Table 1 Simulation results for moment, ML, EM estimates for different parameter values

10

(0.3819; 0.4290) (0.4305; 0.5161)

(0.5330; 0.7897) (0.6306; 0.9422)

(0.5560; 1.1057) (0.6350; 1.3591)

(0.4490; 0.7892) (0.5419; 1.0079)

20

(0.3473; 0.4560) (0.4555; 0.5957)

(0.4871; 0.6023) (0.5500; 0.7010)

(0.3662; 0.5454) (0.4537; 0.6899)

(0.5202; 0.7779) (0.5953; 0.9440)

50

(0.2734; 0.4128) (0.2933; 0.4678)

(0.1971; 0.2388) (0.2319; 0.3022)

(0.2927; 0.3971) (0.4197; 0.5767)

(0.2559; 0.3208) (0.2837; 0.3513)

100

(0.2086; 0.2952) (0.2361; 0.3722)

(0.2050; 0.2653) (0.2250; 0.3083)

(0.1975; 0.2521) (0.2428; 0.3155)

(0.1806; 0.2556) (0.2135; 0.3216)

10

(0.3441; 4.7886) (0.3940; 6.1487)

(0.4563; 6.0390) (0.4968; 7.6046)

(0.1563; 1.2578) (0.2539; 2.0050)

(0.5476; 8.4679) (0.6203; 10.1551)

20

(0.4427; 6.1054) (0.5348; 8.0019)

(0.5069; 8.2839) (0.5310; 9.0880)

(0.1382; 1.4474) (0.3346; 3.2439)

(0.2243; 2.8182) (0.3571; 4.4648)

50

(0.2810; 3.9128) (0.2982; 4.2335)

(0.3375; 4.8599) (0.3980; 6.1233)

(0.1457; 1.7248) (0.1635; 1.9789)

(0.3682; 5.9521) (0.4436; 7.3848)

100

(0.2980; 4.2913) (0.3269; 4.9345)

(0.2281; 2.7206) (0.2440; 2.9904)

(0.2180; 3.1057) (0.2560; 3.6473)

(0.2187; 2.9054) (0.2819; 3.8716)

10

(0.3455; 31.2778) (0.4174; 37.4113)

(0.3251; 31.8195) (0.3651; 40.4183)

(0.0320; 6.6267) (0.0714; 15.6975)

(0.1561; 21.8481) (0.1863; 24.7316)

20

(0.4703; 66.2730) (0.5181; 78.6781)

(0.4256; 62.2380) (0.4959; 81.2181)

(0.0232; 1.8407) (0.0515; 3.9342)

(0.2677; 44.3097) (0.3238; 56.3634)

50

(0.3570; 57.4291) (0.4121; 75.3072)

(0.3372; 45.2799) (0.4119; 63.8644)

(0.0485; 6.3230) (0.0690; 9.3401)

(0.2985; 42.1803) (0.3549; 53.6298)

100

(0.2481; 35.1331) (0.2583; 37.8049)

(0.3825; 50.6405) (0.4070; 54.8860)

(0.0412; 5.3581) (0.0563; 8.0360)

(0.2263; 32.0492) (0.2549; 37.9289)

10

(0.3955; 155.0823) (0.4273; 168.6059)

(0.3385; 118.2894) (0.3807; 151.7710)

(0.0169; 12.4376) (0.0274; 32.4726)

(0.2980; 215.2239) (0.3521; 305.7791)

20

(0.4581; 185.6736) (0.5048; 211.9931)

(0.4414; 180.4513) (0.5424; 249.3666)

(0.0565; 22.2828) (0.0913; 38.1805)

(0.2077; 72.5677) (0.2928; 101.4907)

50

(0.2804; 123.0569) (0.2960; 137.4734)

(0.3819; 129.9446) (0.4090; 145.2682)

(0.0301; 9.2323) (0.0470; 14.5592)

(0.1684; 68.5255) (0.2332; 96.9123)

100

(0.2034; 78.9574) (0.2238; 90.6749)

(0.2601; 104.8366) (0.3032; 130.2829)

(0.0115; 3.6741) (0.0196; 6.4544)

