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statistical functions

Edit detail for statistical functions revision 2 of 2

	1 2
Editor: test1 Time: 2015/06/01 22:24:20 GMT+0
Note:

changed:
-  A: Collection(S) with (finiteAggregate)
  A: Join(Collection(S), finiteAggregate)

changed:
-			center_!: A -> A
			center!: A -> A

changed:
-				stdize_!: A -> A
				stdize!: A -> A

added:


changed:
-					j := map(#1-i,m)
					j := map(xx +-> xx-i, m)

changed:
-					map((#1-i)/k,m)
					map(xx +-> (xx-i)/k,m)

changed:
-					stdize_!(m)==
					stdize!(m)==

changed:
-						j := map(#1-i,m)
						j := map(xx +-> xx - i, m)

changed:
-						map_!((#1-i)/k,m)
-
-
						map!(xx +-> (xx - i)/k, m)

changed:
-				j2 := reduce("+", map(#1*#1,i))
				j2 := reduce("+", map(xx +-> xx*xx,i))

changed:
-					i := map(#1-me,m)
					i := map(xx +-> xx - me, m)

changed:
-					j2 := reduce("+", map(#1*#1,i))
					j2 := reduce("+", map(xx +-> xx*xx,i))

changed:
-					map((#1-me)/k,m)
					map(xx +-> (xx -me)/k,m)

changed:
-	     				stdize_!(m)==
	     				stdize!(m)==

changed:
-						i := map(#1-me,m)
						i := map(xx +-> xx - me,m)

changed:
-						j2 := reduce("+", map(#1*#1,i))
						j2 := reduce("+", map(xx +-> xx*xx, i))

changed:
-						map_!((#1-me)/k,m)
						map!(xx +->(xx - me)/k, m)

changed:
-			i := map(1::S/#1,m)
			i := map(xx +-> 1::S/xx, m)

changed:
-			i := map(#1**n, m)
			i := map(xx +-> xx^n, m)

changed:
-			map(#1-i,m)
			map(xx +-> xx - i, m)

changed:
-	     		center_!(m)==
	     		center!(m)==

changed:
-				map_!(#1-i,m)
				map!(xx +-> xx - i, m)

changed:
-  A: Collection(S) with (finiteAggregate)
  A: Join(Collection(S), finiteAggregate)

changed:
-		i := map(#1**n, m)
		i := map(xx +-> xx^n, m)

added:



changed:
-			center_!: M -> M
			center!: M -> M

changed:
-				stdize_!: M -> M
				stdize!: M -> M

removed:
-	import Lisp

changed:
-				setelt(ret,i-j,fx(column(m,i)))
				setelt!(ret,i-j,fx(column(m,i)))

changed:
-			        ret
				ret

changed:
-					setelt(ret,i-j,moment(column(m,i),pow)$StatPackage(S,Col))
				    setelt!(ret,i,moment(column(m,i),pow)$StatPackage(S,Col))

changed:
-					setColumn_!(ret,i-j,center_!(column(m,i))$StatPackage(S,Col))
-				ret
-     			center_!(m)==
					setColumn!(ret,i-j,center!(column(m,i))$StatPackage(S,Col))
				ret
     			center!(m)==

changed:
-					setColumn_!(m,i-j,center_!(column(m,i))$StatPackage(S,Col))
					setColumn!(m,i-j,center!(column(m,i))$StatPackage(S,Col))

changed:
-						setColumn_!(ret,i-j,stdize_!(column(m,i))$StatPackage(S,Col))
						setColumn!(ret,i-j,stdize!(column(m,i))$StatPackage(S,Col))

changed:
-     				stdize_!(m)==
     				stdize!(m)==

changed:
-						setColumn_!(m,i-j,stdize_!(column(m,i))$StatPackage(S,Col))
						setColumn!(m,i-j,stdize!(column(m,i))$StatPackage(S,Col))

removed:
-

added:


removed:
--- beware, the following is not mathematically justified since
--- median use ordering from OrderedSet (and not OrderedRing)

changed:
-median c
mean c

Anonymous shared the following library of statistical functions with us. Many thanks! (He added, that they are not checked...)

