內(nèi)容講義origin7 0軟件刪g01fec

g01–SimpleCalculationsonStatisticalData g01fec

nagdeviatesbeta(g01fec)

Purpose

nagdeviatesbeta(g01fec)returnsthedeviateassociatedwiththegivenlowertailprobabilityofthebetadistribution.

Speci?cation

#include<nag.h>#include<nagg01.h>

doublenag_deviates_beta(doublep,doublea,doubleb,doubletol,NagError*fail)

Description

Thedeviate,βp,associatedwiththelowertailprobability,p,ofthebetadistributionwithparametersaandbisde?nedasthesolutionto

abZ

Γ(+) βp

0

P(B≤βp:a,b)=p=Γ(a)Γ(b)

Ba?1

(1?B)b?1

dB 0≤βp≤1;a,b>0.

Thealgorithmisamodi?edversionoftheNewton–Raphsonmethod,followingcloselythatofCran

etal(1977).

Aninitialapproximation,β0,toβpisfound(seeCranetal1977),andtheNewton–Raphsonition

f(βi?1)

βi=βi?1?f0(β

i?1)

wheref(β)=P(B≤β:a,b)?pisused,withmodi?cationstoensurethatβremainsintherange(0,1).

Parameters

p

a

b

tol

fail

Input:theprobability,p,fromtherequiredbetadistribution.Constraint:0.0≤p≤1.0.

Input:the?rstparameter,a,oftherequiredbetadistribution.Constraint:0.0<a≤106.

Input:thesecondparameter,b,oftherequiredbetadistribution.Constraint:0.0<b≤106.

Input:therelativeaccuracyrequiredbytheuserintheresult.Ifnagdeviatesbetaisenteredwithtolgreaterthanorequalto1.0orlessthan10timesthemachineprecision(seenagmachineprecision(X02AJC)),thenthevalueof10timesmachineprecisionisusedinstead.

TheNAGerrorparameter,seetheEssentialIntroductiontotheNAGCLibrary.

[NP3275/5/pdf] 3.g01fec.1

nagdeviatesbeta NAGCLibraryManual

ErrorIndicationsandWarnings

OnanyoftheerrorconditionslistedbelowexceptNERESNOTACCandNESOLNOTCONV

nagdeviatesbetareturns0.0.

NEREALARGLT

Onentry,pmustnotbelessthan0.0:p=hvaluei.

NEREALARGGT

Onentry,pmustnotbegreaterthan1.0:p=hvaluei.Onentry,amustnotbegreaterthan106:a=hvaluei.Onentry,bmustnotbegreaterthan106:b=hvaluei.

NEREALARGLE

Onentry,amustnotbelessthanorequalto0.0:a=hvaluei.Onentry,bmustnotbelessthanorequalto0.0:b=hvaluei.

NERESNOTACC

Therequestedaccuracyhasnotbeenachieved.Usealargervalueoftol.

Thereisdoubtconcerningtheaccuracyofthecomputedresult.100itionsoftheNewton-Raphsonmethodhavebeenperformedwithoutsatisfyingtheaccuracycriterion(seeSection6.1).Theresultshouldbeareasonableapproximationofthesolution.

NESOLNOTCONV

Thesolutionhasfailedtoconverge.

However,theresultshouldbeareasonableapproximation.

Requestedaccuracynotachievedwhencalculatingbetaprobability.Theusershouldtrysettingtollarger.

FurtherComments

Thetimetakenbythefunctionwilldependontheshapeofthedistribution.Forhighlyskeweddistributionswithoneofthevaluesofa,blargeandtheothersmall,series(2)willtakelongertoconvergethanfordistributionswhicharemoresymmetric.

Accuracy

Therequiredprecision,givenbytol,shouldbeachievedinmostcircumstances.

References

CranGW,MartinKJandThomasGE(1977)Inverseofthe pleteBetafunctionratio

Appl.Stat.26AlgorithmAS109111–114.

HastingsNAJandPeacockJB(1975)StatisticalDistributionsButterworth.

SeeAlso

nagprobbetadist(g01eec)

Example

Lowertailprobabilitiesarereadforseveralbetadistributions,andthecorrespondingdeviatescalculatedandprinted,untilofdataisreached.

3.g01fec.2 [NP3275/5/pdf]

g01–SimpleCalculationsonStatisticalData g01fec

ProgramText

/*nag_deviates_beta(g01fec)ExampleProgram

*

Copyright1990NumericalAlgorithmsGroup.

*

Mark2revised,1992.

*/

#include<nag.h>#include<stdio.h>#include<nag_stdlib.h>#include<nagg01.h>

main()

{

doublea,b,p,tol,x;staticNagErrorfail;

/* Skipheadingindatafile*/Vscanf("%*[^\n]");

printf("g01fecExampleProgramResults\n");

printf("Probability A B Deviate\n\n");while(scanf("%lf%lf%lf",&p,&a,&b)!=EOF)

{

tol=0.0;

x=g01fec(p,a,b,tol,&fail);if(fail.code==NE_NOERROR)

Vprintf("%9.4f%10.3f%10.3f%10.4f\n",p,a,b,x);else

Vprintf("%9.4f%10.3f%10.3f%10.4f\nNote:%s\n",p,a,b,x,fail.message);

}

exit(EXIT_SUCCESS);

}

ProgramData

g01fecExampleProgramData0