Order Statistics from Exponentiated Gamma. Distribution and Associated Inference

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It J otm Mth Scc Vo 4 9 o 7-9 Od Stttc fom Eottd Gmm Dtto d Aoctd Ifc A I Shw * d R A Bo G og of Edcto PO Bo 369 Jddh 438 Sd A G og of Edcto Dtmt of mthmtc PO Bo 469 Jddh 49 Sd A Atct Od tttc fom ottd gmm EG dtto codd Ect o fo th g d do momt of od tttc fom EG dtto dd Bd o th momt of od tttc th t d tmto BLUE fo th octo d c mt of EG dtto d T-II cog otd Th c d coc of th tmto o td Th mmm hood tmto MLE fo th h mt dd Ao tmto d o od tttc fo th h mt otd F como tw th tmto md d o mto td Mthmtc Sct cfcto 6F; 6F; 6F3; 6G5; 6G3 Kwod Od tttc; Eottd gmm dtto; Momt of od tttc; T-II cog; Mmm hood tmto; Bt d tmto Itodcto Od tttc t m -f cto og dt tg to f ttg td M tho h tdd od tttc d octd fc fo m Dd 98 Bh d oh 99 Aod t 99 d Dd d Ng 3 Bh d Pth 986 otd th t d tmto BLUE of th octo d c mt of hf ogtc dtto d o od tttc Mmm hood tmto MLE of th mt of B XII dtto w dd fo T-II cod m Wgo 993 * Pmt dd Fc of Eg t Sho PO Bo 6 E Md 78 o Egt

7 A I Shw d R A Bo Bh d h 998 h dcd tmto fo og-gmm mt d o od tttc Moo Rq 998 h dcd two t of tmto of octo d c mt d o od tttc fom B X dtto Gt d Kd 999 todcd gzd ot dtto d dd th MLE Rq d Ahh otd th BLUE of th octo d c mt of gzd ot dtto d o od tttc Th BLUE of th mt of o-mt d two-mt ogthmc dcg dtto d T-II cod m w dtmd St t Ao Mhmod t 3 h dd th ct o fo th g d do momt of od tttc fom W dtto d cctd th c d coc Bd o th momt th otd th BLUE of th octo d c mt of W dtto d T-II cod m MLE fom B X dtto d T I d II cog w dcd S d Pdgtt 5 Lt X X X dom m of z fom ottd gmm EG dtto wth ot dt fcto df f ; [ ] > > d th cmt dtto fcto cdf g F ; [ ] > > fo dt ot th dtto Shw d Bo 8c Ao chctzto fom EG dtto d o cod d B tmto o th EG dtto dcd Shw d Bo 8 Wh th h mt oth d g th df d cdf of gmm dtto wth h mt α d c mt β G I th w d th ct o fo th g d th do momt of od tttc fom EG dtto d o T-II cod m cto I cto 3 MLE fo th h mt otd Ao om tmto d o od tttc fo th h mt dd cto 4 I cto 5 w th momt of od tttc to ot th c coffct fo th BLUE of th octo d c mt Th c d coc of th tmto o g Nmc m d mto td fo th tmto codd F cto 6 omo tw th tmto d coco md Od Stttc d Momt Lt X X X th od tttc otd fom EG dtto Th g d do momt of od tttc dd foow

Od tttc fom ottd Gmm dtto 73 Sg momt Th df of th th od tttc X g Dd 98 f [ F ; ] [ F ; ] f ; > wh f d F g d ct d!!! f c wtt wh f d f ; 3 d 4 Not tht th coffct d ot ddt o Th oto m tht f wghtd g of EG dt th Th momt of th th od tttc dotd α d g α E X f d 5 Th ct ct o fo th g momt of od tttc fom EG dtto g th foowg thom Thom Fo d th α 6 Poof Fom 5 3 d w gt α d [ ] d

74 A I Shw d R A Bo Ug th om o w h d d α d Th w gt th t 6 g 4 hc th thom od If ot tg m th th to 6 com α 7 Th g momt of od tttc fom gmm dtto G c otd fom 7 ttg A c c fom 6 th ft g momt m d th cod g momt ct 3 3 α 8 d 4 4 α 9 Do momt Th ot df of X d X < g Dd 98 ] ; [ ] ; ; [ ] ; [ F F F F f ; ; > > f f wh f d F g d ct d!!!! f c wtt ; ; ] ; [ ] ; [ f f F F f