(0.1746; 66.2565) (0.1975; 78.9489)

10

(0.3717; 0.0426) (0.3629; 0.0535)

(0.5123; 0.0529) (0.4926; 0.0719

(0.4609; 0.0831) (0.4811; 0.1192)

(0.6697; 0.1255) (0.6698; 0.1715)

20

(0.3217; 0.0443) (0.3398; 0.0530)

(0.4694; 0.0702) (0.4458; 0.0791

(0.4358; 0.0750) (0.4491; 0.0991)

(0.3200; 0.0492) (0.3301; 0.0603)

50

(0.3540; 0.0474) (0.3450; 0.0524)

(0.2736; 0.0319) (0.2540; 0.0341)

(0.3502; 0.0459) (0.3586; 0.0492)

(0.1795; 0.0220) (0.1538; 0.0213)

100

(0.1570; 0.0193) (0.1319; 0.0193)

(0.2562; 0.0264) (0.1824; 0.0204)

(0.1674; 0.0172) (0.1678; 0.0176)

(0.1996; 0.0220) (0.1450; 0.0159)

10

(0.5543; 0.5408) (0.5215; 0.5529)

(0.5115; 0.6531) (0.4591; 0.7114)

(0.6810; 0.8712) (0.6672; 0.9190)

(0.5306; 0.6258) (0.5184; 0.7046)

20

(0.4436; 0.5750) (0.4105; 0.5916)

(0.4167; 0.3775) (0.4206; 0.4234)

(0.4159; 0.4117) (0.4641; 0.4481)

(0.4431; 0.5409) (0.4599; 0.6300)

50

(0.3695; 0.4175) (0.3499; 0.4394)

(0.2921; 0.2933) (0.2211; 0.2334)

(0.1822; 0.1846) (0.1566; 0.1769)

(0.2421; 0.3087) (0.1937; 0.2976)

100

(0.1999; 0.2411) (0.1416; 0.2194)

(0.1993; 0.1916) (0.1396; 0.1535)

(0.2411; 0.2668) (0.2137; 0.2548)

(0.2038; 0.2215) (0.1343; 0.1502)

10

(0.4461; 4.5711) (0.4257; 4.1085)

(0.5073; 5.6156) (0.4897; 7.4046)

(0.1549; 2.0957) (0.1488; 2.7522)

(0.6790; 7.3133) (0.6839; 7.5797)

20

(0.3167; 3.8858) (0.3364; 5.1648)

(0.4691; 6.4103) (0.4813; 8.6758)

(0.1318; 1.4181) (0.1402; 1.7552)

(0.2355; 2.6073) (0.1795; 2.2731)

50

(0.2459; 2.3518) (0.2212; 2.1697)

(0.2131; 2.1511) (0.1553; 1.7007)

(0.2238; 2.5573) (0.2083; 2.4655)

(0.2574; 2.8351) (0.1860; 2.2699)

100

(0.1941; 2.2066) (0.1392; 1.7672)

(0.2142; 2.3646) (0.1853; 2.2036)

(0.1851; 2.0202) (0.1492; 1.8207)

(0.2388; 2.8016) (0.1965; 2.6684)

10

(0.3444; 13.6255) (0.3562; 20.5479)

(0.4058; 11.4606) (0.3983; 11.9361)

(0.0083; 0.1631) (0.0950; 2.8788)

(0.2777; 8.0010) (0.3672; 10.6504)

20

(0.3146; 7.9388) (0.3077; 7.7036)

(0.1761; 6.0556) (0.1258; 6.7467)

(0.0829; 2.6625) (0.0944; 2.9822)

(0.3651; 13.6145) (0.4316; 16.6203)

50

(0.1978; 5.9274) (0.1392; 4.4230)

(0.2566; 8.6629) (0.2078; 8.3575)

(0.0943; 2.9838) (0.1105; 3.5267)

(0.2816; 9.8190) (0.2150; 8.2843)

100

(0.1460; 4.0423) (0.0941; 2.5510)

(0.1929; 5.4612) (0.1277; 3.9084)

(0.1019; 3.3346) (0.0845; 3.2275)

