Statistics

Stat.binmean

using Gadfly, RDatasets
set_default_plot_size(21cm, 8cm)
p1 = plot(dataset("datasets", "iris"), x="SepalLength", y="SepalWidth",
          Geom.point)
p2 = plot(dataset("datasets", "iris"), x="SepalLength", y="SepalWidth",
          Stat.binmean, Geom.point)
hstack(p1,p2)
SepalLength 4 5 6 7 8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0 3.98 4.00 4.02 4.04 4.06 4.08 4.10 4.12 4.14 4.16 4.18 4.20 4.22 4.24 4.26 4.28 4.30 4.32 4.34 4.36 4.38 4.40 4.42 4.44 4.46 4.48 4.50 4.52 4.54 4.56 4.58 4.60 4.62 4.64 4.66 4.68 4.70 4.72 4.74 4.76 4.78 4.80 4.82 4.84 4.86 4.88 4.90 4.92 4.94 4.96 4.98 5.00 5.02 5.04 5.06 5.08 5.10 5.12 5.14 5.16 5.18 5.20 5.22 5.24 5.26 5.28 5.30 5.32 5.34 5.36 5.38 5.40 5.42 5.44 5.46 5.48 5.50 5.52 5.54 5.56 5.58 5.60 5.62 5.64 5.66 5.68 5.70 5.72 5.74 5.76 5.78 5.80 5.82 5.84 5.86 5.88 5.90 5.92 5.94 5.96 5.98 6.00 6.02 6.04 6.06 6.08 6.10 6.12 6.14 6.16 6.18 6.20 6.22 6.24 6.26 6.28 6.30 6.32 6.34 6.36 6.38 6.40 6.42 6.44 6.46 6.48 6.50 6.52 6.54 6.56 6.58 6.60 6.62 6.64 6.66 6.68 6.70 6.72 6.74 6.76 6.78 6.80 6.82 6.84 6.86 6.88 6.90 6.92 6.94 6.96 6.98 7.00 7.02 7.04 7.06 7.08 7.10 7.12 7.14 7.16 7.18 7.20 7.22 7.24 7.26 7.28 7.30 7.32 7.34 7.36 7.38 7.40 7.42 7.44 7.46 7.48 7.50 7.52 7.54 7.56 7.58 7.60 7.62 7.64 7.66 7.68 7.70 7.72 7.74 7.76 7.78 7.80 7.82 7.84 7.86 7.88 7.90 7.92 7.94 7.96 7.98 8.00 4 6 8 7.6253.0875 7.1400000000000013.2 6.8571428571428563.0714285714285716 6.68000000000000153.0300000000000002 6.5,3.0 6.39999999999999952.9571428571428577 6.2999999999999992.8555555555555556 6.22.8249999999999997 6.052.7916666666666665 5.9000000000000013.0666666666666664 5.7999999999999992.8857142857142857 5.7000000000000013.1 5.60000000000000052.816666666666667 5.4428571428571433.207142857142857 5.2,3.425 5.10000000000000053.477777777777778 4.96253.05625 4.7714285714285713.185714285714286 4.4888888888888893.0777777777777775 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 2.75 3.00 3.25 3.50 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 2.750 2.755 2.760 2.765 2.770 2.775 2.780 2.785 2.790 2.795 2.800 2.805 2.810 2.815 2.820 2.825 2.830 2.835 2.840 2.845 2.850 2.855 2.860 2.865 2.870 2.875 2.880 2.885 2.890 2.895 2.900 2.905 2.910 2.915 2.920 2.925 2.930 2.935 2.940 2.945 2.950 2.955 2.960 2.965 2.970 2.975 2.980 2.985 2.990 2.995 3.000 3.005 3.010 3.015 3.020 3.025 3.030 3.035 3.040 3.045 3.050 3.055 3.060 3.065 3.070 3.075 3.080 3.085 3.090 