(* ::Package:: *)

tri1[name1_, name2_, name3_]:=Module[{tri,line1,line2,centerMass1,centerMass2,centerMass3,text1,text2,text3},

tri=Triangle[{{-1,0},{1,0},{0,1}}];

line1=Line[{(tri[[1]][[1]]+tri[[1]][[3]])/2, (tri[[1]][[2]]+tri[[1]][[3]])/2}];
line2=Line[{(line1[[1]][[1]]+line1[[1]][[2]])/2,(tri[[1]][[1]]+tri[[1]][[2]])/2} ];

centerMass1=(tri[[1]][[1]]+((tri[[1]][[1]]+tri[[1]][[2]])/2)+((line1[[1]][[1]]+line1[[1]][[2]])/2)+((tri[[1]][[1]]+tri[[1]][[3]])/2))/4;
text1=Text[Style[name1,Black,Bold], centerMass1];

centerMass2=(tri[[1]][[2]]+((tri[[1]][[1]]+tri[[1]][[2]])/2)+((line1[[1]][[1]]+line1[[1]][[2]])/2)+((tri[[1]][[2]]+tri[[1]][[3]])/2))/4;
text2=Text[Style[name2,Black,Bold,FontSize->9], centerMass2];

centerMass3=(tri[[1]][[3]]+((tri[[1]][[1]]+tri[[1]][[3]])/2)+((tri[[1]][[2]]+tri[[1]][[3]])/2))/3;
text3=Text[Style[name3,Black,Bold], centerMass3];

Graphics[{EdgeForm[Directive[Thick,Lighter[Blue,.5]]],White,tri,Lighter[Blue,.5],Thick, line1,line2,text1,text2,text3}]
];






plotCONF[\[Mu]_,\[Sigma]_, e1_,e2_]:=Module[{g1,g2,g3,arrow1, arrow2,text1, text2,text3,text4,text5},



g1=Plot[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{x,-3*\[Sigma]+\[Mu],3*\[Sigma]+\[Mu]},Filling->Axis,PlotLabel->Column[{"Normal Distribution\n"<>"\[Mu]="<>"\!\(\*FractionBox[\(X\), \(n\)]\)"<>"="<>ToString[\[Mu]],"\!\(\*SubscriptBox[\(\[Sigma]\), \(p\)]\)=\!\(\*SqrtBox[FractionBox[\(\[Pi] \((1 - \[Pi])\)\), \(n\)]]\)"<>"="<>ToString[\[Sigma]]}],Ticks->{{{e1,TraditionalForm["\[Pi]-\!\(\*SubscriptBox[\(Z\), FractionBox[\(\[Alpha]\), \(2\)]]\)\!\(\*SqrtBox[FractionBox[\(\[Pi] \((1 - \[Pi])\)\), \(n\)]]\)="<>"\n"<>ToString[e1]],1/2,Directive[Red,Thin]},{e2,TraditionalForm["\[Pi]+\!\(\*SubscriptBox[\(Z\), FractionBox[\(\[Alpha]\), \(2\)]]\)\!\(\*SqrtBox[FractionBox[\(\[Pi] \((1 - \[Pi])\)\), \(n\)]]\)="<>"\n"<>ToString[e2]],1/2,Directive[Red,Thin]}},None},AxesStyle->Directive[Gray,Dashed],Axes->{True,False}, PlotRange->Full,ImageSize->500];
g2=Plot[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{x,e1,e2},Filling->Axis, 


(*PlotLabel\[Rule]Column[{"Normal Distribution\n"<>"\[Mu]="<>"X/n"<>"="<>ToString[\[Mu]],"Subscript[\[Sigma], p]=Sqrt[(\[Pi](1-\[Pi]))/n]"<>"="<>ToString[\[Sigma]]}],*) PlotRange->Full,AxesStyle->Directive[Gray,Dashed],Axes->{True,False}

