Descriptive statistics

Descriptive statistics, as follows from its name, describes a distribution by means of figures which characterize distribution parameters. These parameters can be divided into three main groups: central tendency measures, dispersion measures and shape measures.

Central tendency measures

Central tendency measures characterize the central value around which random variable values are distributed. These measures are the mean (first moment of distribution) and the median. The mean is used for the description of close to normal distributions. If the distribution essentially differs from normal (for example, if it has long and wide tails), the mean will converge to "true" mean too slowly. In that case, it is reasonable to use the median to estimate central value.

Dispersion measures

Dispersion measures characterize scattering whose random value is distributed around its central value. These measures are dispersion (and related with it standard deviation) and average deviation. As for central tendency measures, one of these measures (dispersion) is good for close to normal distributions while the second one (average deviation) is better for long-tailed distributions.

Shape measures

Shape measures describe common characteristics of distribution appearance: skewness, kurtosis, percentile.

This article is licensed for personal use only.

Download ALGLIB for C++ / C# / ...

ALGLIB Project offers you two editions of ALGLIB:

ALGLIB Free Edition:
delivered for free
offers full set of numerical functionality
extensive algorithmic optimizations
no low level optimizations
non-commercial license

ALGLIB Commercial Edition:
flexible pricing
offers full set of numerical functionality
extensive algorithmic optimizations
high performance (SMP, SIMD)
commercial license with support plan

Links to download sections for Free and Commercial editions can be found below:

ALGLIB 3.12.0 for C++

C++ library.
Delivered with sources.
Monolithic design.
Extreme portability.
Editions:   FREE   COMMERCIAL

ALGLIB 3.12.0 for C#

C# library with native kernels.
Delivered with sources.
VB.NET and IronPython wrappers.
Extreme portability.
Editions:   FREE   COMMERCIAL

ALGLIB 3.12.0 for Delphi

Delphi wrapper around C core.
Delivered as precompiled binary.
Compatible with FreePascal.
Editions:   FREE   COMMERCIAL

ALGLIB 3.12.0 for CPython

CPython wrapper around C core.
Delivered as precompiled binary.
Editions:   FREE   COMMERCIAL