One-sided asymptotic inferences for a proportion.

Two-sided asymptotic confidence intervals for an unknown proportion p have been the subject of a great deal of literature. Surprisingly, there are very few papers devoted, like this article, to the case of one tail, despite its great importance in practice and the fact that its behavior is usually different from that of the case with two tails. This paper evaluates 47 methods and concludes that (1) the optimal method is the classic Wilson method with a correction for continuity and (2) a simpler option, almost as good as the first, is the new adjusted Wald method (Wald's classic method applied to the data increased in the values proposed by Borkowf: adding a single imaginary failure or success).

Are luminous radio-loud active galactic nuclei triggered by galaxy interactions?

We present the results of a comparison between the optical morphologies of a complete sample of 46 southern 2 Jy radio galaxies at intermediate redshifts (0.05 < z < 0.7) and those of two control samples of quiescent early-type galaxies: 55 ellipticals at redshifts z ≤ 0.01 from the Observations of Bright Ellipticals at Yale (OBEY) survey, and 107 early-type galaxies at redshifts 0.2 < z < 0.7 in the Extended Groth Strip (EGS). Based on these comparisons, we discuss the role of galaxy interactions in the triggering of powerful radio galaxies (PRGs). We find that a significant fraction of quiescent ellipticals at low and intermediate redshifts show evidence for disturbed morphologies at relatively high surface brightness levels, which are likely the result of past or on-going galaxy interactions. However, the morphological features detected in the galaxy hosts of the PRGs (e.g. tidal tails, shells, bridges, etc.) are up to 2 mag brighter than those present in their quiescent counterparts. Indeed, if we consider the same surface brightness limits, the fraction of disturbed morphologies is considerably smaller in the quiescent population (53 per cent at z < 0.2 and 48 per cent at 0.2 ≤ z < 0.7) than in the PRGs (93 per cent at z < 0.2 and 95 per cent at 0.2 ≤ z < 0.7 considering strong-line radio galaxies only). This supports a scenario in which PRGs represent a fleeting active phase of a subset of the elliptical galaxies that have recently undergone mergers/interactions. However, we demonstrate that only a small proportion (≲20 per cent) of disturbed early-type galaxies are capable of hosting powerful radio sources.