A Simple Representation of the Weighted Non-Central Chi-Square Distribution

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SSN: 9-875 raoa Joura o ovav Rarch Scc Whr a o gav gr uco o h r o ro orr a grg a Tchoogy (A S 97: 7 Cr rgaao) Vo u 9 Sbr F h gra hyrgorc uco h hyrboc co uco h o B h ar or urca vauao uro w r o y h u h o h wgh o-cra ch-quar rbuo wh υ gr o ro Sco w r o rqur ca uco a oao o aca urag h ar Sco w rov ha h o h rbuo wh υ gr o ro ca b rr a h u o o a v r ach ha a or ro ur roo ba o h o Sruv a B uco For h v r w oow h a argu a ha gv Ara a Barc (8) Tha our roo ba o o ror o o B uco o h r a o Ho orua or h h -rvav o a coo uco SM SPCA FUNCTNS AND NTATNS Th oowg ar o ca uco ha w b u our rvao - h gaa ucao uco a a - J () h B uco o h r o orr a a J R a - () h o B uco o h r o orr a a arcuar R a () R - H h Sruv uco o h r o orr whch va or a a a H R () () () 5- h o Sruv uco o h r o orr whch va or a a a R 6- Th rvav orua o h o Sruv uco a R (5) (6) Coyrgh o JRST wwwrco 979

SSN: 9-875 raoa Joura o ovav Rarch Scc 7-Th rao bw h o Sruv uco gr gv by grg a Tchoogy (A S 97: 7 Cr rgaao) Vo u 9 Sbr a h o B uco () or o-gav R h oub acora uco a a 8- o v h ara hyrboc co uco a a 9- h v o For or a abou h abov ca uco Arw (99) A SMP FRM F TH PDF F h co w rov ha h o h wgh o-cra ch-quar rbuo wh υ gr o ro ha a or ro Th ro w b gv h oowg hor Th Ma Thor Th robaby y uco o h wgh o-cra ch-quar rbuo wh gr o ro gv by: whr h A ( ) (7) (8) (9) () () Coyrgh o JRST wwwrco 98

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SSN: 9-875 raoa Joura o ovav Rarch Scc grg a Tchoogy (A S 97: 7 Cr rgaao) Vo u 9 Sbr Coyrgh o JRST wwwrco 98 ) (6 Ug h rvav orua o h o Sruv uco (6) wh a w g Hc quao (6) a h or ) (7 b o = (7) w g ) (8 Ug (7) wh a w g (9) Cor h oowg orua o h o B uco o h r o orr gv Ka (6) ) ( C Tag = a () w g C Subug (9) a h (8) w g h ru () b v = (7) w g h ru () For u (6) w g

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SSN: 9-875 raoa Joura o ovav Rarch Scc grg a Tchoogy (A S 97: 7 Cr rgaao) Vo u 9 Sbr Coyrgh o JRST wwwrco 985 RFRNCS [] Ara S a Barc A "Pror o h Probaby Dy Fuco o h No-Cra Ch-Squar Drbuo" Joura o Mahaca Aay a Acao 6 95-8 [] Arw C "Sca Fuco o Mahac or gr" Sco o McGraw-H c Nw Yor 99 [] hry A brah S A a Ab-a Y Y"Corbuo o h Wgh No-Cra Ch-Squar Drbuo" Th gya Saca Joura Ju u o Saca Su a Rarch Caro Uvry gy [] Grau D " Mo o h Ubaac No-Cra Ch-Squar Drbuo" Sac a Probaby r 79 6-67 9 [5] Ka H "Corbuo o h Thory o h No-Cra Ch-Squar Drbuo" raoa Corc o Scc Coug a Vga Nvaa 6 APPNDX Th roo o (6) a (7) gv hry a () a oow Ug h oowg orua gv Ara a Barc (8) () a ug ao (5) () w g ) ( Ug () wh a w g ) ( car ha wh () ruc o h orua o h o h o-cra ch-quar rbuo gv Ka (6) a Ara & Barc (8) To y () cor h ora o B uco o h r o orr : gv Ara a Barc (8) ) ( Tag a h () ca b wr a oow: ) (5 Thror Aga ug h a quao w oba h a orua gv Ara a Barc (8) Now b v (5) w g

SSN: 9-875 raoa Joura o ovav Rarch Scc grg a Tchoogy (A S 97: 7 Cr rgaao) Vo u 9 Sbr Coyrgh o JRST wwwrco 986 Ug h rvav orua ( Ara a Barc (8)) (6) a a a or a a a Wh a a w g Ug () wh a w g h ru (6) Now b o (5) w g Ug (6) wh a a w g Ug () w g Ug () wh a w g Ug h oowg orua gv Ara a Barc (8) a W g h ru o (7)