Od tttc fom ottd Gmm dtto 75 Th do momt of X d X dotd α < d g d d f X X E α Th ct ct o fo th do momt of od tttc fom th EG dtto g th foowg thom Thom Fo < d th α! 3 Poof Fom d w gt d d ] [ ] [ α ] [ d I 4 wh d I ] [ d! 5 Th fom 4 d 5 w h

76 A I Shw d R A Bo d ] [! α! d α Th tg th t qto gmm fcto hc th thom od If ot tg m th th to 3 com α! 6 Th do momt of od tttc fom gmm dtto G c otd fom 6 ttg A c c fom 3 th odct momt of X d X α! 3 3 3 3 7 3 Mmm Lhood Etmto So T-II cod m X X X X wh X th th od tttc Th m otd d codd fom EG dtto wth df d cdf g ct d Th hood fcto LF th c c wtt

Od tttc fom ottd Gmm dtto 77 wh T ; V 3 T [ ] d V Th ogthm of th LF g L ; T V 3 Th MLE of dotd ˆM g ˆ ˆ M M /[ V V ] 33 Th qto mct fom o t m od g mc tto ch Nwto Rho mthod g Mthmtc 4 I th of comt m tht th tmto ˆ M 33 dc to ˆ M 34 [ ] 4 Etmto Bd o Od Stttc Lt U U U th od tttc of dom m of z fom th fom dtto U d V V V th od tttc of dom m of z fom th ot dtto wth m / E Th o mg of th fct tht X U h E oto d mootoc dcg fcto w h X X d V 4 Lt V V V T II cod m fom E oto d cod th cott π π dfd π Not tht π th m of Z wh Z th th od tttc of dom m of z fom th E dtto To tmt th h mt d o th oto fom E w df Rq 998 S V π V

78 A I Shw d R A Bo It foow tht fo / / 3 S dttd mot χ t wth dg of fdom Thfo tmto of dotd ˆ g ˆ S Fom 4 w ot tmto of fcto of od tttc th foowg ˆ 4 [ ] X X X X π d Sc th tmto ˆ / Y wh Y dttd mot χ t foow tht th c of ˆ Vˆ > Not tht c c wh th tmto ˆ 4 th m th MLE of 34 Th tmto ~ dfd ~ [ ] X X X X π 43 mot d tmto fo > wth c / fo > whch m th tht of ˆ B g 4 43 d 33 w h mtd d o Mot-o th of d m q o MSE of ˆ ~ d ˆM I T w h td th fo o choc of d Fom th t w o tht th fomc of ~ tt th of ˆ d ˆ M fo choc of d codd

Od tttc fom ottd Gmm dtto 79 T Smtd of d MSE of ˆ ~ d 5 ˆ ~ ˆ M ˆ ~ ˆ M 3 9834-59444 894 7946 9637 568 8656 346397 84763 69977 68738 67679 3 95653-8978 95653 795-836 795 84444 33477 84444 733 468 733 5 3 5778 44 56649 6547 33 648 6636 799 4585 379 96 36549 5 547588 387 547588 685849 48679 685849 48 3546 48 454 3854 454 7 3 3583 4357 3333 4538 388 4344 39 7947 756 5744 363 953 5 9449-33355 997 469-97 4347 378 773359 3397 735 535 7445 7 468 79497 468 465-344 465 659 8733 659 85367 3679 85367 Not Th ft t th mtd Th cod t th mtd MSE T otd 3 35 ˆ ~ ˆ M ˆ ~ ˆ M 3 588 7 4898 85899 7656 864 44 9664 3694 33675 3436 33548 3 63746 9639 63746 7894-74 7894 9355 749 9355 654 83 654 5 3 743355-536 78398 9937 43389 9754 548645 3577 5474 673 3759 663583 5 7495-839 7495 8 58 8 566 9459 566 7438 43 7438 7 3 535346 396 5958 55-6785 4794 79485 8437 7495 348 36 3336 5 5567 4343 5478 495793-7534 497 78453 8487 77564 8546 93 84674 7 47574-86 47574 5533-58 5533 5388 6956 5388 33844 5939 33844 Not Th ft t th mtd Th cod t th mtd MSE ˆM

8 A I Shw d R A Bo A w c fom T th MSE of ~ th tht of ˆ d ˆ M fo ~ comt d cod m codd Ao w ot tht MSE of ˆ d ˆ M c c d dc c Thfo w c tht ~ tt th ˆ d ˆ M fo choc of d codd Nt w dc th tmto of th octo d c mt of th EG dtto It md tht th h mt ow

