The input data consist of a univariate frequency distribution, denoted by
, for
, and the boundary values of the classes
, for
. Thus the frequency associated with the interval
is
, and
nag_summary_stats_freq (g01adc) assumes that all the values in this interval are concentrated at the point
The following quantities are calculated:
(a) |
total frequency,
|
(b) |
mean,
|
(c) |
standard deviation,
|
(d) |
coefficient of skewness,
|
(e) |
coefficient of kurtosis,
|
The function has been developed primarily for groupings of a continuous variable. If, however, the function is to be used on the frequency distribution of a discrete variable, taking the values
, then the boundary values for the classes may be defined as follows:
(i) |
for ,
|
(ii) |
for ,
|
None.
- 1:
– IntegerInput
-
On entry: , the number of class boundaries, which is one more than the number of classes of the frequency distribution.
Constraint:
.
- 2:
– const doubleInput
-
On entry: the elements of
x must contain the boundary values of the classes in ascending order, so that class
is bounded by the values in
and
, for
.
Constraint:
, for .
- 3:
– const IntegerInput
-
On entry: the
th element of
ifreq must contain the frequency associated with the
th class, for
.
is not used by the function.
Constraints:
- , for ;
- .
- 4:
– double *Output
-
On exit: the mean value, .
- 5:
– double *Output
-
On exit: the standard deviation, .
- 6:
– double *Output
-
On exit: the coefficient of skewness, .
- 7:
– double *Output
-
On exit: the coefficient of kurtosis, .
- 8:
– Integer *Output
-
On exit: the total frequency, .
- 9:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
The method used is believed to be stable.
In the example program, NPROB determines the number of sets of data to be analysed. For each analysis, the boundary values of the classes and the frequencies are read. After nag_summary_stats_freq (g01adc) has been successfully called, the input data and calculated quantities are printed. In the example, there is one set of data, with classes.