fricas

)abbrev package STAT StatPackage
++ Description:
++ This package exports statistic utilities
StatPackage(S,A) : Exports == Implementation where 
  S: SetCategory
  A: Join(Collection(S), finiteAggregate)
  Exports == with
        if A has FiniteLinearAggregate(S) and S has OrderedSet then
                median: A -> S
                ++ median(a) median of a collection (ordering from OrderedSet)
        if S has Field then
                mean: A -> S
                ++ mean(a) arithmetic mean of a collection
                hmean: A -> S
                ++ hmean(a) harmonic mean of a collection
                moment: (A,Integer) -> S
                ++ moment(a,i) i nth moment of a collection
                variance: A -> S
                ++ variance(a) variance of a collection
                center: A -> A
                ++ center(a) center collection
                if A has shallowlyMutable then
                        center!: A -> A
                        ++ center!(a) center collection
                if S has RadicalCategory then
                        gmean: A -> S
                        ++ gmean(a) geometric mean of a collection
                        stdev: A -> S
                        ++ stdev(a) root mean square of a collection
                        stdize: A -> A
                        ++ stdize(a) standardize a collection   
                        if A has shallowlyMutable then
                                stdize!: A -> A
                                ++ stdize!(a) standardize a collection  
  Implementation == add

        if A has FiniteLinearAggregate(S) and S has OrderedSet then
                median(m)==
                        n := sort(m)
                        i:= divide(#m,2)
                        if (zero? i.remainder) then
                                j:= elt(n,i.quotient+minIndex(m)-1)
                        else
                                j:= elt(n,i.quotient+minIndex(m))
                        j

        if S has Field then
                if A has OneDimensionalArrayAggregate(S) then
                        sums: A ->List S
                        sums(m)==
                                j:=0::S
                                j2:=0::S
                                for i in minIndex(m)..maxIndex(m) repeat
                                        h:= elt(m,i)
                                        j := j + h
                                        j2 := j2 + h*h
                                [j,j2]
                        variance(m)==
                                i := center(m)
                                s := sums(i)                
                                k := (s.2 - s.1/#m::S)/(#m::S - 1::S)
                                k
                        if S has RadicalCategory then
                                stdize(m)==
                                        i := mean(m)
                                        j := map(xx +-> xx-i, m)
                                        s := sums(j)
                                        k := sqrt((s.2 - s.1/#m::S)/(#m::S - 1::S))
                                        map(xx +-> (xx-i)/k,m)
                                if A has shallowlyMutable then
                                        stdize!(m)==
                                                i := mean(m)
                                                j := map(xx +-> xx - i, m)
                                                s := sums(j)
                                                k := sqrt((s.2 - s.1/#m::S)/(#m::S - 1::S))
                                                map!(xx +-> (xx - i)/k, m)

                else
                        variance(m)==
                                i := center(m)
                                j := reduce("+",i)
                                j2 := reduce("+", map(xx +-> xx*xx,i))
                                k := (j2 - j/#m::S)/(#m::S - 1::S)
                                k
                        if S has RadicalCategory then
                                stdize(m)==
                                        me:= mean(m)
                                        i := map(xx +-> xx - me, m)
                                        j := reduce("+",i)
                                        j2 := reduce("+", map(xx +-> xx*xx,i))
                                        k := sqrt((j2 - j/#m::S)/(#m::S - 1::S))
                                        map(xx +-> (xx -me)/k,m)
                                if A has shallowlyMutable then
                                        stdize!(m)==
                                                me:= mean(m)
                                                i := map(xx +-> xx - me,m)
                                                j := reduce("+",i)
                                                j2 := reduce("+", map(xx +-> xx*xx, i))
                                                k := sqrt((j2 - j/#m::S)/(#m::S - 1::S))
                                                map!(xx +->(xx - me)/k, m)