Od tttc fom ottd Gmm dtto 8 5 BLUE of Locto d Sc Pmt Th ct d ct o fo th ft d cod g momt of od tttc g 8 d 9 ct ow to t th m d c of od tttc fo m of z Fo th comtto of c d coc th odct momt α < w comtd ft Th dgo mt α α otd fom th ct o g 9 Nt th ct d ct o g 7 w d fo comtto of th odct momt of two od tttc Th w d to t th coc β α α α Th of m c d coc w comtd g Mthmtc 4 c th gmm fcto It mott to m h tht o comtto wh fo gmm dtto G Am Y Y Y to dom m of z fom th EG dtto wth df μ μ / σ μ μ / σ g ; μ σ [ ] > μ σ > σ σ Lt Y Y Y T-II cod m fom th o dom m Th X X X X wh X Y / μ σ odd m fom oto wth th tdd EG dtto df d cdf g d ct Th w c wt th t d tmto BLUE of μ d σ [ Dd 98 Aod t 99 d Dd d Ng 3] ˆ μ Y Y Y 5 ˆ σ Y Y Y 5 T T wh A V A A V ; T T A α α α α α V th of th coc mt V β Vc d coc of th tmto g V ˆ μ d σ V ˆ σ dσ d o ˆ μ ˆ σ d σ 53 d d T wh D A V A d d I T d 3 w h td th coffct of th BLUE of th octo d c mt ct fo 6 / to d 555 Th coffct of th BLUE td T d 3 chcd th codto d Th c d coc of th BLUE g 53 td T 4 tm of σ

8 A I Shw d R A Bo T offct fo th BLUE of μ 5 5 5 6 6 53 756 99 3365 38997 4479 64446 953 65978 9746 3-64748 - 959-9435 - 7869-8965 4-33 - 644-954 - 3368-368 5-3638 - 88537-356 - 6935-9946 6-46 - 684-5834 - 888-366 5 968 3789 43 4793 5539 5453 9 637 9483 3-8749 - 4837-48 - 4535-49477 4-653 - 8567-6 - 5893-7597 5-9656 - 35484-3486 - 443449-599 4 65 44963 637 756 8558 577 3675 8436 4769 8456 3-3434 - 733-836 - 9833-39 4-5736 - 4549-648 - 759595-88664 3 994 788 94854 39 7896 6 3 44333 4465 54838 3-35943 - 7995-99875 - 3756-4338 5 5 35 975 38555 4574 596 79 359 6847 983 35973 3-635 - 6669-835 - 9895-35 4-493 - 3-6797 - 4638-3898 5-63937 - 4548-7643 - 63-3349 4 789 468 56384 6647 7578 57697 6547 43 8735 6 3-84356 - 468-387 - 573-7993 4-554 - 33896-47435 - 59484-6947 3 359 6785 89434 588 938-4756 - 786 35 555 3-344668 - 63695-88559 - 8979-577 4 4 986 39454 5656 65 6943-948 - 36357-893 735 488 3-83687 - 58-379 - 48579-8658 4-9564 - 899-9394 - 3637-48639 3 333 685 87 977 9873-648 - 979-977 - 847-8 3-674 - 5658-73549 - 885469-663 733 7 6498 958 349-733 - 7-6498 - 958-49 3 3 3695 55 73 845 948-6788 - 9935-3739 - 65455-93647 3-96 - 35699-4758 - 574695-65445 6798 88 4368 6883 8979-6798 - 88-4368 - 6883-8979 583 83333 534 487 36553-583 - 83333-534 - 487-36553

