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The term "likelihood" has been in use in English since at least late Middle English. [42] Its formal use to refer to a specific function in mathematical statistics was proposed by Ronald Fisher, [43] in two research papers published in 1921 [44] and 1922. [45]
The estimator of a proportion is ^ = /, where X is the number of 'positive' instances (e.g., the number of people out of the n sampled people who are at least 65 years old). When the observations are independent , this estimator has a (scaled) binomial distribution (and is also the sample mean of data from a Bernoulli distribution ).
Informally, for a first-order formula of arithmetic () with one free variable, the induction principle for expresses the validity of mathematical induction over , while the least number principle for asserts that if has a witness, it has a least one. For a formula (,) in two free variables, the bounding principle for states that, for a fixed ...
The zeta distribution has uses in applied statistics and statistical mechanics, and perhaps may be of interest to number theorists. It is the Zipf distribution for an infinite number of elements. The Hardy distribution, which describes the probabilities of the hole scores for a given golf player.
Log–log graph of the probability that a number starts with the digit(s) n, for a distribution satisfying Benford's law. The points show the exact formula, P(n) = log 10 (1 + 1/n). The graph tends towards the dashed asymptote passing through (1, log 10 e) with slope −1 in log–log scale. The example in yellow shows that the probability of a ...
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
In statistics, the sample maximum and sample minimum, also called the largest observation and smallest observation, are the values of the greatest and least elements of a sample. [1] They are basic summary statistics, used in descriptive statistics such as the five-number summary and Bowley's seven-figure summary and the associated box plot.
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...