Statistics

lastmod 2026-02-24created 2014-10-2323 edits

Statistics is the discipline that studies methods for statistically observing and processing many facts on the basis of quantitative comparison. Statistics as a modern science developed from the discipline established in the mid-19th century by the Belgian Quetelet, who combined Germany's 'Staatenkunde' (the study of states in the broad sense) and England's 'Political Arithmetic' (a quantitative research method for political society) with the 'probability theory' of the natural sciences.

Robust Parameter Estimation

Median absolute deviation (MAD)
Random sample consensus (RANSAC)
Mean absolute deviation
Least absolute deviation

Outlier Detection

Methods for detecting outliers (also called anomalies, outlying values, or extreme values)

Clustering

There are various approaches and algorithms for performing clustering, and they can be divided into three broad categories as follows.

Partition-based clustering : e.g. : k-means, k-median
Hierarchical clustering : e.g. : Agglomerative, Divisive
Density-based clustering : e.g. : DBSCAN

Sample mean and sample variance

The sample mean is a concept contrasted with the population mean; as opposed to the random variables treated in discrete and continuous probability distributions, it refers to the value obtained by drawing samples, computing their mean, and taking that mean as representative of the group. In the sense of computing the probability value, a quota function is involved, and P(x), a Partionism function representing the proportion of the population and its opposition, is used. Proving it by the Standing hypothesis can produce logical errors, so it is used with those errors corrected.