# An Extensive Collection of Distributional Properties

An extensive list of properties can be queried for each supported distribution. In addition, parametric distributions, as well as derived distributions constructed out of them, allow for efficient parameter estimation.
 In[1]:= Xprops = Thread[ HoldForm[{PDF[\[ScriptCapitalD], x], CDF[\[ScriptCapitalD], x], SurvivalFunction[\[ScriptCapitalD], x], HazardFunction[\[ScriptCapitalD], x], DistributionParameterAssumptions[\[ScriptCapitalD]], RandomVariate[(\[ScriptCapitalD] /. \[Lambda] -> 3), 3], EstimatedDistribution[data, \[ScriptCapitalD]], FindDistributionParameters[data, \[ScriptCapitalD]], Quantile[\[ScriptCapitalD], q], InverseCDF[\[ScriptCapitalD], q], InverseSurvivalFunction[\[ScriptCapitalD], q], Median[\[ScriptCapitalD]], InterquartileRange[\[ScriptCapitalD]], QuartileDeviation[\[ScriptCapitalD]], QuartileSkewness[\[ScriptCapitalD]], Quartiles[\[ScriptCapitalD]], Mean[\[ScriptCapitalD]], StandardDeviation[\[ScriptCapitalD]], Variance[\[ScriptCapitalD]], Skewness[\[ScriptCapitalD]], Kurtosis[\[ScriptCapitalD]], Likelihood[\[ScriptCapitalD], {x, y}], LogLikelihood[\[ScriptCapitalD], {x, y}], CharacteristicFunction[\[ScriptCapitalD], t], Moment[\[ScriptCapitalD], r], MomentGeneratingFunction[\[ScriptCapitalD], t], CentralMoment[\[ScriptCapitalD], r], CentralMomentGeneratingFunction[\[ScriptCapitalD], t], Cumulant[\[ScriptCapitalD], r], CumulantGeneratingFunction[\[ScriptCapitalD], t], FactorialMoment[\[ScriptCapitalD], r], FactorialMomentGeneratingFunction[\[ScriptCapitalD], t]}]];
 In[2]:= Xdata = RandomVariate[ExponentialDistribution[5], 10^5]; gridData = Join @@@ ArrayFlatten[ Transpose[ Partition[{Pane[#1 /. HoldPattern[ReplaceAll[e_, rhs_]] :> e, 115], Pane[ Block[{\[ScriptCapitalD] = ExponentialDistribution[\[Lambda]]}, Refine[ReleaseHold[#2], 0 <= q <= 1]], 140, Alignment -> Left]} & @@@ Thread[{props, props}], Ceiling[Length[props]/2], Ceiling[Length[props]/2]]]];
 In[3]:= XLabeled[Pane[ Grid[gridData, Background -> {None, {{Lighter[Blend[{Blue, Green}], .6], GrayLevel[.9]}}}, BaseStyle -> {FontFamily -> "Verdana"}, Dividers -> All, FrameStyle -> Directive[Thick, White], Spacings -> {1, 2}], {550, 900}, ImageSizeAction -> "ResizeToFit", Alignment -> {Center, Top}], Style["Distribution Properties", 18, Bold, FontFamily -> "Verdana"], Top]
 Out[3]=