(0.2194; 7.7674) (0.1791; 7.1549)

10

(0.4846; 0.0113) (0.2573; 0.0063)

(0.7014; 0.0143) (0.2481; 0.0081)

(0.7000; 0.0109) (0.2921; 0.0052)

(0.7637; 0.0108) (0.3041; 0.0051)

20

(0.4787; 0.0083) (0.2079; 0.0036)

(0.6509; 0.0109) (0.2240; 0.0061)

(0.5200; 0.0089) (0.2843; 0.0048)

(0.5983; 0.0111) (0.2889; 0.0064)

50

(0.6111; 0.0106) (0.1988; 0.0033)

(0.6812; 0.0103) (0.2380; 0.0037)

(0.6782; 0.0115) (0.1719; 0.0026)

(0.7056; 0.0103) (0.1998; 0.0021)

100

(0.5729; 0.0095) (0.1725; 0.0025)

(0.6413; 0.0099) (0.1502; 0.0021)

(0.6071; 0.0099) (0.1892; 0.0032)

(0.6108; 0.0100) (0.1777; 0.0027)

10

(0.4892; 0.1172) (0.1959; 0.1301)

(0.6964; 0.1187) (0.1631; 0.0498)

(0.6865; 0.1116) (0.2722; 0.0345)

(0.6737; 0.1339) (0.2742; 0.0610)

20

(0.6058; 0.1000) (0.2497; 0.0474)

(0.6651; 0.1040) (0.1942; 0.0334)

(0.5737; 0.0956) (0.3423; 0.0644)

(0.5784; 0.1081) (0.3023; 0.0697)

50

(0.5760; 0.1028) (0.1671; 0.0279)

(0.6347; 0.1043) (0.1510; 0.0251)

(0.6598; 0.1162) (0.1668; 0.0321)

(0.6670; 0.1184) (0.2531; 0.0473)

100

(0.6451; 0.0990) (0.1823; 0.0208)

(0.6198; 0.0950) (0.1734; 0.0270)

(0.6303; 0.1047) (0.1747; 0.0229)

(0.6188; 0.1014) (0.1253; 0.0206)

10

(0.6795; 1.2128) (0.1585; 0.9660)

(0.6059; 1.0671) (0.1417; 0.5625)

(0.6832; 1.0181) (0.3404; 0.5152)

(0.6502; 1.5538) (0.3275; 1.1916)

20

(0.6957; 1.2371) (0.2184; 0.5714)

(0.6458; 1.0511) (0.2042; 0.3870)

(0.5259; 0.8140) (0.2643; 0.4453)

(0.6212; 1.0367) (0.2875; 0.5246)

50

(0.6684; 1.0214) (0.1378; 0.1628)

(0.6477; 1.0105) (0.1361; 0.3014)

(0.6550; 0.9959) (0.2374; 0.3766)

(0.6311; 0.9262) (0.2507; 0.3527)

100

(0.6354; 1.0162) (0.1679; 0.2285)

(0.6323; 0.9949) (0.1456; 0.2346)

(0.6120; 1.0161) (0.1392; 0.2164)

(0.5899; 0.9988) (0.1893; 0.3216)

10

(0.5661; 2.9674) (0.2097; 1.3517)

(0.5572; 3.1071) (0.2856; 2.7416)

(0.6525; 4.0879) (0.3489; 3.0165)

(0.5420; 2.8224) (0.2985; 1.7626)

20

(0.6527; 3.6483) (0.2922; 1.9112)

(0.6443; 3.0669) (0.1563; 0.8436)

(0.6340; 3.2548) (0.2618; 1.4175)

(0.6871; 3.6108) (0.2115; 1.4077)

50

(0.6667; 3.4335) (0.2030; 1.0722)

(0.5592; 2.7817) (0.2527; 1.4259)

(0.6313; 3.0814) (0.2326; 0.9826)

(0.6583; 3.1923) (0.1929; 1.1181)

100

(0.6198; 3.0107) (0.1390; 0.6702)

(0.5831; 2.7708) (0.1301; 0.6725)

(0.6169; 3.0523) (0.1450; 0.6430)

(0.6374; 3.1514) (0.1758; 0.8689)

