Calculating Integral using R

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I need to calculate this simple integral below:

Thisisthestandardnormalizedquantilfunction,whereweknowfromthefrontthat,q_0.5(z)=0,forexample.

Thatis,foreachtheta(percentile)itgivesmeanumberinstandardizednormaldensity.Thetagoesfrom0to1.

IgeneratedthisfunctioninRandorganizeditintoanarray:

thau=1:99/100qnorm(thau,0,1)matrix=matrix(0,99,2)matrix[,1]=thaumatrix[,2]=qnorm(thau,0,1)colnames(mattrix)=c("theta","q(z)")

How do I calculate this interal in R, given that I already have the function q ??

I thought of calculating the two integrals using the basic rules of integral. Can I do this for this function? I think I can.

Would it be correct? For me it gave -1.170456 .

I would love your help.

Thank you.

    
asked by anonymous 26.10.2016 / 18:22

1 answer

2

According to what I understood about your problem, I believe it can not be resolved. Note that

Thus,theintegralisundefinedbetween0and0.5.Itdivergesinthisinterval.Itwouldbelikeintegrating1/xbetween0and1,forexample.

Youraccountcomesinaresultbecauseitisnotcorrect.Generalizingyourresult,itisequivalentto

Ifwesupposethatf(x)=1,accordingtoyourformula,wehave

Butthisisanindeterminacybecausewehave0/0.Therefore,therewouldbenosolutiontothisproblem.Butsufficeittoseethatiff(x)=1,wehave

which is a clearly defined integral in the interval in which we are interested. So the derivation of your result is not true, and your answer is not -1.170456 . In fact, your integral is divergent and your problem has no solution.

It would be interesting to go back to the original problem and see where this integral came from to understand why it was calculated.

    
26.10.2016 / 21:09
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