                if A has FiniteLinearAggregate(S) and S has OrderedSet then
                        median(m)==
                                n := sort(m)
                                min := minIndex(m)
                                i:= divide(#m,2)
                                if (zero? i.remainder) then
                                        j:= (elt(n,i.quotient+min-1)+elt(n,i.quotient+min))/2::S
                                else
                                        j:=elt(n,i.quotient+min)
                                j
                mean(m)==
                        i := reduce("+", m)
                        (i / (#m::S))

                hmean(m)==
                        i := map(xx +-> 1::S/xx, m)
                        j := reduce("+", i)
                        ((#m::S) / j)

                moment(m,n)==
                        n = 0 => 1
                        n = 1 => mean(m)
                        i := map(xx +-> xx^n, m)
                        j := reduce("+",i)
                        (j / (#m::S))

                center(m)==
                        i := mean(m)
                        map(xx +-> xx - i, m)

                if A has shallowlyMutable then
                        center!(m)==
                                i := mean(m)
                                map!(xx +-> xx - i, m)
                                m
                if S has RadicalCategory then
                        gmean(m)==
                                i := reduce("*", m)
                                nthRoot(i,#m)

                        stdev(m)==
                                sqrt(variance(m))

fricas

)abbrev package IDSTAT IntegralDomainStatPackage
++ Description:
++ This package exports statistic utilities over IntegralDomain
IntegralDomainStatPackage(S,A) : Exports == Implementation where 
  S: IntegralDomain
  A: Join(Collection(S), finiteAggregate)
  Exports == with
        mean: A -> Fraction(S)
        ++ mean(a) arithmetic mean of a collection
        moment: (A,NonNegativeInteger) -> Fraction(S)
        ++ moment(m,n) nth moment of a collection

  Implementation == add
        mean(m)==
                i := reduce("+", m)
                i / #m::S
        moment(m,n)==
                n = 0 => 1
                n = 1 => mean(m)
                i := map(xx +-> xx^n, m)
                j := reduce("+",i)
                j / #m::S

fricas

)abbrev package MSTAT MatrixStatPackage
++ Description:
++ This package exports statistic utilities on two dimensional arrays
++ Function are applied column by column
MatrixStatPackage(S,Row,Col,M) : Exports == Implementation where 
  S: SetCategory
  Row : FiniteLinearAggregate S
  Col : FiniteLinearAggregate S
  M   : TwoDimensionalArrayCategory(S,Row,Col)
  Exports == with
        if Col has shallowlyMutable then
                if S has OrderedSet then
                        median: M -> Col
                        ++ median(a) median of a two dimensional array (ordering from OrderedSet)
                if S has Field then
                        mean: M -> Col
                        ++ mean(a) arithmetic mean of a two dimensional array
                        hmean: M -> Col
                        ++ hmean(a) harmonic mean of a two dimensional array
                        variance: M -> Col
                        ++ variance(a) variance of a two dimensional array
                        moment: (M,Integer) -> Col
                        ++ moment(a,i) i nth moment of a two dimensional array
                        center: M -> M
                        ++ center(a) center two dimensional array
                        center!: M -> M
                        ++ center!(a) center two dimensional array
                        if M has MatrixCategory(S,Row,Col) then
                                cov:  M -> M
                                ++ cov(a): covariance matrix
                        if S has RadicalCategory then
                                gmean: M -> Col
                                ++ gmean(a) geometric mean of a two dimensional array
                                stdev: M -> Col
                                ++ stdev(a) root mean square of a two dimensional array
                                stdize: M -> M
                                ++ stdize(a) standardize two dimensional array
                                stdize!: M -> M
                                ++ stdize!(a) standardize two dimensional array
                                if M has MatrixCategory(S,Row,Col) then
                                        cor:  M -> M
                                        ++ cor(a): correlation matrix

