Simulate Incomes with Dagum Distribution
Simulate Incomes with Dagum Distribution
Fit a DagumDistribution to income data from a state university and simulate possible salaries at such a university.
universityA = Select[ExampleData[{"Statistics", "UniversitySalaries"}], #[[4]] == "A"&];
salaries = Select[Table[If[universityA[[i, 2]] > 0, universityA[[i, 3]] / universityA[[i, 2]], 0], {i, Length[universityA]}], # > 0&];
edist = EstimatedDistribution[salaries, DagumDistribution[p, a, b]];Show[Histogram[salaries, {0, 200000, 10000}, "PDF", ChartStyle -> "BeachColors"], Plot[PDF[TruncatedDistribution[{0, 200000}, edist], x], {x, 0, 200000}, PlotStyle -> Thick], BaseStyle -> {FontFamily -> "Verdana"}, Epilog -> Inset[Framed[Style[Grid[{{"Estimated distribution: "}, {Round[#, .1]& /@ edist}}], 11], Background -> StandardBlue, RoundingRadius -> 3], {Right, Top}, {Right, Top}], ImageSize -> 400]ListPlot[{RandomVariate[edist, 100], Tooltip[{{0, Median[edist]}, {100, Median[edist]}}, "Median"]}, Filling -> {1 -> Axis}, Joined -> {False, True}, AxesOrigin -> {0, 20000}, PlotStyle -> {PointSize[Medium], Thick}, BaseStyle -> {FontFamily -> "Verdana"}, PlotLabel -> "Simulate the incomes for 100 randomly selected employees.", Epilog -> Inset[Style["Median", Bold, 10], {75, Median[edist]}, {Center, Center}], ImageSize -> 400]