Model as no. per unit redshift f(z) = No(1+z)**gamma, find MLE for No, gamma The Lyman alpha line rest wavelength is 1216A and the corresponding Lyman Limit is at rest frame 912A if the column density of NHI is greater than around 2x10**17 /cm**2. ---------------------------------------------------------------------------- All surveys, = 124 Q + 67 LLS not within 3 000 km s^-1 of Q em redshift the Q with a * have a LLS within 3 000 km s^-1 of Q em redshift the Q with a $ have a LLS with opt depth < 1.0, so their z_min=z_LLS NB. For the redshift 4 sample only including systems with z_em > 4.2 'cos of possible selection effects. Q name z_em z_min z_lls opt depth BR_0019-1522 4.52 2.51 4.27 5.8 BR_0103+0032 4.44 2.51 4.31 1.6 BRI0151-0025 4.20 2.51 4.05 3.7 BR_0245-0608* 4.24 2.51 4.23 3.9 BR_0951-0450 4.37 2.84 4.22 3.1 BRI0952-0115 4.43 2.84 4.25 2.1 BRI1013+0033 4.41 2.84 3.78 2.3 BR_1033-0327 4.51 2.84 4.19 3.5 BRI1050-0000 4.29 2.84 4.08 2.5 BRI1114-0822* 4.51 2.84 4.50 3.7 BR_1202-0725 4.69 2.84 4.52 3.0 BRI1328-0433 4.22 2.84 3.31 1.5 BRI1335-0417* 4.40 2.84 4.45 3.1 GB_1508+5714 4.30 2.84 3.88 4.6 BR_2237-0607 4.56 2.51 4.28 2.6 0000-263 4.111 2.51 3.412 0.0 0001+087 3.243 2.51 3.007 0.0 0004+171* 2.890 2.51 2.881 0.0 0014+813 3.384 2.51 2.813 0.0 0029+073 3.259 2.51 3.059 0.0 0045-036 3.135 2.51 2.830 0.0 0054-284* 3.616 2.51 3.585 0.0 0055-264 3.656 2.51 0.0 0.0 0101-304 3.150 2.51 2.907 0.0 0102-190 3.035 2.51 2.940 0.0 0112+029 2.823 2.51 0.0 0.0 0114-089 3.160 2.51 0.0 0.0 0132-198 3.130 2.51 2.484 0.0 0143-015 3.138 2.51 0.0 0.0 0148-097 2.848 2.51 0.0 0.0 0153+045 2.991 2.51 0.0 0.0 0201+365 2.912 2.51 0.0 0.0 0207-003 2.856 2.51 2.531 0.0 0216+080 2.993 2.51 0.0 0.0 0249-222 3.202 2.51 2.937 0.0 0249-184 3.205 2.51 2.665 0.0 0256-000 3.374 2.51 3.090 0.0 0301-006 3.223 2.51 2.947 0.0 0302-003 3.286 2.51 2.530 0.0 0308-193 2.752 2.51 0.0 0.0 0308+190 2.835 2.51 0.0 0.0 0316-203 2.865 2.51 0.0 0.0 0334-204 3.130 2.51 3.020 0.0 0352-275 2.819 2.51 0.0 0.0 0420+007 2.918 2.51 0.0 0.0 0449-134 3.093 2.51 2.963 0.0 0528-250 2.779 2.51 2.839 0.0 0636+680 3.174 2.51 2.909 0.0 0642+449 3.406 2.51 3.295 0.0 0731+663 3.033 2.51 2.912 0.0 0805+046 2.873 2.51 2.651 0.0 0830+115 2.976 2.51 0.0 0.0 0941+261 2.906 2.51 0.0 0.0 0956+122 3.301 2.51 3.096 0.0 1017+109 3.156 2.51 3.048 0.0 1836+511* 2.827 2.51 2.861 0.0 2000-330 3.777 2.51 3.548 0.0 2038-012 2.783 2.51 2.723 0.0 2048+312 3.185 2.51 0.0 0.0 2126-158 3.261 2.51 2.973 0.0 2233+131 3.295 2.51 