  Implementation == add
        import StatPackage(S,Col)
        if Col has shallowlyMutable then
                colReduce: (Col -> S, M) -> Col
                colReduce(fx,m)==
                        ret : Col := new(ncols(m),NIL$Lisp)
                        j := minColIndex(m) - 1
                        for i in j+1..maxColIndex(m) repeat
                                setelt!(ret,i-j,fx(column(m,i)))
                        ret
                if S has OrderedSet then
                        median(m) ==
                                ret := colReduce(median$StatPackage(S,Col),m)
                                ret
                if S has Field then
                        mean(m)==
                                ret := colReduce(mean$StatPackage(S,Col),m)
                                ret
                        hmean(m)==
                                ret := colReduce(hmean$StatPackage(S,Col),m)
                                ret
                        variance(m)==
                                ret := colReduce(variance$StatPackage(S,Col),m)
                                ret
                        moment(m,pow)==
                                ret : Col := new(ncols(m),NIL$Lisp)
                                j := minColIndex(m) - 1
                                for i in j+1..maxColIndex(m) repeat
                                    setelt!(ret,i,moment(column(m,i),pow)$StatPackage(S,Col))
                                ret
                        center(m)==
                                ret : M := new(nrows(m),ncols(m),NIL$Lisp)
                                j := minColIndex(m) - 1
                                for i in j+1..maxColIndex(m) repeat
                                        setColumn!(ret,i-j,center!(column(m,i))$StatPackage(S,Col))
                                ret
                        center!(m)==
                                j := minColIndex(m) - 1
                                for i in j+1..maxColIndex(m) repeat
                                        setColumn!(m,i-j,center!(column(m,i))$StatPackage(S,Col))
                                m
                        if M has MatrixCategory(S,Row,Col) then
                                cov(m)==
                                        ret := center(m)
                                        transpose(ret/(nrows(m)-1)::S) * ret

                        if S has RadicalCategory then
                                gmean(m)==
                                        colReduce(gmean$StatPackage(S,Col),m)
                                stdev(m)==
                                        colReduce(stdev$StatPackage(S,Col),m)
                                stdize(m)==
                                        ret : M := new(nrows(m),ncols(m),NIL$Lisp)
                                        j := minColIndex(m) - 1
                                        for i in j+1..maxColIndex(m) repeat
                                                setColumn!(ret,i-j,stdize!(column(m,i))$StatPackage(S,Col))
                                        ret
                                stdize!(m)==
                                        j := minColIndex(m) - 1
                                        for i in j+1..maxColIndex(m) repeat
                                                setColumn!(m,i-j,stdize!(column(m,i))$StatPackage(S,Col))
                                        m
                                if M has MatrixCategory(S,Row,Col) then
                                        cor(m)==
                                                ret := stdize(m)
                                                (transpose(ret/((nrows(m)-1)::S)) * ret)

fricas

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/172717192283825040-25px.001.spad
      using old system compiler.
   STAT abbreviates package StatPackage 
------------------------------------------------------------------------
   initializing NRLIB STAT for StatPackage 
   compiling into NRLIB STAT 
****** Domain: A already in scope
****** Domain: A already in scope
augmenting A: (FiniteLinearAggregate S)
****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting $: (SIGNATURE $ median (S A))
   compiling exported median : A -> S
Time: 0.03 SEC.

****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (S A))
augmenting $: (SIGNATURE $ hmean (S A))
augmenting $: (SIGNATURE $ moment (S A (Integer)))
augmenting $: (SIGNATURE $ variance (S A))
augmenting $: (SIGNATURE $ center (A A))
****** Domain: A already in scope
augmenting A: (OneDimensionalArrayAggregate S)
   compiling local sums : A -> List S
Time: 0.02 SEC.

   compiling exported variance : A -> S
Time: 0 SEC.

****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting $: (SIGNATURE $ gmean (S A))
augmenting $: (SIGNATURE $ stdev (S A))
augmenting $: (SIGNATURE $ stdize (A A))
   compiling exported stdize : A -> A
Time: 0.01 SEC.

   compiling exported stdize! : A -> A
Time: 0 SEC.

   compiling exported variance : A -> S
Time: 0 SEC.

****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting $: (SIGNATURE $ gmean (S A))
augmenting $: (SIGNATURE $ stdev (S A))
augmenting $: (SIGNATURE $ stdize (A A))
   compiling exported stdize : A -> A
Time: 0 SEC.

