NORMALD_ICDF (LEFT/CENTER/RIGHT)

[Wes Loewer]

(03-03-2020 06:04 AM)parisse Wrote:  Well, this is against the philosophy of separating the GUI and the computing kernel, and it would require coding a GUI for each port of Giac. I think that's the job of HP to add a GUI in one of its app.

StephanP,
In case you're wondering, Parisse is the brains behind the CAS that HP uses for Prime. I think the rest of the Prime mostly comes HP.

I hope HP does put in an easy to use GUI for the probability distributions. If they do, I'm sure it will look much more professional than mine, but in the mean time, feel free to use the following. I've added the rest of the continuous distributions and put in easy to edit strings so that you can put in whatever descriptions you prefer. (I want to eventually do the same for the discrete distributions, but right now in my stats class, I'm covering topics related to continuous distributions, so that's what's on my mind.)

(corrections welcomed)

Code:


#pragma mode( separator(.,;) integer(h64) )

// Probability Distribution UI

// local but persistent
LOCAL x=0, x2=1, mu=0, sigma=1, area=0.05, tail=1;
LOCAL df=30, ddf=30;


// strings
sLeft = "left tail";
sRight = "right tail";
sInner = "inner interval";
sOuter = "outer tails";
sCanceled = "canceled";
sInvalidTail = "invalid tail";


// label strings
lblMean = "Mean:";
lblStdDev = "StdDev:";
lblX = "X:";
lblX1 = "X1:";
lblX2 = "X2:";
lblDF = "df:";
lblNDF = "Num df:";
lblDDF = "Den df:";
lblArea = "Area:";
lblTail = "Tail:";


// help strings
hMean = "mean of the distribution";
hStdDev = "standard deviation of the distribution";
hX = "independent variable x";
hX1 = "left x";
hX2 = "right x";
hDF = "degrees of freedom";
hNDF = "numerator degrees of freedom";
hDDF = "denominator degrees of freedom";
hArea = "area (probability)";
hTail = "left tail, right tail, inner interval, or outer tails area";


//////////////////////////////////////////////////////////////////////////////////////////
// Normal PDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT NormalPDF()
BEGIN
 LOCAL status;

 status:=INPUT(
   {
     {mu,[0],{20,50,0}},
     {sigma,[0],{20,50,1}},
     {x,[0],{20,50,2}}
   },
   "Normal PDF",
   {lblMean,lblStdDev,lblX},
   {hMean,hStdDev,hX}
  );
 IF status==0 THEN
  RETURN sCanceled;
 END;
 RETURN NORMALD(mu, sigma, x);
END;


//////////////////////////////////////////////////////////////////////////////////////////
// Normal CDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT NormalCDF()
BEGIN
 LOCAL status;

 status:=CHOOSE(tail,"Normal CDF Tail",sLeft,sRight,sInner,sOuter);
 IF status==0 THEN
  RETURN sCanceled;
 END;

 CASE
  // left
  IF tail==1 THEN 
   status:=INPUT(
    {
     {mu,[0],{20,50,0}},
     {sigma,[0],{20,50,1}},
     {x,[0],{20,50,2}}
    },
    "Normal CDF Left Tail",
    {lblMean,lblStdDev,lblX},
    {hMean,hStdDev,hX}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  NORMALD_CDF(mu, sigma, x);
  END;

  // right
  IF tail==2 THEN 
   status:=INPUT(
    {
     {mu,[0],{20,50,0}},
     {sigma,[0],{20,50,1}},
     {x,[0],{20,50,2}}
    },
    "Normal CDF Right Tail",
    {lblMean,lblStdDev,lblX},
    {hMean,hStdDev,hX}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  NORMALD_CDF(-mu, sigma, -x); // 1-NORMALD_CDF(mu, sigma, x)
  END;

  // inner
  IF tail==3 THEN 
   status:=INPUT(
    {
     {mu,[0],{20,50,0}},
     {sigma,[0],{20,50,1}},
     {x,[0],{20,50,2}},
     {x2,[0],{20,50,3}}
    },
    "Normal CDF Inner Interval",
    {lblMean,lblStdDev,lblX1,lblX2},
    {hMean,hStdDev,hX1,hX2}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  NORMALD_CDF(mu, sigma, x, x2);
  END;

