August – dB logplot in Mathematica

In our series of Mathematica plotting, here we give an example of how to plot values in dB in a logarithmic plot. Among many other things, the logarithmic plot is handy in visualizing the tails of probability distributions. We represent the values of the complementary cumulative distributions in dB, thus we have to add custom ticks for the abscissa. Also, the font size is increased and plot titles and legends are added.

xmax = 180;
ymax = 1;

{table1, table2, 
   table3} = {Table[{t, 
     1 - CDF[GammaDistribution[3.715287738432738`, 
         16.575007504627795`]][t]}, {t, 0, xmax, xmax/10}], 
   Table[{t, 
     1 - CDF[GammaDistribution[6.502676225156808`, 
         8.60919186301341`]][t]}, {t, 0, xmax, xmax/10}], 
   Table[{t, 
     1 - CDF[GammaDistribution[3.3444580518527207`, 
         16.73897127052263`]][t]}, {t, 0, xmax, xmax/10}]};

Labeled[Show[
  LogPlot[{1 - 
     CDF[GammaDistribution[3.715287738432738`, 16.575007504627795`]][
      x], 1 - CDF[
       GammaDistribution[6.502676225156808`, 8.60919186301341`]][x], 
    1 - CDF[GammaDistribution[3.3444580518527207`, 
        16.73897127052263`]][x]}, {x, 0, xmax}, 
   GridLines -> Automatic, PlotRange -> {{0, xmax}, {0, 1}}, 
   Ticks -> {{{0*xmax, -Infinity},
      {0.1*xmax, NumberForm[10*Log10[(0.1*xmax)], 3]},
      {0.2*xmax, NumberForm[10*Log10[(0.2*xmax)], 3]},
      {0.3*xmax, NumberForm[10*Log10[(0.3*xmax)], 3]},
      {0.4*xmax, NumberForm[10*Log10[(0.4*xmax)], 3]},
      {0.5*xmax, NumberForm[10*Log10[(0.5*xmax)], 3]},
      {0.6*xmax, NumberForm[10*Log10[(0.6*xmax)], 3]},
      {0.7*xmax, NumberForm[10*Log10[(0.7*xmax)], 3]},
      {0.8*xmax, NumberForm[10*Log10[(0.8*xmax)], 3]},
      {0.9*xmax, NumberForm[10*Log10[(0.9*xmax)], 3]},
      {1*xmax, N[NumberForm[10*Log10[(1*xmax)], 3]] "dBm"}
      }, {10^-4, 10^-3, 10^-2, 10^-1, 1}}, 
   BaseStyle -> {FontSize -> 15}, PlotStyle -> Thick], 
  ListLogPlot[{table1, table2, table3}, 
   PlotLegends -> 
    Placed[{"\[CapitalGamma](3.7,16.6)", "\[CapitalGamma](6.5,8.6)", 
      "\[CapitalGamma](3.3,16.7)"}, Right], 
   PlotMarkers -> {Automatic, 10}]
  ], {"Percent of realizations abscissa is exceeded", 
  "Interference power (decibel-milliwats)"}, {Left, Bottom}, 
 RotateLabel -> True]

References:

• reference.wolfram.com