3.095 3.100 3.105 3.110 3.115 3.120 3.125 3.130 3.135 3.140 3.145 3.150 3.155 3.160 3.165 3.170 3.175 3.180 3.185 3.190 3.195 3.200 3.205 3.210 3.215 3.220 3.225 3.230 3.235 3.240 3.245 3.250 3.255 3.260 3.265 3.270 3.275 3.280 3.285 3.290 3.295 3.300 3.305 3.310 3.315 3.320 3.325 3.330 3.335 3.340 3.345 3.350 3.355 3.360 3.365 3.370 3.375 3.380 3.385 3.390 3.395 3.400 3.405 3.410 3.415 3.420 3.425 3.430 3.435 3.440 3.445 3.450 3.455 3.460 3.465 3.470 3.475 3.480 3.485 3.490 3.495 3.500 2.5 3.0 3.5 SepalWidth SepalLength 4 5 6 7 8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0 3.98 4.00 4.02 4.04 4.06 4.08 4.10 4.12 4.14 4.16 4.18 4.20 4.22 4.24 4.26 4.28 4.30 4.32 4.34 4.36 4.38 4.40 4.42 4.44 4.46 4.48 4.50 4.52 4.54 4.56 4.58 4.60 4.62 4.64 4.66 4.68 4.70 4.72 4.74 4.76 4.78 4.80 4.82 4.84 4.86 4.88 4.90 4.92 4.94 4.96 4.98 5.00 5.02 5.04 5.06 5.08 5.10 5.12 5.14 5.16 5.18 5.20 5.22 5.24 5.26 5.28 5.30 5.32 5.34 5.36 5.38 5.40 5.42 5.44 5.46 5.48 5.50 5.52 5.54 5.56 5.58 5.60 5.62 5.64 5.66 5.68 5.70 5.72 5.74 5.76 5.78 5.80 5.82 5.84 5.86 5.88 5.90 5.92 5.94 5.96 5.98 6.00 6.02 6.04 6.06 6.08 6.10 6.12 6.14 6.16 6.18 6.20 6.22 6.24 6.26 6.28 6.30 6.32 6.34 6.36 6.38 6.40 6.42 6.44 6.46 6.48 6.50 6.52 6.54 6.56 6.58 6.60 6.62 6.64 6.66 6.68 6.70 6.72 6.74 6.76 6.78 6.80 6.82 6.84 6.86 6.88 6.90 6.92 6.94 6.96 6.98 7.00 7.02 7.04 7.06 7.08 7.10 7.12 7.14 7.16 7.18 7.20 7.22 7.24 7.26 7.28 7.30 7.32 7.34 7.36 7.38 7.40 7.42 7.44 7.46 7.48 7.50 7.52 7.54 7.56 7.58 7.60 7.62 7.64 7.66 7.68 7.70 7.72 7.74 7.76 7.78 7.80 7.82 7.84 7.86 7.88 7.90 7.92 7.94 7.96 7.98 8.00 4 6 8 5.9,3.0 6.2,3.4 6.5,3.0 6.3,2.5 6.7,3.0 6.7,3.3 6.8,3.2 5.8,2.7 6.9,3.1 6.7,3.1 6.9,3.1 6.0,3.0 6.4,3.1 6.3,3.4 7.7,3.0 6.1,2.6 6.3,2.8 6.4,2.8 7.9,3.8 7.4,2.8 7.2,3.0 6.4,2.8 6.1,3.0 6.2,2.8 7.2,3.2 6.7,3.3 6.3,2.7 7.7,2.8 5.6,2.8 6.9,3.2 6.0,2.2 7.7,2.6 7.7,3.8 6.5,3.0 6.4,3.2 5.8,2.8 5.7,2.5 6.8,3.0 6.4,2.7 6.5,3.2 7.2,3.6 6.7,2.5 7.3,2.9 4.9,2.5 7.6,3.0 6.5,3.0 6.3,2.9 7.1,3.0 5.8,2.7 6.3,3.3 5.7,2.8 5.1,2.5 6.2,2.9 5.7,2.9 5.7,3.0 5.6,2.7 5.0,2.3 5.8,2.6 6.1,3.0 5.5,2.6 5.5,2.5 5.6,3.0 6.3,2.3 6.7,3.1 6.0,3.4 5.4,3.0 6.0,2.7 5.8,2.7 5.5,2.4 5.5,2.4 5.7,2.6 6.0,2.9 6.7,3.0 6.8,2.8 6.6,3.0 6.4,2.9 6.1,2.8 6.3,2.5 6.1,2.8 5.9,3.2 5.6,2.5 6.2,2.2 5.8,2.7 5.6,3.0 6.7,3.1 5.6,2.9 6.1,2.9 6.0,2.2 5.9,3.0 5.0,2.0 5.2,2.7 6.6,2.9 4.9,2.4 6.3,3.3 5.7,2.8 6.5,2.8 5.5,2.3 6.9,3.1 6.4,3.2 7.0,3.2 5.0,3.3 5.3,3.7 4.6,3.2 5.1,3.8 4.8,3.0 5.1,3.8 5.0,3.5 