naginterfaces.library.stat.frequency_​table

naginterfaces.library.stat.frequency_table(x, cb=None)

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

For full information please refer to the NAG Library document for g01ae

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g01/g01aef.html

Parameters

xfloat, array-like, shape $\left(n\right)$

The sample of observations of the variable for which the frequency distribution is required, $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$. The values may be in any order.

cbNone or float, array-like, shape $\left(k\right)$, optional

If $\text{iclass}=0$, the elements of $cb$ need not be assigned values, as frequency_table calculates $k-1$ class boundary values.

If $\text{iclass}=1$, 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 function.

Returns

cbfloat, ndarray, shape $\left(k\right)$

The first $k-1$ elements of $cb$ contain the class boundary values in ascending order.

ifreqint, ndarray, shape $\left(k\right)$

The elements of $ifreq$ contain the frequencies in each class, $f_{\text{i}}$, for $\text{i}=1,2,\dots ,k$. In particular $ifreq\left[0\right]$ contains the frequency of the class up to $cb\left[0\right]$, $f_1$, and $ifreq[k-1]$ contains the frequency of the class greater than $cb[k-2]$, $f_k$.

xminfloat

The smallest value in the sample, $a$.

xmaxfloat

The largest value in the sample, $b$.

Raises

NagValueError

(errno $1$)

On entry, $k=⟨value⟩$.

Constraint: $k\ge 2$.

(errno $2$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $3$)

On entry, $cb[⟨value⟩]=⟨value⟩$ and $cb[⟨value⟩]=⟨value⟩$.

Constraint: $cb[⟨value⟩]<cb[⟨value⟩]$.

Notes

The data consists of a sample of $n$ observations of a continuous variable, denoted by $x_i$, for $\text{i}=1,2,\dots ,n$. Let $a=min(x_1,\dots ,x_n)$ and $b=max(x_1,\dots ,x_n)$.

frequency_table constructs a frequency distribution with $k(>1)$ classes denoted by $f_i$, for $\text{i}=1,2,\dots ,k$.

The boundary values may be either user-supplied, or function-calculated, and are denoted by $y_j$, for $\text{j}=1,2,\dots ,k-1$.

If the boundary values of the classes are to be function-calculated, then they are determined in one of the following ways:

1. 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 $y_1,y_2,\dots ,y_{k-1}$;

2. if $k=2$, $y_1=\frac{1}{2}(a+b)$.

However formed, the values $y_1,\dots ,y_{k-1}$ are assumed to be in ascending order. The class frequencies are formed with

$f_1=$ the number of $x$ values in the interval $(-\infty ,y_1)$

$f_i=$ the number of $x$ values in the interval $[y_{i-1},y_i)$, $i=2,\dots ,k-1$

$f_k=$ the number of $x$ values in the interval $[y_{k-1},\infty )$,

where [ means inclusive, and) means exclusive. If the class boundary values are function-calculated and $k>2$, then $f_1=f_k=0$, and $y_1$ and $y_{k-1}$ are chosen so that $y_1<a$ and $y_{k-1}>b$.

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 $y_1$ and $y_{k-1}$ outlined above) and cause values very close to a class boundary to be assigned to the wrong class.