g08cgf

Purpose

Synopsis

[chisq,p,ndf,eval,chisqi,ifail] = g08cgf(ifreq,cint,dist,par,npest<,prob,...
ifail>)

Description

 
          2                                                    
 The (chi)  goodness of fit test performed by G08CGF is used to 
 test the null hypothesis that a random sample arises from a 
 specified distribution against the alternative hypothesis that 
 the sample does not arise from the specified distribution.
 
 Given a sample of size n, denoted by x ,x ,...,x , drawn from a 
                                       1  2      n              
 random variable X, and that the data have been grouped into k 
 classes,
 
      x<=c ,
          1
 
      c   <x<=c , i=2,3,...k-1,
       i-1     i              
 
      x>c   ,
         k-1
 
               2                                           
 then the (chi)  goodness of fit test statistic is defined by;
 
                                        2
                             k   (O -E ) 
                          2  --    i  i 
                         X = >   --------
                             --     E 
                             i=1     i
 
 where O  is the observed frequency of the ith class, and E  is 
        i                                                  i   
 the expected frequency of the ith class.
 
 The expected frequencies are computed as
 
                             E =p *n,
                              i  i
 
 where p  is the probability that X lies in the ith class, that is
        i                                                       
 
      p =P(X<=c ),
       1       1 
 
      p =P(c   <X<=c ), i=2,3,...k-1,
       i    i-1     i               
 
      p =P(X>c   ).
       k      k-1 
 
 These probabilities are either taken from a common probability 
 distribution or are supplied by the user. The available 
 probability distributions within this routine are:
 
                                                          2
      Normal distribution with mean (mu), variance (sigma) ;
 
      uniform distribution on the interval [a,b];
 
      exponential distribution with probability density function 
                       -(lambda)x
      (pdf) = (lambda)e          ;
 
           2                                         
      (chi)  distribution with f degrees of freedom; and
 
                                         (alpha)-1 -x/(beta)
                                        x         e 
      gamma distribution with pdf = -----------------------------.
                                                          (alpha)
                                    (Gamma)((alpha))(beta) 
 
 The user must supply the frequencies and classes. Given a set of 
 data and classes the frequencies may be calculated using G01AEF.
 
                         2                  2                   
 G08CGF returns the (chi)  test statistic, X , together with its 
                                                                 2
 degrees of freedom and the upper tail probability from the (chi) 
 distribution associated with the test statistic. Note that the 
                 2                                        
 use of the (chi)  distribution as an approximation to the 
 distribution of the test statistic improves as the expected 
 values in each class increase.
 

Parameters

g08cgf

Required Input Arguments:

ifreq (:)                             integer
cint (:)                              real
dist (1)                              string
par (2)                               real
npest                                 integer

Optional Input Arguments:                       <Default>

prob (:)                              real     zeros(length(ifreq),1)
ifail                                 integer  -1

Output Arguments:

chisq                                 real
p                                     real
ndf                                   integer
eval (:)                              real
chisqi (:)                            real
ifail                                 integer