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Several claims have been put forward that an essential fraction oflong-duration BATSE gamma-ray bursts should lie at redshifts larger than 5.This point-of-view follows from the natural assumption that fainter objectsshould, on average, lie at larger redshifts. However, redshifts larger than 5are rare for bursts observed by Swift. The purpose of this article is to showthat the most distant bursts in general need not be the faintest ones. Wederive the cosmological relationships between the observed and emittedquantities, and arrive at a prediction that is tested on the ensembles ofBATSE, Swift and Fermi bursts. This analysis is independent on the assumedcosmology, on the observational biases, as well as on any gamma-ray burstmodel. We arrive to the conclusion that apparently fainter bursts need not, ingeneral, lie at large redshifts. Such a behaviour is possible, when theluminosities (or emitted energies) in a sample of bursts increase more than thedimming of the observed values with redshift. In such a case dP(z)/dz > 0 canhold, where P(z) is either the peak-flux or the fluence. This also means thatthe hundreds of faint, long-duration BATSE bursts need not lie at highredshifts, and that the observed redshift distribution of long Swift burstsmight actually represent the actual distribution.

Cosmological effects on the observed flux and fluence distributions of gamma-ray bursts