g01ae constructs a frequency distribution of a variable, according to either user-supplied, or method-calculated class boundary values.

Syntax

C#
public static void g01ae( int n, int k, double[] x, int iclass, double[] cb, int[] ifreq, out double xmin, out double xmax, out int ifail )

Visual Basic (Declaration)
Public Shared Sub g01ae ( _ n As Integer, _ k As Integer, _ x As Double(), _ iclass As Integer, _ cb As Double(), _ ifreq As Integer(), _ <OutAttribute> ByRef xmin As Double, _ <OutAttribute> ByRef xmax As Double, _ <OutAttribute> ByRef ifail As Integer _ )

Visual Basic (Declaration)

Public Shared Sub g01ae ( _
	n As Integer, _
	k As Integer, _
	x As Double(), _
	iclass As Integer, _
	cb As Double(), _
	ifreq As Integer(), _
	<OutAttribute> ByRef xmin As Double, _
	<OutAttribute> ByRef xmax As Double, _
	<OutAttribute> ByRef ifail As Integer _
)

Visual C++
public: static void g01ae( int n, int k, array<double>^ x, int iclass, array<double>^ cb, array<int>^ ifreq, [OutAttribute] double% xmin, [OutAttribute] double% xmax, [OutAttribute] int% ifail )

F#
static member g01ae : n:int * k:int * x:float[] * iclass:int * cb:float[] * ifreq:int[] * xmin:float byref * xmax:float byref * ifail:int byref -> unit

Parameters

n: Type: System..::.Int32

On entry: n, the number of observations.

Constraint: n≥1.

k: Type: System..::.Int32

On entry: k, the number of classes desired in the frequency distribution. Whether or not class boundary values are user-supplied, k must include the two extreme classes which stretch to ±∞.

Constraint: k≥2.

x: Type: array< System..::.Double >[]()[]
An array of size [n]

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.

iclass: Type: System..::.Int32

On entry: indicates whether class boundary values are to be calculated within g01ae, or are supplied by you.
If iclass=0, then the class boundary values are to be calculated within the method.

If iclass=1, they are user-supplied.

Constraint: iclass=0 or 1.

cb: Type: array< System..::.Double >[]()[]
An array of size [k]

On entry: if iclass=0, then the elements of cb need not be assigned values, as g01ae calculates k-1 class boundary values.
If iclass=1, the first k-1 elements of cb must contain the class boundary values you supplied, in ascending order.

In both cases, the element cb[k-1] need not be assigned, as it is not used in the method.

On exit: the first k-1 elements of cb contain the class boundary values in ascending order.

Constraint: if iclass=1, cb[i-1]<cb[i] for i=1,2,…,k-2.

ifreq: Type: array< System..::.Int32 >[]()[]
An array of size [k]

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 cb[0], f1, and ifreq[k-1] contains the frequency of the class greater than cb[k-2], fk.

xmin: Type: System..::.Double %

On exit: the smallest value in the sample, a.

xmax: Type: System..::.Double %

On exit: the largest value in the sample, b.

ifail: Type: System..::.Int32 %

On exit: ifail=0 unless the method detects an error (see [Error Indicators and Warnings]).

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 .

g01ae 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 method-calculated, and are denoted by yj, for j=1,2,…,k-1.

If the boundary values of the classes are to be method-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

f1= the number of x values in the interval -∞,y1
fi= the number of x values in the interval yi-1 ,ik , i=2,…,k-1
fk= the number of x values in the interval yk-1 ,∞ ,

where [ means inclusive, and ) means exclusive. If the class boundary values are method-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; method-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.