The function may be called by the names: g01adc, nag_stat_summary_freq or nag_summary_stats_freq.
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 g01adc assumes that all the values in this interval are concentrated at the point
The following quantities are calculated:
(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:
1: – IntegerInput
On entry: , the number of class boundaries, which is one more than the number of classes of the frequency distribution.
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 .
, 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.
, 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 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
Either for some , or the sum of frequencies is zero.
The total frequency, , is less than , hence the quantities , and cannot be calculated.
On entry, .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, , and .
The method used is believed to be stable.
8Parallelism and Performance
g01adc is not threaded in any implementation.
The time taken by g01adc increases linearly with .
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 g01adc has been successfully called, the input data and calculated quantities are printed. In the example, there is one set of data, with classes.