  // outer
  IF tail==4 THEN 
   status:=INPUT(
    {
     {mu,[0],{20,50,0}},
     {sigma,[0],{20,50,1}},
     {x,[0],{20,50,2}},
     {x2,[0],{20,50,3}}
    },
    "Normal CDF Outer Tails",
    {lblMean,lblStdDev,lblX1,lblX2},
    {hMean,hStdDev,hX1,hX2}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  NORMALD_CDF(mu, sigma, x)+NORMALD_CDF(-mu, sigma, -x2); //1-NORMALD_CDF(mu, sigma, x, x2)
  END;

  DEFAULT RETURN sInvalidTail;
 END;
END;



//////////////////////////////////////////////////////////////////////////////////////////
// Normal Inverse CDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT NormalInv()
BEGIN
 LOCAL status;

 status:=INPUT(
   {
     {mu,[0],{20,50,0}},
     {sigma,[0],{20,50,1}},
     {area,[0],{20,50,2}},
     {tail,{sLeft,sRight,sInner,sOuter},{20,25,3}}
   },
   "Normal Inverse CDF",
   {lblMean,lblStdDev,lblArea,lblTail},
   {hMean,hStdDev,hArea,hTail}
  );
 IF status==0 THEN
  RETURN sCanceled;
 END;

 CASE
  // left
  IF tail==1 THEN RETURN NORMALD_ICDF(mu,sigma,area); END;
  // right
  IF tail==2 THEN RETURN -NORMALD_ICDF(-mu,sigma,area); END; // NORMALD_ICDF(mu,sigma,1-area)
  // inner
  IF tail==3 THEN RETURN {NORMALD_ICDF(mu,sigma,(1-area)/2),-NORMALD_ICDF(-mu,sigma,(1-area)/2)}; END // NORMALD_ICDF(mu,sigma,(1+area)/2)
  // outer (2 tail)
  IF tail==4 THEN RETURN {NORMALD_ICDF(mu,sigma,area/2),-NORMALD_ICDF(-mu,sigma,area/2)}; END // NORMALD_ICDF(mu,sigma,1-area/2)
  DEFAULT RETURN sInvalidTail;
 END;
END;


//////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////


//////////////////////////////////////////////////////////////////////////////////////////
// Student-t PDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT StudentPDF()
BEGIN
 LOCAL status;

 status:=INPUT(
   {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,1}}
   },
   "Student-t PDF",
   {lblDF,lblX},
   {hDF,hX}
  );
 IF status==0 THEN
  RETURN sCanceled;
 END;
 RETURN STUDENT(df, x);
END;

//////////////////////////////////////////////////////////////////////////////////////////
// Student-t CDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT StudentCDF()
BEGIN
 LOCAL status;

 status:=CHOOSE(tail,"Student-t CDF Tail",sLeft,sRight,sInner,sOuter);
 IF status==0 THEN
  RETURN sCanceled;
 END;

 CASE
  // left
  IF tail==1 THEN 
   status:=INPUT(
    {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,1}}
    },
    "Student-t CDF Left Tail",
    {lblDF,lblX},
    {hDF,hX}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  STUDENT_CDF(df, x);
  END;

  // right
  IF tail==2 THEN 
   status:=INPUT(
    {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,1}}
    },
    "Student-t CDF Right Tail",
    {lblDF,lblX},
    {hDF,hX}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN STUDENT_CDF(df, -x); // 1-STUDENT_CDF(df, x)
  END;


  // inner
  IF tail==3 THEN 
   status:=INPUT(
    {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,2}},
     {x2,[0],{20,50,3}}
    },
    "Student-t CDF Inner Interval",
    {lblDF,lblX1,lblX2},
    {hDF,hX1,hX2}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  STUDENT_CDF(df, x, x2);
  END;

  // outer
  IF tail==4 THEN 
   status:=INPUT(
    {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,2}},
     {x2,[0],{20,50,3}}
    },
    "Student-t CDF Outer Tails",
    {lblDF,lblX1,lblX2},
    {hDF,hX1,hX2}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  STUDENT_CDF(df, x) + STUDENT_CDF(df, -x2); // 1-STUDENT_CDF(df, x, x2)
  END;
 END;
END;


