Skip to main content

Histogram from relative frequency data;


I've got a data set similar to the first and fourth column of this table http://mathworld.wolfram.com/FrequencyDistribution.html where the first column is the midpoint of a fixed range of values (although a solution with arbitrarily spaced segments would be great) and the second column is the corresponding relative frequency of that initial range of values being present.


 A = {{5, 0.0123445}, {15, 0.0342565}, {25, 0.0885784}, {35, 0.184694}, {45, 0.243735}, {55, 0.223433}, {65, 0.111512}, {75, 0.000000}, {85, 0.000000}, {95, 0.1014466}}


I want to plot a histogram/discrete probability distribution. I've found solutions to plotting histograms from pre-binned data https://stackoverflow.com/questions/15117024/histogram-with-frequency-data but this only works on integer values.


My probability data has ~6 significant digits and I would really prefer not to arbitrarily multiply my data by 10^6 to plot it then adjust the plot labels to divide by 10^6.


Am I trying to force a function to do something it's not designed to do, is there a better way of going about this?


Thanks!



Answer



Alternatively, you could use WeightedData.


a = {{5, 0.0123445}, {15, 0.0342565}, {25, 0.0885784}, {35, 
   0.184694}, {45, 0.243735}, {55, 0.223433}, {65, 0.111512}, {75, 
   0.000000}, {85, 0.000000}, {95, 0.1014466}};


Histogram[WeightedData @@ Transpose[a], Length[a]]

enter image description here


You might also consider using DiscretePlot with an EmpiricalDistribution.


dist = EmpiricalDistribution[WeightedData @@ Transpose[a]]

DiscretePlot[PDF[dist, x], {x, a[[All, 1]]}, ExtentSize -> Full]

enter image description here


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more