Generalized Entropy of Kumaraswamy Distribution Based on Order Statistics

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1 Geeaed Eop o Kumaawam Dbuo Baed o Ode Sac Ra Na M.A.K Bag 2 Javd Ga Da 3 Reeach Schoa Depame o Sac Uve o Kahm Saga Ida 2 Aocae Poeo Depame o Sac Uve o Kahm Saga Ida 3 Depame o Mahemac Iamc Uve o Scece ad Techoog Kahm ABSTRACT Iomao heo age coceaed o ucea meaueme o vueabe o pa ad edua eop uco. Ma pocedue uch a uvva uco ad he e eg pobem have bee pu owad o compae he agg poce o aocaed compoe ad ued o deve he emag eme uceae. I h pape eop o ode ac edua eop ad pa edua eop uco baed o Kumaawam KS dbuo ae popoed. Pa edua eop uco howeve ubeced o uppe boud compuao ad eu ae aaed. Kewod- Eop Ode Sac Pa Eop Redua Eop I INTRODUCTON Chaaceao pobem ae age aeced b ode ac. Thee pobem make mmee ue o aaca oo o mahemac ad ae ocaed o he bodee ha ex bewee ac ad pobab. Thee ae umeou oucome o chaaceao o pobab o ode ac. o emed evew oe ma ce chaaceao eu vew o cumuave edua eop ad o-addve eop o ode ac [] ad [2]. The dbuo heo o ode ac ha bee geea depced a ew moogaph compoed b excepoa aa ad hee ae vaou pape commed o he hpohe o ode ac ad appcao ad ao ampoc oucome ad mpcao gh o ode ac. Oe ma meo ode ac popee o he Lomax appopao [3] ad Expoeaed Paeo dbuo [4]. Ode ac have bee ued a a pa o a exeve vae o ue cudg m aca emao decao o aomae goode o e examao o ceoed ampe. Daa popee o ode ac vew o Shao eop [5] ad Kuback-Lebe [7] meaue ug pobab ega aomao have bee examed b Ebahm e.a [6]. Two paamec geeaed eop he Vema 2479 P a g e

2 eop [8] [9] ad coceaed coex wh ode ac. Thee ae vaou pcpe o Shao' eop [5] whch ae avaabe he eaue o omao heo. Deo. A adom vaabe wh aage o vaue ad o have he kumaawam dbuo om ow owad abbevaed a KS he pobab de uco pd o KS dbuo Whee ad ae he hape o egave hape paamee. The cumuave dbuo uco cd ad he uvva uco o KS dbuo gve b 2 ad 3 The KS dbuo a couou pobab dbuo wh boh ed bouded. I udamea he ame a he bea dbuo ad ca expec a kg va vae o hape ad be ued o how umeou aba pocedue ad uceae. I ha bee ued o Impoved po emao [] Caca ad Baea emao [] Pedco baed o ogoma ecod vaue [2]. Deo2. A mpeave dea omao heo oduced b Shao 8 he oo o eop. I aume a udamea pa a a meaue o cac ad ucea dee ed uch a maea cece eecoc ad egeeg o decbe ma chaoc em. e popoed a meaue o ucea o a o egave adom vaabe wh a pobab dbuo havg a aboue couou cumuave dbuo uco cd ucea meaue deed a og d E og Popee o Eop Baed o Ode Sac Le 2 be a adom ampe om a dbuo... ac o h ampe deed b he aageme o V V2... V. The de o V 2... ad pobab dbuo uco pd. The he bac. 4 wh de uco The ode om he mae o he age b V V P a g e

3 248 P a g e Now e U U U... 2 be a adom ampe om U wh he ode ac The de o B 6 whee B The eop o he bea dbuo og Whee ad dw w d w og og g E V 7 Ug he ubuo equao 7 ad... 2 he pobab ega aomao he eope o ode ac ae obaed a: o evauag V we have ad he expecao em 7 obaed a oow: og og E g 8 Ug equao 8 equao 7 we oba og V

