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Mathematica
8: Parameter Estimation and Testing
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Core Algorithms
Use General Hypothesis Test Functions to Automatically Select Tests
LocationTest
automates the process of testing assumptions and picking tests of location. Here it performs a
test under a particular onesided alternative.
In[1]:=
X
d1 = NormalDistribution[.5, 1]; d2 = NormalDistribution[1.5, 1]; data = BlockRandom[SeedRandom[6]; RandomVariate[d2, 100]];
In[2]:=
X
Show[Plot[{PDF[d1, x], PDF[d2, x]}, {x, 6, 7}, PlotStyle > {{Thick, Darker[Green]}, {Thick, Darker[Red]}}, Axes > {True, False}, Ticks > None, PlotLabel > Text[Style[ "\!\(\*SubscriptBox[\(H\), \(o\)]\): t \[LessEqual] \ \!\(\*SubscriptBox[\(t\), \(o\)]\)" , Bold, FontSize > 14]]], Plot[PDF[d1, x], {x, 1.5, 7}, PlotRange > All, Filling > Axis], Graphics[{Dashed, Red, Line[{{1.5, 0}, {1.5, PDF[d2, 1.5]}}]}], Graphics[{Dashed, Green, Line[{{.5, 0}, {.5, PDF[d1, .5]}}]}], Graphics[{Arrowheads[Small], Arrow[{{4., 0.1}, {1.9, 0.015}}], Text[ Style["\!\(\*SubscriptBox[\(P\), SubscriptBox[\(H\), \(o\)]]\)[ t \ > \!\(\*SubscriptBox[\(t\), \(obs\)]\) ]", Bold, FontSize > 12], {4, 0.1}, {1, 1}]}], Graphics[{Arrowheads[Small], Arrow[{{1.5, 0.1}, {.5, 0.1}}], Text[ Style["\!\(\*SubscriptBox[\(t\), \(o\)]\)", Bold, FontSize > 12], {1.9, 0.09}, {1, 1}]}], Graphics[{Arrowheads[Small], Arrow[{{3., 0.25}, {1.5, 0.25}}], Text[ Style["\!\(\*SubscriptBox[\(t\), \(obs\)]\)", Bold, FontSize > 12], {3.25, 0.24}, {1, 1}]}], ImageSize > 300]
Out[2]=
In[3]:=
X
Subscript[\[Mu], 0] = 1.4; LocationTest[data, Subscript[\[Mu], 0], "TestDataTable", AlternativeHypothesis > "Greater"]
Out[3]=