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reading structures from a file ← ↑ → string conversions

statistical functions
last edited 11 months ago by page

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

axiom
)abbrev package STAT StatPackage
++ Description:
++ This package exports statistic utilities
StatPackage(S,A) : Exports == Implementation where
  S: SetCategory
  A: Collection(S) with (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(#1-i,m)
                                        s := sums(j)
                                        k := sqrt((s.2 -
s.1/#m::S)/(#m::S - 1::S))
                                        map((#1-i)/k,m)
                                if A has shallowlyMutable then
                                        stdize_!(m)==
                                                i := mean(m)
                                                j := map(#1-i,m)
                                                s := sums(j)
                                                k := sqrt((s.2 -
s.1/#m::S)/(#m::S - 1::S))
                                                map_!((#1-i)/k,m)

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

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

                center(m)==
                        i := mean(m)
                        map(#1-i,m)

                if A has shallowlyMutable then
                        center_!(m)==
                                i := mean(m)
                                map_!(#1-i,m)
                                m
                if S has RadicalCategory then
                        gmean(m)==
                                i := reduce("*", m)
                                nthRoot(i,#m)

                        stdev(m)==
                                sqrt(variance(m))
axiom
)abbrev package IDSTAT IntegralDomainStatPackage
++ Description:
++ This package exports statistic utilities over IntegralDomain
IntegralDomainStatPackage(S,A) : Exports == Implementation where
  S: IntegralDomain
  A: Collection(S) with (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(#1**n, m)
                j := reduce("+",i)
                j / #m::S
axiom
)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 Lisp
        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-j,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)
axiom
Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/1059333137717529116-25px.001.spad using 
      old system compiler.
   STAT abbreviates package StatPackage 
------------------------------------------------------------------------
   initializing NRLIB STAT for StatPackage 
   compiling into NRLIB STAT 
****** Domain: A already in scope
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: 0.07 SEC.

   compiling exported variance : A -> S
Time: 0.02 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: 0.06 SEC.

   compiling exported variance : A -> S
Time: 0.01 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.

augmenting A: (ATTRIBUTE A shallowlyMutable)
augmenting $: (SIGNATURE $ stdize! (A A))
augmenting $: (SIGNATURE $ center! (A A))
   compiling exported stdize! : A -> A
Time: 0.01 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: 0.01 SEC.

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

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

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

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

augmenting A: (ATTRIBUTE 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: 0.01 SEC.

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

augmenting A: (ATTRIBUTE 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))
augmenting A: (ATTRIBUTE 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: A already in scope
augmenting A: (FiniteLinearAggregate S)
****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting $: (SIGNATURE $ median (S 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: 0.06 SEC.

   Cumulative Statistics for Constructor StatPackage
      Time: 0.30 seconds

   finalizing NRLIB STAT 
   Processing StatPackage for Browser database:
--------(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))---------
--------constructor---------
------------------------------------------------------------------------
   StatPackage is now explicitly exposed in frame initial 
   StatPackage will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/STAT.NRLIB/code

   IDSTAT abbreviates package IntegralDomainStatPackage 
------------------------------------------------------------------------
   initializing NRLIB IDSTAT for IntegralDomainStatPackage 
   compiling into NRLIB IDSTAT 
   compiling exported mean : A -> Fraction S
Time: 0.06 SEC.

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

(time taken in buildFunctor:  0)

;;;     ***       |IntegralDomainStatPackage| REDEFINED

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

   Cumulative Statistics for Constructor IntegralDomainStatPackage
      Time: 0.06 seconds

   finalizing NRLIB IDSTAT 
   Processing IntegralDomainStatPackage for Browser database:
--------(mean ((Fraction S) A))---------
--------(moment ((Fraction S) A (NonNegativeInteger)))---------
--------constructor---------
------------------------------------------------------------------------
   IntegralDomainStatPackage is now explicitly exposed in frame initial

   IntegralDomainStatPackage will be automatically loaded when needed 
      from /var/zope2/var/LatexWiki/IDSTAT.NRLIB/code

   MSTAT abbreviates package MatrixStatPackage 
------------------------------------------------------------------------
   initializing NRLIB MSTAT for MatrixStatPackage 
   compiling into NRLIB MSTAT 
   importing Lisp
   importing StatPackage(S,Col)
augmenting Col: (ATTRIBUTE Col shallowlyMutable)
   compiling local colReduce : (Col -> S,M) -> Col
Time: 0.02 SEC.