4 o he ampe mmum og. V og og o he ampe maxmum og. V og og 2 Whee he Eue coa. II RESIDUAL ENTROP O ORDER STATISTICS I he eve ha a pa kow o have uvved o age a ha po Shao' Eop ' appopae ode o meaue he ucea o he emag eme o he em. Theeoe Ebahm ad Peee [3] chaaceed he edua eop whch meaue he ucea uch cae. o a adom eme o o em a me he edua eop deed a whee og d he pd o he vaabe ad gve b og d P a g e

5 2483 P a g e Whee he uvva uco o. The edua eop o eme gve b 3. Aaogou o expeo 3 he edua eop o ode ac gve b d og 4 I cea ha he edua eop o ode ac obaed b ubug he ug pobab ega aomao equao 4 ad ug equao 3 ad 6 we have og og og d 5 whee og og d 2 6 Ug equao 6 equao 5 we ge og og og III PAST ENTROP I eaoabe o aume ha umeou ccumace ucea ' ea deed wh uue e ca kewe aude o pa o ace deoe he eme o a em o o vg ogam a me a em obeved o a cea peaged me obeved o be dow he he ucea o he

6 2484 P a g e em e ee.e. o whch mome ha aed. I vew o he hough Dceceo ad Logobad [4] have coempaed he pa eop ove ad chaaceed a o d x og 7 whee he cumuave dbuo uco. Aaogou o expeo 7 he pa edua eop o he h ode ac deed a o d og 8 I cea ha he pa edua eop o h ode ac obaed b ubug ad ug pobab ega aomao equao 8 ad ug equao 3 a we have d o og og og 9 d og og 2 Theeoe ug equao 2 equao 9 we ge og og og o 2 A Uppe Boud o he Pa Eop o Ode Sac We pee he uppe boud o he pa eop o ode ac ude he codo ha

7 2485 P a g e d og d og og o og. We oba 22 Subug equao 22 ad ug equao 2 ad 6 ad pobab ega aomao we oba og og 2 og og 2 Subug equao 22 ad ug equao 2 ad 6 ad pobab ega aomao we oba og og 2

8 og og 2 IV CONCLUSION we have peeed ad codeed he eop o ode ac baed o kumaawam dbuo. We have popoed ome pema eu o edua eop pa edua eop uco o KS dbuo. We ao aae he eu o uppe boud o he pa edua eop uco. The hpoheca oucome go h pape ca be ued o go uhe ad vegae he appcao dee ode whee he ucea ex. REERENCES Thapa R.Taea.C.25. Chaaceao eu baed o o-addve eop o ode ac. Eeve Phca Oma Kam 26. O Damc Cumuave Redua Eop o Ode Sac Sac Appcao & pobab Javd D. Bade A-aha. 26. O Some Ode Sac Popee ohe Mukheee-Iam dbuo J. Mah. Compu. Sc Behbooda J. Tahmaeb. 28. Some Popee o Eop o he Expoea Paeo Dbuo baed o Ode Sac. Mahemaca Exeo Shao C. E A mahemaca heo o commucao. Be Sem Techca Joua ad Ebahm N. e.a 24. Iomao popee o ode ac ad pacg. IEEE Ta. Iomao Theo Kuback.S Iomao Theo ad Sac. We New ok. 8 Thapa R.Taea.C. 22 Geeaed eop o ode ac. Apped Mahemac Vema R.S. 966 Geeaao o Re Eop o Ode α. Joua o Mahemaca Scece Vo. pp P a g e

9 Au J. Lemoe2 Impoved po emao o he Kumaawam dbuo Saca Compuao ad Smuao Sukhdev S. ogeh M. 27. Baea emao ad pedco baed o ogoma ecod vaue. Joua o Apped pobab Kııaa. & Nada M. 26. Emao ad pedco o he Kumaawam dbuo baed o ecod vaue ad e ecod me. Saca Compuao ad Smuao Ebahm N. ad Peee. 995 New paa odeg o uvva uco baed o he oo o ucea. Joua o Apped pobab Ceceo A.D. ad Logobad M. 24 A meaue o dcmao bewee pa e me dbuo Sa.Pob.Le P a g e