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1 . Iroduco Probblsc oe-moh forecs gudce s mde b 50 esemble members mproved b Model Oupu scs (MO). scl equo s mde b usg hdcs d d observo d. We selec some prmeers for modfg forecs o use mulple regresso formul. Probbles re mde b he use of Guss-dsrbuo mehod d modfed forecs d. Relbl dgrm d Brer kll core (B), ROC curves re mde b hdcs d whch hve bee clculed for he ps 0 ers (98-00). These smple source progrms re wre FORTRA 90 code. These progrms clude smple mulple regresso progrm, mke-probbl progrm, d mke-verfco score progrm. mple pu fles re prepred, whch he re ll e form, d he re es o chge. Chper descrbes how o eecue progrms d dels of pu fles. Techcl descrpo of ech progrm s wre Chper 3.. User's Isrucos. Eecug progrm. Decompresso Dowlod fle s smple_src.r.gz. I s rchved, so move dowlod folder d eecue he followg commd. guzp smple_src.r.gz r -vf smple_src.r Decompresso dgrm smpler_src (source fles d mkefles) b (br fles) --- sh (smple shells) --- pu (smple pu fles) b. mke Move decompresso folder, eer mke commd. (mke cle) mke Afer hs commd, 3 progrms(clc_mul.ee, mke_prob.ee, d mke_ver.ee) re creed b deful. c. Eecug of progrms

2 Mul regresso progrm clc_mul.ee pu_fle. pu_fle. oupu. or fer move sh folder bsh clc_mul.sh pu_fle. forecs d (some prmeers)(eplg vrbles) pu_fle. observo d (objecve vrbles) oupu. chose prmeers d regresso coeffces, slope, sdrd sdrd devo of error. Mke-probbl progrm mke_prob.ee pu_fle. pu_fle. oupu. or fer move sh folder bsh mke_prob.sh pu_fle. forecs d (some prmeers) pu_fle. oupu of mul regresso progrm oupu. probbl des ech forecs Mke-verfco-score progrm mke_ver.ee pu_fle. pu_fle. oupu. or fer move sh folder bsh mke_prob.sh pu_fle. observo d pu_fle. oupu of mke-probbl progrm oupu. B, relbl dgrm, ROC curve. Ipu fles. Forecs d Colum epresses vlue of forecs prmeers ech forecs cse, row represes forecs cse. -- smple pu_fle.-- # pu vlue

3 smple ed -- b. observo d Ths fle defes observo vlue wh forecs d. The umber of observo d should be sme wh he umber of forecs. -- smple pu_fle.-- #vlue smple ed Techcl Descrpo 3. Mul regresso progrm We use sepwse mehod s seleco mehod hs progrm. Mul regresso formul s L b : objecve vr ble observo : he : regresso coeffces b : slope of mul regresso ( ) umber of eplg vr bles : eplg vr bles (forecs) To clcule regresso coeffces, mehod of les squres s used. Vrce clculo s doe wh ech vrble. j k ( X X )( X X ) k kj j

4 L L L L Ech regresso coeffce s clculed wh solvg hese orml equos. Geerl epresso, We clcule verse mr, d ge regresso coeffces. Eplg vrble of he lrges F-vlue s seleced s he frs fcor. Resdul sum of squres s e, regresso sum of squres s r, d s he umber of d. r r e F d e r The vrbles h hve he lrges F-vlue crese d he crese of F-vlue s more h.0 re seleced s secod or oher fcor., r L r,, e ( ) F d e, e, e, Whe o prmeers re seleced, hs process eds. Ad he e s sep-dow procedure. The prmeers h hve he lrges decrese of F-vlue seleced formul d he decrese of F-vlue s less h.0 re removed.

5 F e, e, e, ( ) d If he prmeers mulple regresso formul re o chged, hs progrm fshes, or f he prmeers re removed, sep-up mehod proceeds g. 3. Mke-probbl progrm Ths progrm mke probbl des from forecs d wh he use of Guss-dsrbuo mehod (00, ug). Ths mehod ssumes observos d forecss re d he error bewee forecss d observos re dsrbued lke ormlzed dsrbuo. ormlzed dsrbuo s follow, P ( ) : vlue ep ( ) πσ σ : forecs P : probbl σ vlue ech vlue : Resdul sum of squres Resdul sums of squres re clculed b he follow relo. σ σ s σ σ s ll sum of squre (vrce of observo), modfed forecs). σ s s regresso sum of squre (vrce of 3.3 Mke-verfco-score progrm Ths progrm geeres Brer kll core, Relbl dgrm, ROC curve.. Brer kll core Brer kll core s defed s followg equo, B ( p v )

6 : he p : probbl v : br umber of forecss of forecs probbl of observo ( f he eve occurs, v s,f o,v s 0) Chge bove formul o represe ech probbl. B : frequec M : frequec ( p ) M ( p 0) ( M ) of forecs probbl of pperce ech probbl Epdg bove equo s B p M M M M M Rgh frs erm s defed s relbl skll, hs s brel p M Rgh secod erm s resoluo skll bres m M m M m Geerll B, brel, d bres re redefed s he followg equos, B B B B B brel Brel B bres Bres buc B s clculed ssumg he clmologcl forecs probbl. o f B s posve vlue, he forecs s useful, f B s egve, he forecs s'.

7 b. Relbl dgrm Relbl dgrm s represeed s he followg mge. X-s s forecs probbl (%/00), d -s s observo frequec (%/00). Red-le s relbl dgrm. Ths mes wheher occurrece re gs forecs probbles s sme. If red le slopes 45-degree, s possble o s h hs forecs s relble. c. ROC curve ROC curve s represeed s he followg mge. X-s s flse lrm re (%), -s s h re (%). Clcule forecs frequec d occurrece re whch re more h ech probbl. (see ble )

8 Tble. Mr of ech frequec whch s more h P. (Yes: eve occurs, o: o occur) observo forecs Yes o Yes A B o C D Ech frequec s clculed s A C 0 0 : umber M B M D 0 ( M ) ( M ) 0 of ech probbl M : occurece umber : forecs umber ech probbl ech probbl H re d flse lrm re s defed s A hr A C B fr B D hr : h fr : flse lrm re re more h ech probbll more h ech probbll

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