10

(0.6143; 0.0071) (0.3933; 0.0048)

(0.7565; 0.0086) (0.2204; 0.0036)

(0.8192; 0.0107) (0.2439; 0.0033)

(0.7333; 0.0109) (0.3113; 0.0036)

20

(0.6665; 0.0079) (0.3182; 0.0032)

(0.7730; 0.0083) (0.2121; 0.0032)

(0.7321; 0.0086) (0.2844; 0.0021)

(0.9318; 0.0099) (0.1212; 0.0025)

50

(0.6855; 0.0085) (0.2732; 0.0024)

(0.8523; 0.0094) (0.1123; 0.0013)

(0.7905; 0.0096) (0.2251; 0.0026)

(0.9186; 0.0103) (0.1473; 0.0021)

100

(0.7465; 0.0090) (0.2198; 0.0016)

(0.8935; 0.0103) (0.0622; 0.0011)

(0.8215; 0.0093) (0.1361; 0.0014)

(0.9268; 0.0100) (0.0812; 0.0009)

10

(0.6462; 0.0862) (0.3381; 0.0378)

(0.7013; 0.0908) (0.2623; 0.0309)

(0.8431; 0.1020) (0.1934; 0.0374)

(0.9185; 0.1006) (0.2451; 0.0267)

20

(0.8678; 0.1015) (0.1223; 0.0214)

(0.8388; 0.0995) (0.1228; 0.0269)

(0.7909; 0.1014) (0.2685; 0.0406)

(0.8270; 0.0988) (0.2316; 0.0419)

50

(0.7725; 0.0956) (0.1698; 0.0121)

(0.7720; 0.0887) (0.2027; 0.0209)

(0.8624; 0.1042) (0.2035; 0.0226)

(0.7946; 0.0890) (0.2022; 0.0216)

100

(0.7852; 0.0952) (0.1698; 0.0153)

(0.8895; 0.1031) (0.0870; 0.0180)

(0.9620; 0.1093) (0.1088; 0.0157)

(0.9496; 0.1016) (0.1028; 0.0099)

10

(0.5889; 0.7639) (0.3829; 0.4564)

(0.6355; 0.9238) (0.3500; 0.4046)

(0.8911; 1.2604) (0.1467; 0.4797)

(0.8847; 1.0496) (0.1907; 0.3918)

20

(0.6091; 0.7758) (0.3424; 0.4521)

(0.6895; 0.9191) (0.2611; 0.2828)

(0.7729; 0.8300) (0.2886; 0.3351)

(0.9399; 1.1832) (0.1065; 0.3144)

50

(0.6475; 0.7636) (0.3288; 0.3296)

(0.8115; 0.9372) (0.2038; 0.1594)

(0.8992; 1.0015) (0.1707; 0.2070)

(0.8752; 0.9595) (0.1696; 0.1752)

100

(0.7548; 0.8831) (0.2393; 0.2185)

(0.7883; 0.8887) (0.1605; 0.1674)

(0.9435; 1.1117) (0.1080; 0.1885)

(0.8962; 1.0487) (0.1629; 0.1792)

10

(0.5325; 2.3452) (0.4575; 1.3839)

(0.8471; 3.0594) (0.1205; 0.6364)

(0.9126; 2.8102) (0.1976; 0.6489)

(0.8290; 2.9299) (0.2637; 1.3058)

20

(0.6708; 2.3101) (0.3300; 0.9030)

(0.8174; 3.1643) (0.1580; 0.7843)

(0.8827; 3.0024) (0.1854; 0.7117)

(0.8202; 2.8625) (0.2537; 0.7691)

50

(0.8508; 3.2611) (0.1162; 0.6055)

(0.8560; 2.8071) (0.1108; 0.4488)

(0.8717; 3.1389) (0.1911; 0.9120)

(0.9140; 2.9894) (0.1193; 0.3799)

100

(0.8442; 2.7397) (0.1149; 0.4302)

(0.8867; 2.9404) (0.0769; 0.3865)

(0.8969; 2.9607) (0.1110; 0.3967)

(0.9193; 2.9727) (0.1070; 0.4539)