PlotRange->Full,AxesOrigin->{\[Mu],0},FillingStyle->{Red},ImageSize->500];


arrow1=Graphics@Arrow[{{((e1-3.5*\[Sigma]+\[Mu])/2),PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]/3},{((e1-3*\[Sigma]+\[Mu])/2),PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]*0.03}}];
text1=Graphics@Text[TraditionalForm["\!\(\*FractionBox[\(\[Alpha]\), \(2\)]\)"], {((e1-3.5*\[Sigma]+\[Mu])/2),PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]*0.06+PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]/3}];


arrow2=Graphics@Arrow[{{((e2+3.5*\[Sigma]+\[Mu])/2),PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]/3},{((e2+3*\[Sigma]+\[Mu])/2),PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]*0.03}}];
text2=Graphics@Text[TraditionalForm["\!\(\*FractionBox[\(\[Alpha]\), \(2\)]\)"], {((e2+3.5*\[Sigma]+\[Mu])/2),PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]*0.06+PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]/3}];

text3=Graphics[{Yellow,Text[TraditionalForm["1-\[Alpha]"], {\[Mu],PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]/2}]}];

text4=Graphics[{Black,Text["\[Pi]\n"<>ToString[\[Mu]], {\[Mu],-PDF[NormalDistribution[\[Mu],\[Sigma]],\[Mu]]*0.06}]}];

g3=NumberLinePlot[{\[Mu]>=x>=e1,\[Mu]<=x<=e2},x,PlotStyle->{{Blue,Dashed},{Green,Dashed}},PlotLegends->Placed[{"e","e"},Right]];




Show[g1,g2,arrow1, text1, arrow2,text2,text3,text4,g3,ImageSize->500,PlotRange->All](*PlotRange\[Rule]All is a must to show everything and nothing clipped*)

];



(*TODO: the annotations are matched to certain variation in QMS202 questions*)
plotCONFLINE[\[Mu]_,\[Sigma]_, e1_,e2_]:=Module[{g1,g2,g3,arrow1, arrow2,text1, text2,text3,text4,text5},






text4=Graphics[{Black,Text["\!\(\*OverscriptBox[\(X\), \(_\)]\)\n", {\[Mu],-1}]}]; (*FIXME: -1 hardwired*)

g3=NumberLinePlot[{\[Mu]>=x>=e1,\[Mu]<=x<=e2},x,Ticks->{{{e1,TraditionalForm["\!\(\*OverscriptBox[\(X\), \(_\)]\)-\!\(\*SubscriptBox[\(Z\), FractionBox[\(\[Alpha]\), \(2\)]]\)\!\(\*FractionBox[\(\[Sigma]\), SqrtBox[\(n\)]]\)"],1/2,Directive[Red,Thin]},{e2,TraditionalForm["\!\(\*OverscriptBox[\(X\), \(_\)]\)+\!\(\*SubscriptBox[\(Z\), FractionBox[\(\[Alpha]\), \(2\)]]\)\!\(\*FractionBox[\(\[Sigma]\), SqrtBox[\(n\)]]\)"],1/2,Directive[Red,Thin]}},None},PlotStyle->{{Blue,Dashed},{Green,Dashed}},PlotLegends->Placed[{ToString[e1]<>" (-error)",ToString[e2]<>" (+error)"},Right]];




Show[g3,text4,ImageSize->500,PlotRange->All](*PlotRange\[Rule]All is a must to show everything and nothing clipped*)

];



slidingPLOT[\[Sigma]_,\[Mu]0_,\[Mu]1_,\[Mu]2_,conf_,a_]:=Module[{},

Column[{

Show[
Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,-a*\[Sigma]+\[Mu]0,a*\[Sigma]+\[Mu]0},AxesOrigin->{\[Mu]0,0},Ticks->{{\[Mu]2,{conf,conf,{0.6,0},Directive[Red,Dashed]},\[Mu]1,\[Mu]0,{\[Mu]0-conf+\[Mu]0,\[Mu]0-conf+\[Mu]0,{0.6,0},Directive[Red,Dashed]}},None},
Filling->Axis,PlotStyle->LightGray, Axes->{True,False},ImageSize->400,PlotRange->Full,TicksStyle->Directive[Orange,8],PlotLegends->Column@{"\!\(\*SubscriptBox[\(H\), \(0\)]\):\[Mu]="<>ToString[\[Mu]0],"\!\(\*SubscriptBox[\(H\), \(1\)]\):\[Mu]\[NotEqual]"<>ToString[\[Mu]0]}],

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,\[Mu]0-conf+\[Mu]0,a*\[Sigma]+\[Mu]0},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Red, Axes->False,ImageSize->400,PlotRange->Full],

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,-a*\[Sigma]+\[Mu]0,conf},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Red, Axes->False,ImageSize->400,PlotRange->Full],