****** Domain: A already in scope
augmenting A: (shallowlyMutable)
augmenting $: (SIGNATURE $ stdize! (A A))
augmenting $: (SIGNATURE $ center! (A A))
   compiling exported stdize! : A -> A
Time: 0.02 SEC.

****** Domain: A already in scope
augmenting A: (FiniteLinearAggregate S)
****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting $: (SIGNATURE $ median (S A))
   compiling exported median : A -> S
Time: 0 SEC.

   compiling exported mean : A -> S
Time: 0 SEC.

   compiling exported hmean : A -> S
Time: 0 SEC.

   compiling exported moment : (A,Integer) -> S
Time: 0 SEC.

   compiling exported center : A -> A
Time: 0 SEC.

****** Domain: A already in scope
augmenting A: (shallowlyMutable)
augmenting $: (SIGNATURE $ center! (A A))
   compiling exported center! : A -> A
Time: 0 SEC.

****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting $: (SIGNATURE $ gmean (S A))
augmenting $: (SIGNATURE $ stdev (S A))
augmenting $: (SIGNATURE $ stdize (A A))
   compiling exported gmean : A -> S
Time: 0 SEC.

   compiling exported stdev : A -> S
Time: 0 SEC.

****** Domain: A already in scope
augmenting A: (FiniteLinearAggregate S)
****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting $: (SIGNATURE $ median (S A))
****** Domain: A already in scope
augmenting A: (shallowlyMutable)
****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (S A))
augmenting $: (SIGNATURE $ hmean (S A))
augmenting $: (SIGNATURE $ moment (S A (Integer)))
augmenting $: (SIGNATURE $ variance (S A))
augmenting $: (SIGNATURE $ center (A A))
augmenting $: (SIGNATURE $ center! (A A))
****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting $: (SIGNATURE $ gmean (S A))
augmenting $: (SIGNATURE $ stdev (S A))
augmenting $: (SIGNATURE $ stdize (A A))
augmenting $: (SIGNATURE $ stdize! (A A))
****** Domain: A already in scope
augmenting A: (shallowlyMutable)
****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (S A))
augmenting $: (SIGNATURE $ hmean (S A))
augmenting $: (SIGNATURE $ moment (S A (Integer)))
augmenting $: (SIGNATURE $ variance (S A))
augmenting $: (SIGNATURE $ center (A A))
augmenting $: (SIGNATURE $ center! (A A))
****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (S A))
augmenting $: (SIGNATURE $ hmean (S A))
augmenting $: (SIGNATURE $ moment (S A (Integer)))
augmenting $: (SIGNATURE $ variance (S A))
augmenting $: (SIGNATURE $ center (A A))
****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting $: (SIGNATURE $ gmean (S A))
augmenting $: (SIGNATURE $ stdev (S A))
augmenting $: (SIGNATURE $ stdize (A A))
****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (S A))
augmenting $: (SIGNATURE $ hmean (S A))
augmenting $: (SIGNATURE $ moment (S A (Integer)))
augmenting $: (SIGNATURE $ variance (S A))
augmenting $: (SIGNATURE $ center (A A))
(time taken in buildFunctor:  0)

;;;     ***       |StatPackage| REDEFINED

;;;     ***       |StatPackage| REDEFINED
Time: 0.02 SEC.

   Warnings: 
      [1] median:  remainder has no value
      [2] median:  quotient has no value

   Cumulative Statistics for Constructor StatPackage
      Time: 0.10 seconds

   finalizing NRLIB STAT 
   Processing StatPackage for Browser database:
--------constructor---------
--------(median (S A))---------
--------(mean (S A))---------
--------(hmean (S A))---------
--------(moment (S A (Integer)))---------
--------(variance (S A))---------
--------(center (A A))---------
--------(center! (A A))---------
--------(gmean (S A))---------
--------(stdev (S A))---------
--------(stdize (A A))---------
--------(stdize! (A A))---------
; compiling file "/var/aw/var/LatexWiki/STAT.NRLIB/STAT.lsp" (written 24 FEB 2018 04:52:50 AM):

