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Paper text:
studying the optical transients ( ot ) of grbs is one of the major tasks of the swift satellite .
however , a significant fraction of grbs does not show detectable ot fluences .
it means in the number of cases one measured only an upper limit instead of a real event . treating only those bursts exceeding the limit of detection with a high certainty one
never can be sure how representative is the sample obtained in this way for the whole population of the grbs detected by the bat .
survival analysis offers a solution to overcome this difficulty .
if one knows a lower / upper bound for the measured data instead of concrete values they are considered as censored . in mathematical terms let we have two independent stochastic variables : @xmath4 $ ] .
if @xmath5 then @xmath6 is detected , otherwise @xmath7 which is an upper bound for @xmath6 in this way .
a sample representing these observations consists of a mixture of real and censored ( upper bound ) data . in our case
@xmath6 represents the brightness of an ot and @xmath7 an upper bound for the non real ( censored ) detection .
kaplan and meier  @xcite showed it is possible to estimate the true distribution of a sample even in the case of censorship ( for the astronomical context see feigelson and nelson  @xcite ) .
according to kaplan and meier the following estimate gives the survival function :    @xmath8    where @xmath9 is is the probability distribution function and    @xmath10^{\delta_i}\ ] ]    @xmath11 means the number of data , @xmath12 equals 1 at non censored data and 0 in the censored case .
it means the estimated survival function jumps at real data and remains constant in the case of censoring .
until preparing this work swift observed 144 events and detected ot in 31 cases .
73 bursts have only upper limits and the rest has no optical data . before making the survival analysis the effect of the foreground extinction
has to be removed .
we used the data of schlegel et al .  @xcite . performing the analysis we derived the true cumulative distribution of the v visual magnitudes which can be compared with that of the measured optical events , as displayed in figure [ surv1 ] .
it is worth mentioning that a homogeneous spatial distribution in euclidean space would resulted in a coefficient of 0.6 instead of 0.234 , as obtained .
this result gives an important constraint on estimating the spatial distribution of ot events .
the bat on the swift satellite measured the fluence , peak flux and @xmath3 duration in the 15 - 150 kev energy range .
we computed the pearson linear correlation between the extinction - corrected @xmath0 visual magnitude of the ots and the logarithms of quantities mentioned .
we obtained significant correlation only with the logarithmic peak flux at the 99.7% level ( see fig .
[ surv2 ] ) .
in a systematic search of the ots at grbs the swift satellite determined only an upper limit of the apparent brightness in a significant fraction of cases . combining these upper limits with the really measured ot brightness we obtained a sample well suited to survival analysis . performing a kaplan - meier product limit estimation we obtained an unbiased cumulative distribution of the @xmath0 visual brightness . 
 the @xmath1 logarithmic cumulative distribution can be well fitted with a linear function of @xmath0 in the form of @xmath2 . 
 we studied the dependence of @xmath0 on the gamma ray properties of the bursts . 
 we tested the dependence on the fluence , @xmath3 duration and peak flux . 
 we found a dependence on the peak flux on the 99.7% significance level .