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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.
A frequency distribution shows a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc.
Both the overall letter distribution and the word-initial letter distribution approximately match the Zipf distribution and even more closely match the Yule distribution. [19] Often the frequency distribution of the first digit in each datum is significantly different from the overall frequency of all the digits in a set of numeric data, an ...
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.
Frequency distribution: a table that displays the frequency of various outcomes in a sample. Relative frequency distribution: a frequency distribution where each value has been divided (normalized) by a number of outcomes in a sample (i.e. sample size). Categorical distribution: for discrete random variables with a finite set of values.
The above data can be grouped in order to construct a frequency distribution in any of several ways. One method is to use intervals as a basis. The smallest value in the above data is 8 and the largest is 34. The interval from 8 to 34 is broken up into smaller subintervals (called class intervals). For each class interval, the number of data ...
It has been found to apply to many other types of data studied in the physical and social sciences. In mathematical statistics, the concept has been formalized as the Zipfian distribution: A family of related discrete probability distributions whose rank-frequency distribution is an inverse power law relation.
For example, the parameter (the expectation) can be estimated by the mean of the data and the parameter (the variance) can be estimated from the standard deviation of the data. The mean is found as = /, where is the data value and the number of data, while the standard deviation is calculated as = (). With these parameters many distributions, e ...