/////////////////////////////////////////////
// Student-t Inverse CDF
/////////////////////////////////////////////
EXPORT StudentInv()
BEGIN
 LOCAL status, t;

 status:=INPUT(
   {
     {df,[0],{20,50,0}},
     {area,[0],{20,50,1}},
     {tail,{sLeft,sRight,sInner,sOuter},{20,25,2}}
   },
   "Student-t Inverse CDF",
   {lblDF,lblArea,lblTail},
   {hDF,hArea,hTail}
  );
 IF status==0 THEN
  RETURN sCanceled;
 END;
 CASE
  // left
  IF tail==1 THEN RETURN STUDENT_ICDF(df,area); END;
  // right
  IF tail==2 THEN RETURN -STUDENT_ICDF(df,area); END;
  // inner
  IF tail==3 THEN 
    t:=STUDENT_ICDF(df,(1-area)/2);
    RETURN {t,-t};
  END
  // outer (2 tail)
  IF tail==4 THEN
   t:=STUDENT_ICDF(df,area/2);
   RETURN {t,-t}; 
  END
  DEFAULT RETURN sInvalidTail;
 END;
END;


//////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////

//////////////////////////////////////////////////////////////////////////////////////////
// Chi Square PDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT ChiSqPDF()
BEGIN
 LOCAL status;

 status:=INPUT(
   {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,1}}
   },
   "Chi Square PDF",
   {lblDF,lblX},
   {hDF,hX}
  );
 IF status==0 THEN
  RETURN sCanceled;
 END;
 RETURN CHISQUARE(df, x);
END;


//////////////////////////////////////////////////////////////////////////////////////////
// Chi Square CDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT ChiSqCDF()
BEGIN
 LOCAL status;

 status:=CHOOSE(tail,"Chi Square CDF Tail",sLeft,sRight,sInner,sOuter);
 IF status==0 THEN
  RETURN sCanceled;
 END;

 CASE
  // left
  IF tail==1 THEN 
   status:=INPUT(
    {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,1}}
    },
    "Chi Square CDF Left Tail",
    {lblDF,lblX},
    {hDF,hX}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  CHISQUARE_CDF(df, x);
  END;

  // right
  IF tail==2 THEN 
   status:=INPUT(
    {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,1}}
    },
    "Chi Square CDF Right Tail",
    {lblDF,lblX},
    {hDF,hX}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN 1-CHISQUARE_CDF(df, x);
  END;

  // inner
  IF tail==3 THEN 
   status:=INPUT(
    {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,2}},
     {x2,[0],{20,50,3}}
    },
    "Chi Square CDF Inner Interval",
    {lblDF,lblX1,lblX2},
    {hDF,hX1,hX2}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN CHISQUARE_CDF(df, x, x2);
  END;

  // outer
  IF tail==4 THEN 
   status:=INPUT(
    {
     {df,[0],{20,50,0}},
     {x,[0],{20,50,2}},
     {x2,[0],{20,50,3}}
    },
    "Chi Square CDF Outer Tails",
    {lblDF,lblX1,lblX2},
    {hDF,hX1,hX2}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN 1-CHISQUARE_CDF(df, x, x2);
  END;
 END;
END;



/////////////////////////////////////////////
// Chi Square Inverse CDF
/////////////////////////////////////////////

EXPORT ChiSqInv()
BEGIN
 LOCAL status;

 status:=INPUT(
   {
     {df,[0],{20,50,0}},
     {area,[0],{20,50,1}},
     {tail,{sLeft,sRight,sInner,sOuter},{20,25,2}}
   },
   "Inverse Chi Square CDF",
   {lblDF,lblArea,lblTail},
   {hDF,hArea,hTail}
  );
 IF status==0 THEN
  RETURN sCanceled;
 END;

 CASE
  // left
  IF tail==1 THEN RETURN CHISQUARE_ICDF(df,area); END;
  // right
  IF tail==2 THEN RETURN CHISQUARE_ICDF(df,1-area); END;
  // inner
  IF tail==3
   THEN RETURN {CHISQUARE_ICDF(df,(1-area)/2),CHISQUARE_ICDF(df,(1+area)/2)}; END
  // outer (2 tail)
  IF tail==4 THEN RETURN {CHISQUARE_ICDF(df,area/2),CHISQUARE_ICDF(df,1-area/2)}; END
  DEFAULT
   RETURN sInvalidTail;
 END;
END;