4.4,3.2 4.5,2.3 5.0,3.5 5.1,3.4 4.4,3.0 4.9,3.6 5.5,3.5 5.0,3.2 4.9,3.1 5.5,4.2 5.2,4.1 5.4,3.4 4.8,3.1 4.7,3.2 5.2,3.4 5.2,3.5 5.0,3.4 5.0,3.0 4.8,3.4 5.1,3.3 4.6,3.6 5.1,3.7 5.4,3.4 5.1,3.8 5.7,3.8 5.1,3.5 5.4,3.9 5.7,4.4 5.8,4.0 4.3,3.0 4.8,3.0 4.8,3.4 5.4,3.7 4.9,3.1 4.4,2.9 5.0,3.4 4.6,3.4 5.4,3.9 5.0,3.6 4.6,3.1 4.7,3.2 4.9,3.0 5.1,3.5 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71 3.72 3.73 3.74 3.75 3.76 3.77 3.78 3.79 3.80 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89 3.90 3.91 3.92 3.93 3.94 3.95 3.96 3.97 3.98 3.99 4.00 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.30 4.31 4.32 4.33 4.34 4.35 4.36 4.37 4.38 4.39 4.40 4.41 4.42 4.43 4.44 4.45 4.46 4.47 4.48 4.49 4.50 2 3 4 5 SepalWidth

Stat.density

using DataFrames, Gadfly, Distributions
set_default_plot_size(21cm, 8cm)
x = -4:0.1:4
Da = [DataFrame(x=x, ymax=pdf.(Normal(μ),x), u="μ=$μ") for μ in [-1,1]]
Db = [DataFrame(x=randn(200).+μ, u="μ=$μ") for μ in [-1,1]]

p1 = plot(vcat(Da...), x=:x, y=:ymax, ymin=[0.0], ymax=:ymax, color=:u,
    Geom.line, Geom.ribbon, Guide.ylabel("Density"), Theme(alphas=[0.6]),
    Guide.colorkey(title="", pos=[2.5,0.6]), Guide.title("Parametric PDF")
)
p2 = plot(vcat(Db...), x=:x, color=:u, Theme(alphas=[0.6]),
    Stat.density(bandwidth=0.5), Geom.polygon(fill=true, preserve_order=true),
    Coord.cartesian(xmin=-4, xmax=4, ymin=0, ymax=0.4),
    Guide.colorkey(title="", pos=[2.5,0.6]), Guide.title("Kernel PDF")
)
hstack(p1,p2)
x -4 -2 0 2 4 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 -4.00 -3.95 -3.90 -3.85 -3.80 -3.75 -3.70 -3.65 -3.60 -3.55 -3.50 -3.45 -3.40 -3.35 -3.30 -3.25 -3.20 -3.15 -3.10 -3.05 -3.00 -2.95 -2.90 -2.85 -2.80 -2.75 -2.70 -2.65 -2.60 -2.55 -2.50 -2.45 -2.40 -2.35 -2.30 -2.25 -2.20 -2.15 -2.10 -2.05 -2.00 -1.95 -1.90 -1.85 -1.80 -1.75 -1.70 -1.65 -1.60 -1.55 -1.50 -1.45 -1.40 -1.35 -1.30 -1.25 -1.20 -1.15 -1.10 -1.05 -1.00 -0.95 -0.90 -0.85 -0.80 -0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 -5 0 5 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? μ=-1 μ=1 0.0 0.1 0.2 0.3 0.4 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.054 0.056 0.058 0.060 0.062 0.064 0.066 0.068 0.070 0.072 0.074 0.076 0.078 0.080 0.082 0.084 0.086 0.088 0.090 0.092 0.094 0.096 0.098 0.100 0.102 0.104 0.106 0.108 0.110 0.112 0.114 0.116 0.118 0.120 0.122 0.124 0.126 0.128 0.130 0.132 0.134 0.136 0.138 0.140 0.142 0.144 0.146 0.148 0.150 0.152 0.154 0.156 0.158 0.160 0.162 