ner_tags: O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Survey O B-TextGarbage I-TextGarbage B-URL O O O O O O O B-Survey O O O O O B-Survey O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Telescope O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: instead. In addition, some R 50 of SLSN hosts are provided in Lunnan et al. ( 2015 ). Otherwise, we use the the half-light radius within the SDSS catalog 13 13 http://www.sdss3.org/ by matching the SN host galaxies with SDSS galaxies within 3′′. In the SDSS catalog, the half-light radius is estimated from the r -band Petrosian half-light radius R 50,petro and the Petrosian 90% radius R 50,petro following R 50 = R 50,petro /(1 – 8 × 10 −6 ( R 90,petro / R 50,petro ) 8.47 ) (Graham et al. 2005 ). We also update the offset parameters from the literatures. Lunnan et al. ( 2015 ) calculated the projected R off from HST images for SLSNe. Anderson et al. ( 2016 ) reported the projected R off from SNe II to the nearest H ii regions. Kelly Kirshner ( 2012 ) provided the deprojected r off = R off / R 50 for SNe II and SNe Ibc. Although projected offsets and deprojected offsets are statistically consistent, they are different for specific objects. Since most offsets in the literature and catalogs are projected, we use these deprojected offsets only when projected offsets are not available. We also convert them to r off when R 50 is available in our catalog. The sample sizes for SLSNe, SNe Ibc, SNe II, and SNe Ia with host galaxy properties are 107, 900, 4251, and 7221, respectively. To have a consistent z range as the FRB sample, we screen the samples with z 1. This gives sample sizes of 95, 874, 2829, and 7003 for the four types, respectively. Most SNe Ibc, SNe II, and SNe Ia have z 1. The excluded objects are mostly those without redshift information. The sample size for each parameter for each type of stellar transient is presented in Table 2 . 3. Multivariate Comparison We would like to perform a comparative study of the host galaxy properties between FRBs and other stellar transients. Since multiple parameters are involved, multivariate analysis methods are needed. We perform two tests. First, taking all the FRBs as a whole sample, we compare it with other samples using the multivariate Kolmogorov–Smirnov (KS) test. Second, we also compare each individual FRB with other samples to see which type it most likely belongs to. For easy understanding, we use the naive Bayes method to test individual FRBs in the FRB sample to see how they may be consistent with various types of stellar transients. We try to classify LGRBs, SLSNe, SNe Ib/Ic, SNe II, SNe Ia, and SGRBs with their host galaxy properties using the naive Bayes method and then apply the same method to each FRB. Galaxies evolve with redshift, and the FRBs in our sample all have redshift z 1, so to enable a direct comparison, in the following we compare the FRBs with the transients with redshifts z 1 only. 3.1. Multivariate KS Test 3.1.1. Method The classical KS test compares the cumulative distribution function (CDF) of two distributions P ( x ) and P ( x ′), which could be one data sample and one model sample, or two data samples. The largest distance between the two CDFs is defined as D