVME | MPSE | LSE | PCE | RTADE | WLSE | LTADE |
| | 20 | BIAS | | 0.521184{5} | 0.467495{2} | 0.753993{9} | 0.426985{1} | 0.581814{7} | 0.491352{3} | 0.526135{6} | 0.503814{4} | 0.701128{8} | | | 0.076772{2} | 0.076104{1} | 0.102718{8} | 0.078158{3} | 0.086544{5} | 0.148815{9} | 0.090632{6} | 0.084575{4} | 0.096793{7} | | MSE | | 0.604624{6} | 0.411346{2} | 3.032123{9} | 0.331002{1} | 0.801514{7} | 0.575714{4} | 0.596513{5} | 0.540103{3} | 1.553027{8} | | | 0.010574{3} | 0.009815{2} | 0.02066{8} | 0.009109{1} | 0.01216{5} | 0.03465{9} | 0.014927{6} | 0.012094{4} | 0.016837{7} | | MRE | | 0.208474{5} | 0.186998{2} | 0.301597{9} | 0.170794{1} | 0.232726{7} | 0.196541{3} | 0.210454{6} | 0.201525{4} | 0.280451{8} | | | 0.153544{2} | 0.152208{1} | 0.205435{8} | 0.156317{3} | 0.173088{5} | 0.297631{9} | 0.181264{6} | 0.16915{4} | 0.193587{7} | | | 23{3.5} | 10{1.5} | 51{9} | 10{1.5} | 36{6} | 37{7} | 35{5} | 23{3.5} | 45{8} |
| | 60 | BIAS | | 0.265319{3} | 0.273776{6} | 0.306174{8} | 0.238352{1} | 0.290567{7} | 0.257912{2} | 0.271254{4} | 0.273431{5} | 0.339426{9} | | | 0.041686{2} | 0.044312^({3}) | 0.052367{8} | 0.041296{1} | 0.050037{6} | 0.112478{9} | 0.048004{5} | 0.045441{4} | 0.05171{7} | | MSE | | 0.125759{4} | 0.132248{6} | 0.181615{8} | 0.090083{1} | 0.140764{7} | 0.110871{2} | 0.126727{5} | 0.125333{3} | 0.215019{9} | | | 0.002811{2} | 0.003134{3} | 0.004529{8} | 0.002637{1} | 0.004102{6} | 0.020149{9} | 0.003732{5} | 0.00343{4} | 0.004432{7} | | MRE | | 0.106128{3} | 0.10951{6} | 0.12247{8} | 0.095341{1} | 0.116227{7} | 0.103165{2} | 0.108502{4} | 0.109372{5} | 0.135771{8} | | | 0.083371{2} | 0.088625{3} | 0.104733{8} | 0.082593{1} | 0.100074{6} | 0.224957{9} | 0.096009{5} | 0.090882{4} | 0.103419{7} | | | 16{2} | 27{4} | 48^({8.5}) | 6{1} | 39{7} | 33{6} | 28{5} | 25{3} | 48{8.5} |
| | 100 | BIAS | | 0.199122{2} | 0.206032{4} | 0.22673{7} | 0.19245{1} | 0.229466{8} | 0.220894{6} | 0.199846{3} | 0.208453{5} | 0.25666{9} | | | 0.032435{1} | 0.034336{3} | 0.038934{6} | 0.033479{2} | 0.039013{7} | 0.092339{9} | 0.036641{5} | 0.035227{4} | 0.039599{8} | | MSE | | 0.066608{3} | 0.071395{4} | 0.089779{7} | 0.057914{1} | 0.090105{8} | 0.08029{6} | 0.066601{2} | 0.073165{5} | 0.116057{9} | | | 0.001705{2} | 0.001877{3} | 0.002458{7} | 0.001685{1} | 0.002398{6} | 0.014214{9} | 0.002186{5} | 0.001999{4} | 0.002515{8} | | MRE | | 0.079649{2} | 0.082413{4} | 0.090692{7} | 0.07698{1} | 0.091786{8} | 0.088358{6} | 0.079938{3} | 0.083381{5} | 0.102664{9} | | | 0.064871{1} | 0.068673{3} | 0.077867{6} | 0.066958{1} | 0.078027{7} | 0.184678{9} | 0.073282{5} | 0.070454{4} | 0.079197^({8}) | | | 11{2} | 21{3} | 40{6} | 8{1} | 44{7} | 45{8} | 23{4} | 27{5} | 51{9} |