Od tttc fom ottd Gmm dtto 83 T otd 3 35 4 45 5 6 6 446 4876 535 56944 664 893 37 54 6554 7635 3-54 - 39-69 - 39-3384 4-4964 - 64769-7844 - 985-67 5-486 - 46975-66658 - 843-33 6-64596 - 8966-3488 - 3949-346584 5 6636 67533 7884 778 8367 847 3837 5537 6945 884 3-549 - 58995-63855 - 68685-73369 4-9769 - 7-3447 - 4984-64 5-58588 -63745-685874 - 7938-76796 4 8964 976 4849 464 7539 34 3675 57 6783 888 3-68 - 83-354 -38957-4668 4-9937 - 878-6967 -435-357 3 463 53743 646 74477 8353 83799 879 354 4849 6454 3-6 - 7466-8767 -9936-9956 5 5 585 63596 68587 737 7748 579 65468 7664 854 9364 3-688 - 38468-49748 - 63-787 4-688 - 93789-36576 - 33747-35577 5-33876 - 3697-39584 - 49493-44754 4 845 943 9886 458 9749 97 4979 5438 63775 74 3-98679 - 644-3554 - 4753-639 4-77838 - 84874-9684 - 957843-775 3 3839 4395 539 6943 743 7397 848 9568 4658 444 3-39979 - 543-63478 - 7349-8387 4 4 7697 83546 8953 94978 99985 449 6876 789 795 774 3-3865 -347388-3733 - 39644-4777 4-464954 -5495-545 - 575-599357 3 8 393 3976 47758 557-8343 -8534-8839 - 9838-9575 3-737 -398-399 - 38575-45499 346 3635 378334 39376 477-46 -635-78334 - 9376-377 3 3 449 355 9679 63 3338-39995 -3446-366335 - 38736-466 3-749 -779437-83457 - 875976-97 3759 335 3378 34965 3648-759 -35-378 - 4965-648 4849 58865 6839 7668 8377-4849 -58865-6839 - 7668-8377

84 A I Shw d R A Bo T 3 offct fo th BLUE of σ 5 5 5 6 6-3549 - 5544-47668 - 4365-4936 - 378 59 34946 5884-4348 3 58339 94793 8564 768 684 4 738 5556 865 565 4 5 63847 76 3 88 648 6 8653 36373 983 945 897 5-559573 - 6454-575359 - 5863-5696 - 8697 6445 4634 9478-73 3 9883 7775 99736 998 84796 4 49 48 394 974 764 5 43496 3653 347 9858 979 4-86648 - 8356-738367 - 689-653 - 96 88479 57887 8368 365 3 76937 57393 3385 7 5487 4 8968 58683 546675 539554 534446 3-5666 - 346-5534 - 976985-93834 8535 39358 9577 4598 737 3 5575 64 96764 935387 9764 5 5-434989 - 545885-49848 - 4657-45578 - 6469 8475 635 38993 8967 3 6654 33354 656 4536 833 4 3697 5654 5444 493 48533 5 88 774 6386 6938 645 4-74838 - 787-63973 - 59768-577577 - 7 364 846 54435 4696 3 545 7634 5876 5895 464 4 5739 488 39636 3998 389777 3-55 - 57-953 - 85783-88875 435 74657 347 96 73686 3 38 8558 78554 76664 75589 4 4-637 - 577-58548 - 53-494 438 8596 98863 8938 3 433 4 8978 8597 83755 4 7983 948 7 833 737 3-446 - 89793-75685 - 79584-7356 3746 547 7768 58 37395 3 787 64386 57987 56876 5696-494 - 5795-43 - 359-39 494 5795 43 359 39 3 3-6964 - 68844-577 - 5535-5439 858 6635 47 785 934 3 43 3459 33 3648 3458-47456 - 63-736 - 354-458 47456 63 736 354 458-7646 - 666667-639 - 677-657 7646 666667 639 677 657

Od tttc fom ottd Gmm dtto 85 T 3 otd 3 35 4 45 5 6 6-49594 - 4649-397635 - 393995-395 - 9785-46 - 753-95 - 57 3 658 6385 6554 64 59545 4 36 48 7 866 78 5 6 74 98 38 33 6 8634 8585 8634 874 884 5-4947 -48657-479993 - 47554-4738 - 9359-465 - 8657-735 - 48 3 858 7869 76856 75478 74444 4 6388 566 57 498 4754 5 96533 964 96587 96843 9748 4-63775 -6665-688 - 6536-6833 - 5437-75 - 779-7 -495 3 96 7897 569 49 79 4 5355 5343 5975 5957 59637 3-95376 -89986-88889 -88863-87495 876-395 - 7458-839 -7 3 9666 9 89677 8937 896 5 5-44745 -435583-437 -484-4574 33 8655 546 598 58 3 8533 6979 595 548 4593 4 4885 48 4884 4835 48468 5 6896 688 687 6963 67 4-56574 -55764-55843 - 547663-544597 344 853 495 848 89 3 439 45 39769 3886 3874 4 38848 387939 387878 387999 3883 3-8577 -799897-7977 - 785787-785 6333 55353 4948 44795 4388 3 748344 744544 7499 7499 743 4 4-489 - 47785-474333 - 47834-4749 83585 793 7685 73779 7946 3 85 889 8433 847 869 4 6835 675 675 688 6934 3-688879 -6887-6759 - 6753-66949 94 369 878 5434 84 3 559664 5588 5573 55679 556586-99 -756-6557 - 5849-5337 99 756 6557 5849 5337 3 3-53884 -534673-5375 - 53665-59559 46 385 99 744 695 3 3367 3388 3385 335 33364-34 -99453-989345 - 98584-98337 34 99453 989345 98584 98337-6778 -6588-64685 - 645-63734 6778 6588 64685 645 63734