; /var/aw/var/LatexWiki/STAT.NRLIB/STAT.fasl written
; compilation finished in 0:00:00.143
------------------------------------------------------------------------
   StatPackage is now explicitly exposed in frame initial 
   StatPackage will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/STAT.NRLIB/STAT

   IDSTAT abbreviates package IntegralDomainStatPackage 
------------------------------------------------------------------------
   initializing NRLIB IDSTAT for IntegralDomainStatPackage 
   compiling into NRLIB IDSTAT 
****** Domain: A already in scope
   compiling exported mean : A -> Fraction S
Time: 0 SEC.

   compiling exported moment : (A,NonNegativeInteger) -> Fraction S
Time: 0.01 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |IntegralDomainStatPackage| REDEFINED

;;;     ***       |IntegralDomainStatPackage| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor IntegralDomainStatPackage
      Time: 0.01 seconds

   finalizing NRLIB IDSTAT 
   Processing IntegralDomainStatPackage for Browser database:
--------constructor---------
--------(mean ((Fraction S) A))---------
--------(moment ((Fraction S) A (NonNegativeInteger)))---------
; compiling file "/var/aw/var/LatexWiki/IDSTAT.NRLIB/IDSTAT.lsp" (written 24 FEB 2018 04:52:50 AM):

; /var/aw/var/LatexWiki/IDSTAT.NRLIB/IDSTAT.fasl written
; compilation finished in 0:00:00.055
------------------------------------------------------------------------
   IntegralDomainStatPackage is now explicitly exposed in frame initial

   IntegralDomainStatPackage will be automatically loaded when needed 
      from /var/aw/var/LatexWiki/IDSTAT.NRLIB/IDSTAT

   MSTAT abbreviates package MatrixStatPackage 
------------------------------------------------------------------------
   initializing NRLIB MSTAT for MatrixStatPackage 
   compiling into NRLIB MSTAT 
   importing StatPackage(S,Col)
****** Domain: Col already in scope
augmenting Col: (shallowlyMutable)
   compiling local colReduce : (Col -> S,M) -> Col
Time: 0 SEC.

****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting $: (SIGNATURE $ median (Col M))
   compiling exported median : M -> Col
Time: 0 SEC.

****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (Col M))
augmenting $: (SIGNATURE $ hmean (Col M))
augmenting $: (SIGNATURE $ variance (Col M))
augmenting $: (SIGNATURE $ moment (Col M (Integer)))
augmenting $: (SIGNATURE $ center (M M))
augmenting $: (SIGNATURE $ center! (M M))
   compiling exported mean : M -> Col
Time: 0 SEC.

   compiling exported hmean : M -> Col
Time: 0 SEC.

   compiling exported variance : M -> Col
Time: 0 SEC.

   compiling exported moment : (M,Integer) -> Col
Time: 0 SEC.

   compiling exported center : M -> M
Time: 0.01 SEC.

   compiling exported center! : M -> M
Time: 0.01 SEC.

****** Domain: M already in scope
augmenting M: (MatrixCategory S Row Col)
augmenting $: (SIGNATURE $ cov (M M))
   compiling exported cov : M -> M
Time: 0 SEC.

****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting $: (SIGNATURE $ gmean (Col M))
augmenting $: (SIGNATURE $ stdev (Col M))
augmenting $: (SIGNATURE $ stdize (M M))
augmenting $: (SIGNATURE $ stdize! (M M))
   compiling exported gmean : M -> Col
Time: 0.01 SEC.

   compiling exported stdev : M -> Col
Time: 0 SEC.

   compiling exported stdize : M -> M
Time: 0 SEC.

   compiling exported stdize! : M -> M
Time: 0.01 SEC.

****** Domain: M already in scope
augmenting M: (MatrixCategory S Row Col)
augmenting $: (SIGNATURE $ cor (M M))
augmenting $: (SIGNATURE $ cov (M M))
   compiling exported cor : M -> M
Time: 0.01 SEC.