//////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////

//////////////////////////////////////////////////////////////////////////////////////////
// Fisher PDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT FisherPDF()
BEGIN
 LOCAL status;

 status:=INPUT(
   {
     {df,[0],{25,50,0}},
     {ddf,[0],{25,50,1}},
     {x,[0],{25,50,2}}
   },
   "Chi Square PDF",
   {lblNDF,lblDDF,lblX},
   {hNDF,hDDF,hX}
  );
 IF status==0 THEN
  RETURN sCanceled;
 END;
 RETURN FISHER(df,ddf,x);
END;


//////////////////////////////////////////////////////////////////////////////////////////
// Fisher CDF
//////////////////////////////////////////////////////////////////////////////////////////

EXPORT FisherCDF()
BEGIN
 LOCAL status;

 status:=CHOOSE(tail,"F CDF Tail",sLeft,sRight,sInner,sOuter);
 IF status==0 THEN
  RETURN sCanceled;
 END;

 CASE
  // left
  IF tail==1 THEN 
   status:=INPUT(
    {
     {df,[0],{25,50,0}},
     {ddf,[0],{25,50,1}},
     {x,[0],{25,50,2}}
    },
    "F CDF Left Tail",
    {lblNDF,lblDDF,lblX},
    {hNDF,hDDF,hX}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN  FISHER_CDF(df,ddf,x);
  END;

  // right
  IF tail==2 THEN 
   status:=INPUT(
    {
     {df,[0],{25,50,0}},
     {ddf,[0],{25,50,1}},
     {x,[0],{25,50,2}}
    },
    "F CDF Right Tail",
   {lblNDF,lblDDF,lblX},
    {hNDF,hDDF,hX}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN 1-FISHER_CDF(df,ddf,x);
  END;

  // inner
  IF tail==3 THEN 
   status:=INPUT(
    {
     {df,[0],{25,50,0}},
     {ddf,[0],{25,50,1}},
     {x,[0],{25,50,2}},
     {x2,[0],{25,50,3}}
    },
    "F CDF Inner Interval",
    {lblNDF,lblDDF,lblX1,lblX2},
    {hNDF,hDDF,hX1,hX2}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN FISHER_CDF(df,ddf,x,x2);
  END;

  // outer
  IF tail==4 THEN 
   status:=INPUT(
    {
     {df,[0],{25,50,0}},
     {ddf,[0],{25,50,1}},
     {x,[0],{25,50,2}},
     {x2,[0],{25,50,3}}
    },
    "F CDF Outer Tails",
    {lblNDF,lblDDF,lblX1,lblX2},
    {hNDF,hDDF,hX1,hX2}
   );   
   IF status==0 THEN
    RETURN sCanceled;
   END;
   RETURN 1-FISHER_CDF(df,ddf,x,x2);
  END;
 END;
END;


/////////////////////////////////////////////
// Fisher Inverse CDF
/////////////////////////////////////////////

EXPORT FisherInv()
BEGIN
 LOCAL status;

 status:=INPUT(
   {
     {df,[0],{25,50,0}},
     {ddf,[0],{25,50,1}},
     {area,[0],{25,50,2}},
     {tail,{sLeft,sRight,sInner,sOuter},{25,25,3}}
   },
   "Inverse F Distribution CDF",
   {lblNDF,lblDDF,lblArea,lblTail},
   {hNDF,hDDF,hArea,hTail}
  );
 IF status==0 THEN
  RETURN sCanceled;
 END;
 CASE
  // left
  IF tail==1 THEN RETURN FISHER_ICDF(df,ddf,area); END;
  // right
  IF tail==2 THEN RETURN FISHER_ICDF(df,ddf,1-area); END;
  // inner
  IF tail==3
   THEN RETURN {FISHER_ICDF(df,ddf,(1-area)/2),FISHER_ICDF(df,ddf,(1+area)/2)}; END
  // outer (2 tail)
  IF tail==4 THEN RETURN {FISHER_ICDF(df,ddf,area/2),FISHER_ICDF(df,ddf,1-area/2)}; END
  DEFAULT
   RETURN sInvalidTail;
 END;
END;