3.165 0.0 2233+136 3.209 2.51 3.035 0.0 2311-036 3.041 2.51 0.0 0.0 2348-011 3.005 2.51 2.949 0.0 2359-022 2.817 2.51 0.0 0.0 2359+003 2.896 2.51 0.0 0.0 2359+068 3.234 2.51 0.0 0.0 NAB_0024+22 1.118 0.404 0.0 0.0 PKS_0044+030 0.624 0.404 0.0 0.0 Q0349-1438 0.614 0.404 0.0 0.0 Q0850+4400 0.513 0.404 0.0 0.0 Q0916+5118 0.553 0.404 0.0 0.0 Q1022+1927 0.828 0.404 0.546 1.42 Q1038+0625 1.270 0.404 0.456 1.15 Q1040+1219 1.028 0.404 0.0 0.0 PKS_1055+2007 1.110 0.404 1.036 2.68 1130+106Y 0.510 0.404 0.0 0.0 PKS_1136-13 0.554 0.404 0.0 0.0 PG_1206+459 1.158 0.404 0.0 0.0 MC_1215+113 1.230 0.404 0.0 0.0 B2_1244+32B 0.949 0.404 0.0 0.0 PKS_1252+11 0.870 0.404 0.0 0.0 PG_1259+593 0.472 0.404 0.0 0.0 Q1317+2743 1.022 0.404 0.649 4.43 PG_1333+176 0.554 0.404 0.0 0.0 PG_1338+416 1.219 0.404 0.0 0.0 B2_1340+29 0.905 0.404 0.0 0.0 Q_1347+5356 0.976 0.404 0.0 0.0 PG_1352+0106 1.121 0.404 0.677 6.70 PKS_1354+1919 0.720 0.404 0.470 1.70 PG_1407+265 0.944 0.404 0.0 0.0 MC_1415+172 0.821 0.404 0.0 0.0 PKS_1424-1150 0.805 0.404 0.666 2.20 Q_1618+1743 0.555 0.404 0.0 0.0 PKS_1656+053 0.879 0.404 0.0 0.0 Q_2251+1552 0.859 0.404 0.0 0.0 PSS_J0003+2730 4.240 2.858 3.97 2.6 BR_J0006-6208 4.455 3.079 4.14 1.8 PSS_J0034+1639* 4.293 2.858 4.26 4.1 SDSS_J0035+0040$ 4.747 4.590 0.0 0.0 PSS_J0106+2601 4.309 2.858 4.05 2.3 PSS_J0131+0633* 4.417 3.079 4.37 2.1 PSS_J0134+3307 4.532 2.858 4.32 2.1 SDSS_J0211-0009 4.874 3.079 4.81 1.2 BR_J0234-1806* 4.301 3.079 4.27 2.4 PSS_J0248+1802 4.422 2.858 4.13 2.0 BR_J0307-4945 4.728 3.079 4.50 2.8 SDSS_J0310-0014 4.658 4.090 0.0 0.0 BR_J0324-2918 4.622 3.079 4.209 1.5 BR_J0334-1612 4.363 2.858 4.237 1.4 SDSS_J0338+0021 5.010 3.035 4.93 2.2 BR_J0355-3811 4.545 3.079 4.43 2.0 BR_J0403-1703 4.227 4.175 0.0 0.0 BR_J0419-5716 4.461 3.079 4.33 1.1 BR_J0426-2202$ 4.320 3.970 0.0 0.0 PMN_J0525-3343 4.383 3.079 4.09 2.3 BR_J0529-3526* 4.413 3.079 4.39 1.7 BR_J0714-6455* 4.462 3.078 4.46 2.4 PSS_J0747+4434 4.430 2.858 4.29 1.8 RX_J1028-0844 4.276 2.857 3.62 3.0 FIRST_J1410+3409 4.351 2.857 3.87 1.2 PSS_J1456+2007 4.249 2.857 4.17 3.5 BR_J1603+0721* 4.385 2.857 4.38 2.5 PSS_J1618+4125 4.213 2.857 3.94 2.0 PSS_J1633+1411* 4.351 2.857 4.33 1.4 RX_J1759+6638$ 4.320 4.200 0.0 0.0 PMN_J2134-0419 4.334 3.079 4.19 1.6 PSS_J2154+0335 4.363 3.990 0.0 0.0 PSS_J2155+1358* 4.256 3.079 4.23 2.9 BR_J2216-6714 4.469 3.079 3.98 1.2 PSS_J2241+1352 4.441 3.079 4.31 1.8 BR_J2328-4513 4.359 3.079 4.19 2.0 PSS_J2344+0342 4.239 3.079 3.98 1.5 BR_J2349-3712* 4.208 3.079 4.17 2.5