Statistics with Klong

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A data set is stored in a Klong vector. There are various ways to create data sets. Key them in:

[30 28 31 30 31 30 31 31 30 31 30 31] |

Use the Enumerate or Expand operators:

5+&10 |

Or create a data set following a
probability distribution
with
`dist`

. For instance, the following program creates a data set
of
normally distributed
data:

```
&dist(ndf;7;[-2 2])
``` |

The `dist`

function itself returns a
frequency distribution
which can then be expanded to a data set using Expand:

```
dist(ndf;7;[-2 2])
``` |

The parameters of
`dist`

are the
probability density function
(PDF) of the
desired distribution, the number of different data points to generate,
and the desired range of the PDF. The above example creates 7 standard
normally distributed data points (using the `ndf`

function)
from −2σ to +2σ.

A data set can be converted (back) to a frequency distribution using the idiom Size-Each Group:

```
#'=[0 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 6]
``` |

Larger data sets are best visualized using the interactive plotter interface. For instance, the following program creates the histogram plot in fig.1 from a frequency distribution.

X::&dist(ndf;30;[-3 3]) v.bar(#'=X) |

The `v.bar`

function sets up a grid and plots a data
set as a bar graph. The Klong program linked below the image does not
use the interactive interface, but similar instructions for batch
plotting.

A normally distributed random
error
can be added to a data set by
using the `err`

function. For instance:

1.0+&20 |

The first parameter of `err`

specifies the number of
distinct error values, taken from the interval −0.5≤x≤0.5
with equal space between them. The lowest value is always −0.5
and the highest value is 0.5. The second parameter is multiplied with
the error values, so the above example generates the error values
{−2, −1, 0, +1, +2}.

An x/y set or paired set or map is represented by a vector of tuples. It is normally used to pair the values of two random variables that may be correlated or not. Like a data set it can be keyed in or created using various operators and functions. A data set can be turned into an x/y set by pairing each value in the set with some other value, e.g.:

[3 6 7 13 17 17 21] |

An x/y set can be divided into two separate data sets using the First-Each and (At-one)-Each idioms:

XY::[[1 3] [2 6] [3 7] [4 13] [5 17] [6 17] [7 21]] *'XY |

Larger x/y sets are best visualized as scatter plots. For example, the program

v.scatter2((!30),'err(20;20;0.5*!30)) |

will display a scatter plot like the one shown in fig.2. Of course,
the actual values plotted by the program may differ from those in the
figure due to the *random* error added.

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