86 A I Shw d R A Bo T 4 Vc d oc of th BLUE of μ d σ tm of d 5 5 5 6 6 9497 3697 46855 5739 7663 8377 456 388 38 978-977 -8453-777 -7976-578 5 94744 5769 45354 64545 8635 9374 76789 643 68 59486-5 -4579-886 -658-37 4 99864 948 55 76497 978976 39697 3659 65 4984 78-356 -895-78 -3449-437 3 6537 357 66759 98878 893 57776 35937 3976 38348 35435-7 -76347-3957 -5459-58797 5 5 9965 358 54865 756 93483 838 8645 6846 6647 6449-94 -69-7978 -85548-3886 4 383 363353 6749 88534 57 395 3957 36 8449 594-5935 -8-95493 -369368-4584 3 5669 448 789754 49 4638 5933 364 334636 337 3749-349 - 375-438 -5394-6 4 4 999 4864 785 697 399 343537 454 948 5647 33-545 - 483-3377 -4545-46777 3 993 58 98565 37366 76 548 367338 34679 33547 33356-5589 - 3593-48578 -5887-6769 764 863495 5456 338 8689 459 758 7863 6938 6864-398 - 68695-9987 -47-3564 3 3 354695 83775 377 76638 587 577 37696 354 34735 3496-75486 - 48854-5565 -66596-75386 4736 436 6758 8586 3564 4686 76664 764 69764 688677-55 - 8379-78 -837-44846 955777 3835 4435 498695 956465 777778 73794 778 78-69549 - 5556-3365 -54555-748 σ

Od tttc fom ottd Gmm dtto 87 T 4 otd 5 45 4 35 3 d 7396 7847 76 96637 8467 6 6 86 89 86 8499 8935-36949 -3457-3656 -35349-876 4838 3688 459 377 975 5 575 5756 57385 5773 58336-439947 -49573-39683 -3764-34555 83494 6868 5758 35777 7544 4 9578 9773 57 49 74-5758 -548799-5868 -48457-445559 593 337 764 8799 567 3 333 356 384 3368 3337-857 -89-765468 -73888-6558 6434 594 39 5 5 5 5 6943 68 634 673 633-46579 -44478-493 -39448-36446 5 85989 694 5589 3353 4 485 855 348 43-688 -574757-54447 -553-47857 7539 5875 893 33 75866 3 3877 336 375 3357 34774-886546 -845698-885 -74889-696 8858 33 94565 75466 5478 4 4 935 9635 9 65 58-64448 -66537-585396 -555-5985 3949 858 6485 3334 4 3 34984 3555 3694 379 38734-93663 -895484-84994 -79867-73979 54634 55 457 474 345656 676 6734 67375 6755 67779-843 -7584-6656 -5669-4486 366755 34943 3336 83534 5 3 3 336488 3373 33774 33879 3439-38 -9886-9358 -8833-893 638465 58955 537463 4863 4497 6747 675489 6779 679557 68376-9883 -8995-8738 -739-5858 833 76775 7844 64447 57493 696986 69839 763 774 7636-5999 -7559-883 -9769-85549

88 A I Shw d R A Bo Fom th ct o 8 9 d 7 w comt th g th do momt of od tttc d th c fo 6 d 55 5 Th c coffct 5 d 5 qd fo th BLUE of μ d σ ct c otd d o th comtto of th m c d coc of od tttc fom EG dtto T d 3 od th coffct of th BLUE of μ d σ ct fo 6 / to d 555 I T 4 w comt th c d coc of th BLUE g 53 d w ot tht fo m Vμˆ c c d dc Othw V σˆ dc c d c dc Ao o ˆ μ ˆ σ dc c d dc Nmc tto I od to tt th f of th fc ocd dcd th cto w cod th m Em Lt cod th c wh th comot h f tm whch foow EG dtto wth So tht w o th foowg mtd od f tm fom EG μ σ 684 88 487 85 4964 Thfo th odd f tm 85 487 684 88 4964 H th fo th odd dt wth 5 5 α d V d o 8 9 d 7 Th coffct 5 d 5 td T d 3 ct Thfo th BLUE of μ d σ comtd to ˆ μ 99 d ˆ σ 58593 Th coodg c d coc of μˆ d σˆ comtd to V ˆ μ 756σ V ˆ σ 6647σ d o ˆ μ ˆ σ 85548σ Lt cod th t oto m ζ E Y μ 75 σ Hd w d & ζ Y th m m W wod h & ζ 96 d tdd o SE ζ & 44768 Th BLUE of ζ ˆ ζ ˆ μ 75 ˆ σ 95 Th tdd o of ζˆ comtd to SEζˆ 377 Thfo th BLUE fom tt th th m m th of th tdd o fo comt m Em od th o dt t wth 5 d 3 thfo th cod dt 85 487 684