Graphics[{Dashed,Line[{{\[Mu]0,0}, {\[Mu]0,PDF[NormalDistribution[\[Mu]0,\[Sigma]],\[Mu]0]}}],Black,Text["\!\(\*FractionBox[\(\[Alpha]\), \(2\)]\)",{\[Mu]0-conf+\[Mu]0+4, PDF[NormalDistribution[\[Mu]0,\[Sigma]],\[Mu]0]/9}],Text["\!\(\*FractionBox[\(\[Alpha]\), \(2\)]\)",{conf-2, PDF[NormalDistribution[\[Mu]0,\[Sigma]],\[Mu]0]/9}]}] ],

Show[

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,-a*\[Sigma]+\[Mu]0,a*\[Sigma]+\[Mu]0},AxesOrigin->{\[Mu]0,0},Ticks->{{\[Mu]2,{conf,conf,{0.6,0},Directive[Red,Dashed]},\[Mu]1,\[Mu]0,{\[Mu]0-conf+\[Mu]0,\[Mu]0-conf+\[Mu]0,{0.6,0},Directive[Red,Dashed]}},None},
Filling->Axis,PlotStyle->LightGray, Axes->{True,False},ImageSize->400,PlotRange->Full,TicksStyle->Directive[Orange,8],PlotLegends->Row@{"\[Mu]=",ToString[\[Mu]2]}],

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,\[Mu]0-conf+\[Mu]0,a*\[Sigma]+\[Mu]0},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Red, Axes->False,ImageSize->400,PlotRange->Full],

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,-a*\[Sigma]+\[Mu]0,conf},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Red, Axes->False,ImageSize->400,PlotRange->Full],

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]2}}],{x,-a*\[Sigma]+\[Mu]0,a*\[Sigma]+\[Mu]0},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Orange, Axes->False,ImageSize->400,PlotRange->Full],


Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]2}}],{x,conf,\[Mu]0-conf+\[Mu]0},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Green, Axes->False,ImageSize->400,PlotRange->Full],

Graphics[{Dashed,Line[{{\[Mu]2,0}, {\[Mu]2,PDF[NormalDistribution[\[Mu]2,\[Sigma]],\[Mu]2]}}],Text["\[Beta]",{conf+4, PDF[NormalDistribution[\[Mu]0,\[Sigma]],\[Mu]0]/9}] }]
],


Show[

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,-a*\[Sigma]+\[Mu]0,a*\[Sigma]+\[Mu]0},AxesOrigin->{\[Mu]0,0},Ticks->{{\[Mu]2,{conf,conf,{0.6,0},Directive[Red,Dashed]},\[Mu]1,\[Mu]0,{\[Mu]0-conf+\[Mu]0,\[Mu]0-conf+\[Mu]0,{0.6,0},Directive[Red,Dashed]}},None},
Filling->Axis,PlotStyle->LightGray, Axes->{True,False},ImageSize->400,PlotRange->Full,TicksStyle->Directive[Orange,8],
PlotLegends->Row@{"\[Mu]=",ToString[\[Mu]1]}],

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,\[Mu]0-conf+\[Mu]0,a*\[Sigma]+\[Mu]0},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Red, Axes->False,ImageSize->400,PlotRange->Full],

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]0}}],{x,-a*\[Sigma]+\[Mu]0,conf},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Red, Axes->False,ImageSize->400,PlotRange->Full],

Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]1}}],{x,-a*\[Sigma]+\[Mu]0,a*\[Sigma]+\[Mu]0},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Orange, Axes->False,ImageSize->400,PlotRange->Full],


Plot[Evaluate@Table[PDF[NormalDistribution[\[Mu],\[Sigma]],x],{\[Mu],{\[Mu]1}}],{x,conf,\[Mu]0-conf+\[Mu]0},AxesOrigin->{\[Mu]0,0},Filling->Axis,PlotStyle->Green, Axes->False,ImageSize->400,PlotRange->Full],

Graphics[{Dashed,Line[{{\[Mu]1,0}, {\[Mu]1,PDF[NormalDistribution[\[Mu]1,\[Sigma]],\[Mu]1]}}],Text["\[Beta]",{conf+4, PDF[NormalDistribution[\[Mu]0,\[Sigma]],\[Mu]0]/9}]}]
]


}
]

];