'******************************************************
'*         Computing the means and moments            *
'*           of a statistical variable                *
'*                                                    *
'* -------------------------------------------------- *
'* REFERENCE:  "Mathematiques et statistiques By H.   *
'*              Haut, PSI Editions, France, 1981" [13]*
'* -------------------------------------------------- *
'* SAMPLE RUN:                                        *
'*                                                    *
'* TUTORIAL                                           *
'*                                                    *
'* Means and moments of a statistical variable X(i)   *
'* with frequency F(i)                                *
'*                                                    *
'* 1. Input number n of data                          *
'*                                                    *
'* 2. Input successively the n values X(i) and F(i)   *
'*                                                    *
'* Number of data: 3                                  *
'*                                                    *
'* 1  ?  1 6                                          *
'* 2  ?  3 4                                          *
'* 3  ?  5 8                                          *
'*                                                    *
'* Calculate generalized mean for t= 2                *
'*                                                    *
'*                                                    *
'* Arithmetic mean:  3.22222222                       *
'* Geometric mean :  2.61023904                       *
'* Harmonic mean  :  2.01492537                       *
'*                                                    *
'* Moments:                                           *
'*                                                    *
'*   M1=    3.22222222                                *
'*   M2=    3.06172840                                *
'*   M3=   -1.16323733                                *
'*   M4=   12.56881570                                *
'*                                                    *
'* Flatness coefficient....:   1.34079084             *
'* Coefficient of asymmetry:  -0.21712925             *
'*                                                    *
'* Gen. mean M(2): 3.66666667                         *
'*                                                    *
'******************************************************
defint i-n
defdbl a-h,o-z

  cls
  print
  print " TUTORIAL"
  print
  print " Means and moments of a statistical variable X(i)"
  print " with frequency F(i)"
  print
  print " 1. Input number n of data"
  print
  print " 2. Input sucessively the n values X(i) and F(i)"
  print
  input " Number of data: ", n
  print

  dim X(n), F(n)

  for i=1 to n
    print "  ";i;"  "; : input X(i), F(i)
  next i
  print
  input " Calculate generalized mean for t= ", t
  print

  gosub 1000

  'print results
  cls
  f$="####.########"
  print
  print " Arithmetic mean: "; : print using f$; a
  print
  print " Geometric mean : "; : print using f$; g
  print
  if ite=1 then
    print " Harmonic mean undefined."
  else
    print " Harmonic mean  : "; : print using f$; h
  end if
  print
  print " Moments:"
  print
  print "   M1= "; : print using f$; xm1
  print "   M2= "; : print using f$; xm2
  print "   M3= "; : print using f$; xm3
  print "   M4= "; : print using f$; xm4
  print
  print " Flatness coefficient....: "; : print using f$; ap
  print " Coefficient of asymmetry: "; : print using f$; asy
  print
  print " Gen. mean M(";t;"): "; : print using f$; xmt
  print

END

1000 'Subroutine to calculate the means and moments of a
'     statistical variable X(i)
'*****************************************************
'* INPUTS:                                           *
'*          n: number of data X(i) and F(i)          *
'*          X: n values X(i)                         *
'*          F: n values F(i), frequency of X(i)      *
'*          t: coefficient of generalized mean M(t)  *
'*             to calculate                          *
'* OUTPUTS:                                          *
'*          a: arithmetic mean of X(i)               *
'*          g: geometric mean of X(i)                *
'*          h: harmonic mean of X(i)                 *
'*        xm1: moment of first order                 *
'*        xm2: moment of second order                *
'*        xm3: moment of third order                 *
'*        xm4: moment of fourth order                *
'*         ap: flatness coefficient                  *
'*        asy: coefficient of assymetry              *
'*        xmt: generalized mean M(t)                 *
'*        ite: test flag (if ite=1, harmonic mean h  *
'*             is not defined                        *
'*****************************************************
  ite=0
  v1=0# : v2=0# : v3=0# : v4=0#
  v5=1# : v6=0# : v7=0# : xm=0#
  'Calculate necessary sums
  for i=1 to n
    vt=F(i)*X(i)
    v1=v1+vt
    v2=v2+vt*X(i)
    v3=v3+vt*X(i)^2
    v4=v4+vt*X(i)^3
    xm=xm+F(i)
    v7=v7+F(i)*X(i)^t
    'test for a X(i)=0
    if X(i)=0 then
      ite=1
      goto 100
    end if
    'if one X(i)=0, the harmonic mean is undefined
    'and the geometric mean = 0
    if ite=1 then goto 100
    v5=v5*X(i)^F(i)
    v6=v6+F(i)/X(i)
100 next i
  'prepare outputs
  a=v1/xm
  xmt=(v7/xm)^(1#/t)
  xm1=a
  xm2=(v2-2#*a*v1+a*a*xm)/xm
  xm3=(v3-3#*a*v2+3#*a*a*v1-xm*a^3)/xm
  xm4=(v4-4#*a*v3+6#*a*a*v2-4#*v1*a^3+xm*a^4)/xm
  ap=xm4/xm2/xm2
  asy=xm3/(xm2^1.5#)
  if ite=1 then  'one X(i)=0
    g=0#
    return
  end if
  g=v5^(1#/xm)
  h=xm/v6
return

'End of file moment.bas