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function draw_categorical(n) // where n is the number of samples to draw from the categorical distribution r = 1 s = 0 for i from 1 to k // where k is the number of categories v = draw from a binomial(n, p[i] / r) distribution // where p[i] is the probability of category i for j from 1 to v z[s++] = i // where z is an array in which the results ...
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.
Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample. This is an example of a univariate (=single variable) frequency table. The frequency of each response to a survey question is depicted.
This is a list of statistical procedures which can be used for the analysis of categorical data, also known as data on the nominal scale and as categorical variables. General tests [ edit ]
The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 × 2 contingency table. In principle, any number of rows and columns may be used. There may also be more than two variables, but higher order contingency tables are difficult to represent visually.
This stems from the fact that it is sometimes convenient to express the outcome of a categorical distribution as a "1-of-k" vector (a vector with one element containing a 1 and all other elements containing a 0) rather than as an integer in the range …; in this form, a categorical distribution is equivalent to a multinomial distribution over ...
The Dirichlet distribution is the conjugate prior distribution of the categorical distribution (a generic discrete probability distribution with a given number of possible outcomes) and multinomial distribution (the distribution over observed counts of each possible category in a set of categorically distributed observations).
For example, in econometric time series analysis, dummy variables may be used to indicate the occurrence of wars, or major strikes. It could thus be thought of as a Boolean , i.e., a truth value represented as the numerical value 0 or 1 (as is sometimes done in computer programming ).