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Estimate the Induction Time Distribution for a Disease

A group of 258 patients with AIDS had been exposed to HIV through blood transfusion on a known date. Patients who had not developed AIDS before the end of the study are not included (right truncation).

    
Create a kernel density estimate of the AIDS induction time distribution and compute its mean:
Wolfram Language code: 𝒟 = KernelMixtureDistribution[EventData[258], .75]; Mean[𝒟]
The probability a person will survive more than 6 years without developing AIDS:
Wolfram Language code: Probability[t > 6, t𝒟]
The expected induction time given AIDS has not developed by 6 years:
Wolfram Language code: NExpectation[tt ≥ 6, t𝒟]
Wolfram Language code: aids = EventData[258]; dist = KernelMixtureDistribution[aids, h]; aidsDist = dist /. h -> .75; Labeled[Plot[Evaluate@Table[PDF[dist /. h -> bw, t], {bw, .25, 1.25, .25}], {t, 0, 10}, ImageSize -> 450, PlotRange -> All, PlotStyle -> Thick, GridLines -> Automatic, GridLinesStyle -> Dotted, PlotLegends -> Placed[LineLegend[Automatic, Table[Style[i, Bold, FontFamily -> "Helvetica"], {i, .25, 1.25, .25}], LegendLabel -> Style["Bandwidth", Bold, FontFamily -> "Helvetica"]], Below]], Column[{Style["Smoothed AIDS Induction Distribution", Bold, FontSize -> 18, FontFamily -> "Helvetica"], Style["Adults Infected by Blood Transfusion", Bold, FontColor -> Gray, FontSize -> 14, FontFamily -> "Helvetica"]}], {{Top, Left}}]