Od tttc fom ottd Gmm dtto 89 Fom t d 3 th BLUE of μ d σ comtd to ˆ μ 94499 d ˆ σ 49543 Th coodg c d coc of μˆ d σˆ comtd to V ˆ μ 49σ V ˆ σ 337σ d o ˆ μ ˆ σ 5394σ Lt cod th t oto m ζ E Y μ 75 σ Hd w d & ζ Y th m m W wod h & ζ 46 d tdd o SE ζ & 48338 Th BLUE of ζ ˆ ζ ˆ μ 75 ˆ σ 836 Th tdd o of ζˆ comtd to SEζˆ 37469 Thfo th BLUE fom tt th th m m th of th tdd o fo cod m 6 oco d omo I th wo th t of tmto of d o om od od tttc fom EG dtto h otd I ddto th BLUE of μ d σ otd Fom T 3 d 4 w cocd th foowg ot A w c fom T th MSE of ~ th tht of ˆ d ˆ M fo ~ comt d cod m codd Ao w ot tht MSE of ˆ d ˆ M c c d dc c Th coffct of th BLUE td T d 3 chcd th codto d 3 Fom T 4 w ot tht fo m - V μˆ c c d dc - V σˆ dc c d c dc - o ˆ μ ˆ σ dc c d dc 4 Fom Em d w tht th tdd o of BLUE th tht of th m m I coco w c tht ~ fom tt th ˆ d ˆ M fo choc of d codd Ao th BLUE of μ d σ fom tt th th m m th of tdd o fo comt d cod m

9 A I Shw d R A Bo Rfc [] A I Shw d R A Bo B d o-b tmto o th ottd gmm dtto Ad Mthmtc Scc 5 8 5-53 [] A I Shw d R A Bo t chctzto of th ottd gmm dtto Acctd fo cto JATA 8c [3] A I Shw d R A Bo hctzto fom ottd gmm dtto d o cod Acctd fo cto JSTA o 7 8 [4] B Aod N Bh d H N Ng A Ft o Od Stttc W Nw Yo 99 [5] D R Wgo Mmm hood tmto of B XII dtto mt d t II cog Mcocto R 339 993 5-57 [6] H A Dd Od Stttc Scod Edto W Nw Yo 98 [7] H A Dd d H N Ng Od Stttc Thd Edto W Nw J 3 [8] J G S d W J Pdgtt Som ot of cd B t X dtto Jo of Stttc Pg d Ifc 8 5 7-8 [9] K S St A hd d N Bh A ogthmc-dcg dtto Ifc fo o-mt d two-mt c Pocdg of th Sth Mtg of SAMS 4-6 [] M A W Mhmod K S St d S M Am Od tttc fom W dtto d octd fc omtto Stttc & Dt A 4 3 49-63 [] M Z Rq d M Ahh Etmto of th octo d c mt of gzd ot dtto d o od tttc J Sttt omt Sm 69 9-3 [] M Z Rq Od tttc fom th B t X mod omt Mth Ac 364 998 - [3] N Bh d A oh Od Stttc d Ifc Etmto Mthod Acdmc P S Dgo 99

Od tttc fom ottd Gmm dtto 9 [4] N Bh d P S h Log-gmm od tttc d tmto of mt I Bh N d Ro R Ed Hdoo of Stttc Vo 7 E Scc Amtdm 998 6-83 [5] N Bh d S Pth Bt d tmto of octo d c mt of th hf ogtc dtto J Sttt omt Sm 5 986 93-4 [6] R D Gt d D Kd Gzd ot dtto Nw Zd J Sttt 4 999 73-88 Rcd J 8