****** Domain: Col already in scope
augmenting Col: (shallowlyMutable)
****** Domain: M already in scope
augmenting M: (MatrixCategory S Row Col)
****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (Col M))
augmenting $: (SIGNATURE $ hmean (Col M))
augmenting $: (SIGNATURE $ variance (Col M))
augmenting $: (SIGNATURE $ moment (Col M (Integer)))
augmenting $: (SIGNATURE $ center (M M))
augmenting $: (SIGNATURE $ center! (M M))
augmenting $: (SIGNATURE $ cov (M M))
****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting $: (SIGNATURE $ gmean (Col M))
augmenting $: (SIGNATURE $ stdev (Col M))
augmenting $: (SIGNATURE $ stdize (M M))
augmenting $: (SIGNATURE $ stdize! (M M))
augmenting $: (SIGNATURE $ cor (M M))
****** Domain: Col already in scope
augmenting Col: (shallowlyMutable)
****** Domain: M already in scope
augmenting M: (MatrixCategory S Row Col)
****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (Col M))
augmenting $: (SIGNATURE $ hmean (Col M))
augmenting $: (SIGNATURE $ variance (Col M))
augmenting $: (SIGNATURE $ moment (Col M (Integer)))
augmenting $: (SIGNATURE $ center (M M))
augmenting $: (SIGNATURE $ center! (M M))
augmenting $: (SIGNATURE $ cov (M M))
****** Domain: Col already in scope
augmenting Col: (shallowlyMutable)
****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (Col M))
augmenting $: (SIGNATURE $ hmean (Col M))
augmenting $: (SIGNATURE $ variance (Col M))
augmenting $: (SIGNATURE $ moment (Col M (Integer)))
augmenting $: (SIGNATURE $ center (M M))
augmenting $: (SIGNATURE $ center! (M M))
****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting $: (SIGNATURE $ gmean (Col M))
augmenting $: (SIGNATURE $ stdev (Col M))
augmenting $: (SIGNATURE $ stdize (M M))
augmenting $: (SIGNATURE $ stdize! (M M))
****** Domain: Col already in scope
augmenting Col: (shallowlyMutable)
****** Domain: S already in scope
augmenting S: (Field)
augmenting $: (SIGNATURE $ mean (Col M))
augmenting $: (SIGNATURE $ hmean (Col M))
augmenting $: (SIGNATURE $ variance (Col M))
augmenting $: (SIGNATURE $ moment (Col M (Integer)))
augmenting $: (SIGNATURE $ center (M M))
augmenting $: (SIGNATURE $ center! (M M))
****** Domain: Col already in scope
augmenting Col: (shallowlyMutable)
****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting $: (SIGNATURE $ median (Col M))
(time taken in buildFunctor:  0)

;;;     ***       |MatrixStatPackage| REDEFINED

;;;     ***       |MatrixStatPackage| REDEFINED
Time: 0.01 SEC.

   Cumulative Statistics for Constructor MatrixStatPackage
      Time: 0.06 seconds

   finalizing NRLIB MSTAT 
   Processing MatrixStatPackage for Browser database:
--------constructor---------
--------(median (Col M))---------
--------(mean (Col M))---------
--------(hmean (Col M))---------
--------(variance (Col M))---------
--------(moment (Col M (Integer)))---------
--------(center (M M))---------
--------(center! (M M))---------
--------(cov (M M))---------
--------(gmean (Col M))---------
--------(stdev (Col M))---------
--------(stdize (M M))---------
--------(stdize! (M M))---------
--------(cor (M M))---------
; compiling file "/var/aw/var/LatexWiki/MSTAT.NRLIB/MSTAT.lsp" (written 24 FEB 2018 04:52:51 AM):

; /var/aw/var/LatexWiki/MSTAT.NRLIB/MSTAT.fasl written
; compilation finished in 0:00:00.139
------------------------------------------------------------------------
   MatrixStatPackage is now explicitly exposed in frame initial 
   MatrixStatPackage will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MSTAT.NRLIB/MSTAT

