Computable Properties 

In[2]:=

X distTable[list_List] := TraditionalForm[ Grid[list, Dividers -> All, Spacings -> {1, 2}, Alignment -> {Center, Center}, Frame -> All, FrameStyle -> Directive[White, Thick], Background -> {None, {Lighter[Blue, .9], {Hue[.6, .15, .9], GrayLevel[.9]}}}, BaseStyle -> {FontFamily -> "Helvetica", FontSize -> 11}, ItemStyle -> {Automatic, {Directive[Bold, FontSize -> 12]}}, ItemSize -> {Automatic, {2, Automatic}}]]

In[3]:=

X lis = {{"Function", "Result"}, {"CDF", CDF[\[ScriptCapitalR], t]}, {"Central Moment", CentralMoment[\[ScriptCapitalR], r]}, {"Central Moment Generating Function", CentralMomentGeneratingFunction[\[ScriptCapitalR], t]}, {"Characteristic Function", CharacteristicFunction[\[ScriptCapitalR], t]}, {"Cumulant", Cumulant[\[ScriptCapitalR], r]}, {"Expectation", Expectation[t, t \[Distributed] \[ScriptCapitalR]]}, {"Factorial Moment", FactorialMoment[\[ScriptCapitalR], 2]}, {"Factorial Moment Generating Function", FactorialMomentGeneratingFunction[\[ScriptCapitalR], t]}, {"Hazard Function", HazardFunction[\[ScriptCapitalR], t]}, {"Interquartile Range", InterquartileRange[\[ScriptCapitalR]]}, {"Inverse CDF", InverseCDF[\[ScriptCapitalR], t]}, {"Inverse Survival Function", InverseSurvivalFunction[\[ScriptCapitalR], t]}, {"Kurtosis", Kurtosis[\[ScriptCapitalR]]}, {"Likelihood", Likelihood[\[ScriptCapitalR], Array[x, 2]]}, {"Log Likelihood", LogLikelihood[\[ScriptCapitalR], Array[x, 2]]}, {"Mean", Mean[\[ScriptCapitalR]]}, {"Median", Median[\[ScriptCapitalR]]}, {"Moment Generating Function", MomentGeneratingFunction[\[ScriptCapitalR], t]}, {"Probability", Probability[t > k, t \[Distributed] \[ScriptCapitalR]]}, {"PDF", PDF[\[ScriptCapitalR], t]}, {"Quantile", Quantile[\[ScriptCapitalR], q]}, {"Quartiles", Quartiles[\[ScriptCapitalR]]}, {"Quartile Deviation", QuartileDeviation[\[ScriptCapitalR]]}, {"Quartile Skewness", QuartileSkewness[\[ScriptCapitalR]]}, {"Skewness", Skewness[\[ScriptCapitalR]]}, {"Standard Deviation", StandardDeviation[\[ScriptCapitalR]]}, {"Survival Function", SurvivalFunction[\[ScriptCapitalR], t]}, {"Variance", Variance[\[ScriptCapitalR]]}, {"Structural Importance", StructuralImportance[\[ScriptCapitalR]]}, {"Improvement Importance", ImprovementImportance[\[ScriptCapitalR], t]}, {"Birnbaum Importance", BirnbaumImportance[\[ScriptCapitalR], t]}, {"BarlowProschan Importance", BarlowProschanImportance[\[ScriptCapitalR]]}, {"Risk Achievement Importance", RiskAchievementImportance[\[ScriptCapitalR], t]}, {"Risk Reduction Importance", RiskReductionImportance[\[ScriptCapitalR], t]}, {"Criticality Failure Importance", CriticalityFailureImportance[\[ScriptCapitalR], t]}, {"Criticality Success Importance", CriticalitySuccessImportance[\[ScriptCapitalR], t]}, {"FussellVesely Importance", FussellVeselyImportance[\[ScriptCapitalR], t]}};

In[4]:=

X distTable@lis

In[1]:=

X \[ScriptCapitalR] = ReliabilityDistribution[ x \[And] y, {{x, ExponentialDistribution[Subscript[\[Lambda], 1]]}, {y, ExponentialDistribution[Subscript[\[Lambda], 2]]}}];

Out[4]//TraditionalForm=

Out[5]=