nag_frequency_table (g01aec) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_frequency_table (g01aec)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_frequency_table (g01aec) constructs a frequency distribution of a variable, according to either user-supplied, or function-calculated class boundary values.

2  Specification

#include <nag.h>
#include <nagg01.h>
void  nag_frequency_table (Integer n, const double x[], Integer num_class, Nag_ClassBoundary classb, double cint[], Integer ifreq[], double *xmin, double *xmax, NagError *fail)

3  Description

The data consists of a sample of n observations of a continuous variable, denoted by xi, for i=1,2,,n. Let a = minx1,,xn  and b = maxx1,,xn .
nag_frequency_table (g01aec) constructs a frequency distribution with k>1 classes denoted by fi, for i=1,2,,k.
The boundary values may be either user-supplied, or function-calculated, and are denoted by yj, for j=1,2,,k-1.
If the boundary values of the classes are to be function-calculated, then they are determined in one of the following ways:
(a) if k>2, the range of x values is divided into k-2 intervals of equal length, and two extreme intervals, defined by the class boundary values y1,y2,,yk-1;
(b) if k=2, y1=12a+b.
However formed, the values y1,,yk-1 are assumed to be in ascending order. The class frequencies are formed with where [ means inclusive, and ) means exclusive. If the class boundary values are function-calculated and k>2, then f1=fk=0, and y1 and yk-1 are chosen so that y1<a and yk-1>b.
If a frequency distribution is required for a discrete variable, then it is suggested that you supply the class boundary values; function-calculated boundary values may be slightly imprecise (due to the adjustment of y1 and yk-1 outlined above) and cause values very close to a class boundary to be assigned to the wrong class.

4  References


5  Arguments

1:     nIntegerInput
On entry: n, the number of observations.
Constraint: n1.
2:     x[n]const doubleInput
On entry: the sample of observations of the variable for which the frequency distribution is required, xi, for i=1,2,,n. The values may be in any order.
3:     num_classIntegerInput
On entry: k, the number of classes desired in the frequency distribution. Whether or not class boundary values are user-supplied, num_class must include the two extreme classes which stretch to ±.
Constraint: num_class2.
4:     classbNag_ClassBoundaryInput
On entry: indicates whether class boundary values are to be calculated within nag_frequency_table (g01aec), or are supplied by you.
If classb=Nag_ClassBoundaryComp, then the class boundary values are to be calculated within the function.
If classb=Nag_ClassBoundaryUser, they are user-supplied.
Constraint: classb=Nag_ClassBoundaryComp or Nag_ClassBoundaryUser.
5:     cint[num_class]doubleInput/Output
On entry: if classb=Nag_ClassBoundaryComp, then the elements of cint need not be assigned values, as nag_frequency_table (g01aec) calculates k-1 class boundary values.
If classb=Nag_ClassBoundaryUser, the first k-1 elements of cint must contain the class boundary values you supplied, in ascending order.
On exit: the first k-1 elements of cint contain the class boundary values in ascending order.
Constraint: if classb=Nag_ClassBoundaryUser, cint[i-1]<cint[i], for i=1,2,,k-2.
6:     ifreq[num_class]IntegerOutput
On exit: the elements of ifreq contain the frequencies in each class, fi, for i=1,2,,k. In particular ifreq[0] contains the frequency of the class up to cint[0], f1, and ifreq[k-1] contains the frequency of the class greater than cint[k-2], fk.
7:     xmindouble *Output
On exit: the smallest value in the sample, a.
8:     xmaxdouble *Output
On exit: the largest value in the sample, b.
9:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n1.
On entry, num_class=value.
Constraint: num_class2.
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.
On entry, cint[value]=value and cint[value]=value.
Constraint: cint[value]<cint[value].

7  Accuracy

The method used is believed to be stable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

The time taken by nag_frequency_table (g01aec) increases with num_class and n. It also depends on the distribution of the sample observations.

10  Example

This example summarises a number of datasets. For each dataset the sample observations and optionally class boundary values are read. nag_frequency_table (g01aec) is then called and the frequency distribution and largest and smallest observations printed.

10.1  Program Text

Program Text (g01aece.c)

10.2  Program Data

Program Data (g01aece.d)

10.3  Program Results

Program Results (g01aece.r)

nag_frequency_table (g01aec) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014