| | 200 | BIAS | | 0.139654{3} | 0.145635{5} | 0.162861{8} | 0.132133{1} | 0.161872{7} | 0.157093{6} | 0.136732{2} | 0.144871{4} | 0.178635{9} | | | 0.022005{1} | 0.023786{3} | 0.028828{8} | 0.023118{2} | 0.026891{6} | 0.075261{9} | 0.025796{5} | 0.024335{4} | 0.027892{7} | | MSE | | 0.030723{3} | 0.033699{5} | 0.043523{8} | 0.026881{1} | 0.041419{6} | 0.042857{7} | 0.030332{2} | 0.032729{4} | 0.053613{9} | | | 0.000777{1} | 0.000882{3} | 0.001319{8} | 0.000815{2} | 0.001169{6} | 0.009177{9} | 0.001054{5} | 0.00094{4} | 0.001226{7} | | MRE | | 0.055862{3} | 0.058254{5} | 0.065144{8} | 0.052853{1} | 0.064749{7} | 0.062837{6} | 0.054693{2} | 0.057948{4} | 0.071454{9} | | | 0.044011{1} | 0.047571{3} | 0.057656{8} | 0.046236{2} | 0.053782{6} | 0.150522{9} | 0.051593{5} | 0.04867{4} | 0.055783{7} | | | 12{2} | 24{4.5} | 48{8} | 9{1} | 38{6} | 46{7} | 21{3} | 24{4.5} | 48{8.5} |
| | 350 | BIAS | | 0.104313{3} | 0.109432{5} | 0.118824{8} | 0.09866{1} | 0.117734{6} | 0.125123{8} | 0.102642{2} | 0.106265{4} | 0.144369{9} | | | 0.016325{1} | 0.018767{5} | 0.020675{8} | 0.016489{2} | 0.021033{8} | 0.061037{9} | 0.019663{5} | 0.018562{3} | 0.020636{6} | | MSE | | 0.017754{3} | 0.018707{5} | 0.023275{8} | 0.015368{1} | 0.022592{6} | 0.027329{8} | 0.016928{2} | 0.018148{4} | 0.033717{9} | | | 0.000429{2} | 0.00054{4} | 0.00069{8} | 0.000426{1} | 0.000691{8} | 0.006229{9} | 0.000617{5} | 0.000534{3} | 0.000671{6} | | MRE | | 0.041725{3} | 0.043773{5} | 0.047529{8} | 0.039464{1} | 0.047094{6} | 0.050049{8} | 0.041057{2} | 0.042506{4} | 0.057747{9} | | | 0.03265{1} | 0.037534{4} | 0.04135{8} | 0.032979{2} | 0.042065{8} | 0.122074{9} | 0.039325{5} | 0.037124{3} | 0.041273{6} | | | 13{2} | 27{5} | 42{6.5} | 8{1} | 42{6.5} | 51{9} | 21{3.5} | 21{3.5} | 45{8} |
| | 500 | BIAS | | 0.080085{1} | 0.092965{5} | 0.098139{6} | 0.082415{2} | 0.101594{7} | 0.114768{9} | 0.088289{3} | 0.091908{4} | 0.109989{8} | | | 0.013154{1} | 0.015722{4} | 0.017762{7} | 0.014324{3} | 0.017534{6} | 0.055976{9} | 0.016353{5} | 0.014203{2} | 0.018341{8} | | MSE | | 0.010171{1} | 0.013879{5} | 0.015258{6} | 0.011104{2} | 0.016673{7} | 0.026277{9} | 0.012824{3} | 0.012978{4} | 0.019589{8} | | | 0.000286{1} | 0.000386{4} | 0.000488{7} | 0.000316{2} | 0.000486{6} | 0.005328{9} | 0.000412{5} | 0.000322{3} | 0.000527{8} | | MRE | | 0.032034{1} | 0.037186{5} | 0.039256{6} | 0.032966{2} | 0.040637{7} | 0.045907{9} | 0.035316{3} | 0.036763{4} | 0.043995{8} | | | 0.026307{1} | 0.031444{4} | 0.035524{7} | 0.028648{3} | 0.035067{6} | 0.111952{9} | 0.032707{5} | 0.028405{2} | 0.036682{8} | | | 6{1} | 27{5} | 39{6.5} | 14{2} | 39{6.5} | 54{9} | 24{4} | 19{3} | 48{8} |
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