And

fricas

a:= ["a","c","d","g","z","a","d","g","f"]

$\label{eq1}\begin{array}{@{}l} \displaystyle \left[ \verb#"a"# , \: \verb#"c"# , \: \verb#"d"# , \: \verb#"g"# , \: \verb#"z"# , \: \right. \ \ \displaystyle \left.\verb#"a"# , \: \verb#"d"# , \: \verb#"g"# , \: \verb#"f"# \right]$

(1)

Type: List(String)

fricas

b:= [1,7,8,9,2,4,6,17,18,14,32]

$\label{eq2}\left[ 1, \: 7, \: 8, \: 9, \: 2, \: 4, \: 6, \:{17}, \:{18}, \:{14}, \:{32}\right]$

(2)

Type: List(PositiveInteger?)

fricas

median a

$\label{eq3}\verb#"d"#$

(3)

Type: String

fricas

median b

$\label{eq4}8$

(4)

Type: PositiveInteger?

fricas

mean b

$\label{eq5}{118}\over{11}$

(5)

Type: Fraction(Integer)

fricas

hmean b

$\label{eq6}{125664}\over{28705}$

(6)

Type: Fraction(Integer)

fricas

moment(b,1)

$\label{eq7}{118}\over{11}$

(7)

Type: Fraction(Integer)

fricas

moment(b,2)

$\label{eq8}{2084}\over{11}$

(8)

Type: Fraction(Integer)

fricas

moment(b,3)

$\label{eq9}{48130}\over{11}$

(9)

Type: Fraction(Integer)

fricas

variance b

$\label{eq10}{900}\over{11}$

(10)

Type: Fraction(Integer)

fricas

stdev b

$\label{eq11}{30}\over{\sqrt{11}}$

(11)

Type: AlgebraicNumber?

fricas

gmean b

$\label{eq12}2 \ {\root{11}\of{1619352}}$

(12)

Type: AlgebraicNumber?

fricas

center b

$\label{eq13}\begin{array}{@{}l} \displaystyle \left[ -{{107}\over{11}}, \: -{{41}\over{11}}, \: -{{30}\over{1 1}}, \: -{{19}\over{11}}, \: -{{96}\over{11}}, \: -{{74}\over{1 1}}, \: -{{52}\over{11}}, \:{{69}\over{11}}, \:{{80}\over{11}}, \:{{36}\over{11}}, \right. \ \ \displaystyle \left.\:{{234}\over{11}}\right]$

(13)

Type: List(Fraction(Integer))

fricas

stdize b

$\label{eq14}\begin{array}{@{}l} \displaystyle \left[ -{{{107}\ {\sqrt{11}}}\over{330}}, \: -{{{41}\ {\sqrt{1 1}}}\over{330}}, \: -{{\sqrt{11}}\over{11}}, \: -{{{19}\ {\sqrt{1 1}}}\over{330}}, \: -{{{16}\ {\sqrt{11}}}\over{55}}, \: \right. \ \ \displaystyle \left.-{{{37}\ {\sqrt{11}}}\over{165}}, \: -{{{26}\ {\sqrt{11}}}\over{1 65}}, \:{{{23}\ {\sqrt{11}}}\over{110}}, \:{{8 \ {\sqrt{11}}}\over{3 3}}, \:{{6 \ {\sqrt{11}}}\over{55}}, \:{{{39}\ {\sqrt{11}}}\over{5 5}}\right]$

(14)

Type: List(AlgebraicNumber?)

fricas

c := [3+7*%i,5+8*%i,8+3*%i,4+5*%i]

$\label{eq15}\left[{3 +{7 \ i}}, \:{5 +{8 \ i}}, \:{8 +{3 \ i}}, \:{4 +{5 \ i}}\right]$

(15)

Type: List(Complex(Integer))

fricas

mean c

$\label{eq16}{{20}+{{23}\ i}}\over 4$

(16)

Type: Fraction(Complex(Integer))