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8의 신기능: 매개 변수 확률 분포
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핵심 알고리즘
다양한 분포의 특성
지원되는 각각의 분포에 대한 극명한 특성 목록을 질의할 수 있습니다. 또한 모수 분포뿐만 아니라 분포에서 파생되어 나온 분포에서도 효율적인 모수 추정이 가능합니다.
In[1]:=
X
props = 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]:=
X
data = 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]:=
X
Labeled[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]=