Date: Fri, 7 Oct 2022 09:05:51 +0000 (UTC) Message-ID: <1523178672.8193.1665133551852@localhost> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_8192_386823816.1665133551851" ------=_Part_8192_386823816.1665133551851 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Estimate of the elapsed period t

# Estimate of the elapsed period t

We can estimate the period t tha= t has elapsed if we know =CE=BB and the number of events a that have = occurred in time t. The mathematics are exactly the same as the es= timate for =CE=BB. The reader = may like to verify that, by using a prior of p(t) =3D 1/ t we obtain a posterior distribution: t<= /em> =3D Gamma(1/=CE=BB,=CE=B1) which is the same result we would obtain if we were trying to predict fo= rward (i.e. determine a distribution of variability of) the time required t= o observe a events given =CE=BB =3D 1/=CE=B2. Also, if we can reasonably describe our prior belief = of the elapsed period t with a Gamma(b,a) distribution, the posterior is given by a Gamma(b/ (1 + b=CE=BB),=CE=B1 + a) distribution.

Note that here we use the parameterizatio= n Gamma(b, a)  where <= em>b =3D Scale and a =3D Shape,=  whereas in other sections of ModelAssist we might report a three= -parameter version of the Gamma distribution.

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