****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting $: (SIGNATURE $ median (Col M))
   compiling exported median : M -> Col
Time: 0.01 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: 0.01 SEC.

   compiling exported center : M -> M
Time: 0.02 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: 0.03 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 SEC.

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

   compiling exported stdize : M -> M
Time: 0.02 SEC.

   compiling exported stdize! : M -> M
Time: 0.06 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: 0.02 SEC.

****** Domain: M already in scope
augmenting M: (MatrixCategory S Row Col)
****** Domain: S already in scope
augmenting S: (Field)
augmenting Col: (ATTRIBUTE Col shallowlyMutable)
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: M already in scope
augmenting M: (MatrixCategory S Row Col)
****** Domain: S already in scope
augmenting S: (Field)
****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting Col: (ATTRIBUTE Col shallowlyMutable)
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))
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: S already in scope
augmenting S: (Field)
augmenting Col: (ATTRIBUTE Col shallowlyMutable)
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: (Field)
****** Domain: S already in scope
augmenting S: (RadicalCategory)
augmenting Col: (ATTRIBUTE Col shallowlyMutable)
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 $ gmean (Col M))
augmenting $: (SIGNATURE $ stdev (Col M))
augmenting $: (SIGNATURE $ stdize (M M))
augmenting $: (SIGNATURE $ stdize! (M M))
****** Domain: S already in scope
augmenting S: (OrderedSet)
augmenting Col: (ATTRIBUTE Col shallowlyMutable)
augmenting $: (SIGNATURE $ median (Col M))
(time taken in buildFunctor:  0)

;;;     ***       |MatrixStatPackage| REDEFINED

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

   Warnings: 
      [1] median: not known that (Collection S) is of mode (CATEGORY Col (ATTRIBUTE shallowlyMutable))
      [2] median: not known that (ATTRIBUTE finiteAggregate) is of mode (CATEGORY Col (ATTRIBUTE shallowlyMutable))

   Cumulative Statistics for Constructor MatrixStatPackage
      Time: 0.21 seconds

   finalizing NRLIB MSTAT 
   Processing MatrixStatPackage for Browser database:
--------(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))---------
--------constructor---------
------------------------------------------------------------------------
   MatrixStatPackage is now explicitly exposed in frame initial 
   MatrixStatPackage will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MSTAT.NRLIB/code

And

axiom
a:= ["a","c","d","g","z","a",&q
uot;d","g","f"]
LatexWiki Image(1)
Type: List String
axiom
b:= [1,7,8,9,2,4,6,17,18,14,32]
LatexWiki Image(2)
Type: List PositiveInteger
axiom
median a
LatexWiki Image(3)
Type: String
axiom
median b
LatexWiki Image(4)
axiom
mean b
LatexWiki Image(5)
Type: Fraction Integer
axiom
hmean b
LatexWiki Image(6)
Type: Fraction Integer
axiom
moment(b,1)
LatexWiki Image(7)
Type: Fraction Integer
axiom
moment(b,2)
LatexWiki Image(8)
Type: Fraction Integer
axiom
moment(b,3)
LatexWiki Image(9)
Type: Fraction Integer
axiom
variance b
LatexWiki Image(10)
Type: Fraction Integer
axiom
stdev b
LatexWiki Image(11)
axiom
gmean b
LatexWiki Image(12)
axiom
center b
LatexWiki Image(13)
Type: List Fraction Integer
axiom
stdize b
LatexWiki Image(14)
Type: List AlgebraicNumber
axiom
-- beware, the following is not mathematically justified since
-- median use ordering from OrderedSet (and not OrderedRing)
c := [3+7*%i,5+8*%i,8+3*%i,4+5*%i]
LatexWiki Image(15)
Type: List Complex Integer
axiom
median c
LatexWiki Image(16)
Type: Complex Integer



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