Sharp MD-M11Z Manuel d'utilisateur télécharger pdf (Page 7)

1 The Monte Furl IVIu1h0d` uu Immductmu 69

l’(X:[) :p,;O.

Zn, 1 .

mi) mx g i) Ep,

with Fʼ(X ij [hc pmhahiliry 0IOUwm i. F i< the (cmxmlmixc; disuihmion. Lu 5

hc a uniform random number nu [O, 1], ruche theca random xariahlc X with X i if

FQ — 1] < { § FQ) is distributed according to F.

3.2.2.1 Inversion Method

'l'l1cim‘ersion method provides random samples z from u disuibxuion F by convert

ing uniform random numbers §. '1 his is simply alone by setting

;: min(.r\F(:r) 2 E) ~ F. (3.10)

[I` F i< <u·ict|y m0n0mn0u<, than z F *(E). For example, il` is [hcidsu·i—

button density function (pdf) no be genemmcd, hen msn Gnu nhc chumming function

1·'{1·) : fx ri! [fz], pick u uniform random number { on[(),1]zmdscl§ :

and Hnully invert this to Und random number z, which is then distributed according

no [Qu).

The same transfurnxwmion rules as for any density function apply also for a pdf.

Hence [hc gcucml qmtcgy is: Try m transform A gixcu pdf ff.) m another disbar

Huron f, <ouch [hat theca imcrw of [hc new cnunulmixc diurilamion F is cxplicirly

known. Then apply [hc method of micro<i<m and u·an<{m·m hack. Figure 5.2 llu<—

tmtc<thcmcthm1 of im Carson for [hc vmrnml (Gaussian; diswihmion

, 1 .¤ V.,

” mq

I .r d$(:r) dt m(t) T 1 4 cr. T . (3.11) . 2 V 2

Unfortunately, the Gaussian error function curfew] and hence cannot be inverted

in closed form. We will show how to generate Gaussian random numbers. even

without numerical inversion. further below.

lmm this procedure follows directly the natural and best forename for storing (also

umlrhdiumxsional; mhulatcd dam for random sampling in Mum Carlo appliqué

dom: Form theca iuxcrsc cmnulatixc disuihmion function F"(.r) (Lu.: [hc quintile

fuucriom and smirk hi< for .r uniformly spaced in IO, 1 |. Theca tack {mm a uniI`m·m

diswihmion 0u|O,l|am1 hud F'1(€) by imcrpolaricm iNathimholc.

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Sharp MD-M11Z Manuel d'utilisateur Page 7