0.164 0.166 0.168 0.170 0.172 0.174 0.176 0.178 0.180 0.182 0.184 0.186 0.188 0.190 0.192 0.194 0.196 0.198 0.200 0.202 0.204 0.206 0.208 0.210 0.212 0.214 0.216 0.218 0.220 0.222 0.224 0.226 0.228 0.230 0.232 0.234 0.236 0.238 0.240 0.242 0.244 0.246 0.248 0.250 0.252 0.254 0.256 0.258 0.260 0.262 0.264 0.266 0.268 0.270 0.272 0.274 0.276 0.278 0.280 0.282 0.284 0.286 0.288 0.290 0.292 0.294 0.296 0.298 0.300 0.302 0.304 0.306 0.308 0.310 0.312 0.314 0.316 0.318 0.320 0.322 0.324 0.326 0.328 0.330 0.332 0.334 0.336 0.338 0.340 0.342 0.344 0.346 0.348 0.350 0.352 0.354 0.356 0.358 0.360 0.362 0.364 0.366 0.368 0.370 0.372 0.374 0.376 0.378 0.380 0.382 0.384 0.386 0.388 0.390 0.392 0.394 0.396 0.398 0.400 0.0 0.5 Kernel PDF x -4 -2 0 2 4 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 -4.00 -3.95 -3.90 -3.85 -3.80 -3.75 -3.70 -3.65 -3.60 -3.55 -3.50 -3.45 -3.40 -3.35 -3.30 -3.25 -3.20 -3.15 -3.10 -3.05 -3.00 -2.95 -2.90 -2.85 -2.80 -2.75 -2.70 -2.65 -2.60 -2.55 -2.50 -2.45 -2.40 -2.35 -2.30 -2.25 -2.20 -2.15 -2.10 -2.05 -2.00 -1.95 -1.90 -1.85 -1.80 -1.75 -1.70 -1.65 -1.60 -1.55 -1.50 -1.45 -1.40 -1.35 -1.30 -1.25 -1.20 -1.15 -1.10 -1.05 -1.00 -0.95 -0.90 -0.85 -0.80 -0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 -5 0 5 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? μ=-1 μ=1 0.0 0.1 0.2 0.3 0.4 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.054 0.056 0.058 0.060 0.062 0.064 0.066 0.068 0.070 0.072 0.074 0.076 0.078 0.080 0.082 0.084 0.086 0.088 0.090 0.092 0.094 0.096 0.098 0.100 0.102 0.104 0.106 0.108 0.110 0.112 0.114 0.116 0.118 0.120 0.122 0.124 0.126 0.128 0.130 0.132 0.134 0.136 0.138 0.140 0.142 0.144 0.146 0.148 0.150 0.152 0.154 0.156 0.158 0.160 0.162 0.164 0.166 0.168 0.170 0.172 0.174 0.176 0.178 0.180 0.182 0.184 0.186 0.188 0.190 0.192 0.194 0.196 0.198 0.200 0.202 0.204 0.206 0.208 0.210 0.212 0.214 0.216 0.218 0.220 0.222 0.224 0.226 0.228 0.230 0.232 0.234 0.236 0.238 0.240 0.242 0.244 0.246 0.248 0.250 0.252 0.254 0.256 0.258 0.260 0.262 0.264 0.266 0.268 0.270 0.272 0.274 0.276 0.278 0.280 0.282 0.284 0.286 0.288 0.290 0.292 0.294 0.296 0.298 0.300 0.302 0.304 0.306 0.308 0.310 0.312 0.314 0.316 0.318 0.320 0.322 0.324 0.326 0.328 0.330 0.332 0.334 0.336 0.338 0.340 0.342 0.344 0.346 0.348 0.350 0.352 0.354 0.356 0.358 0.360 0.362 0.364 0.366 0.368 0.370 0.372 0.374 0.376 0.378 0.380 0.382 0.384 0.386 0.388 0.390 0.392 0.394 0.396 0.398 0.400 0.0 0.5 Density Parametric PDF