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The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
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 simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
In a histogram, each bin is for a different range of values, so altogether the histogram illustrates the distribution of values. But in a bar chart, each bar is for a different category of observations (e.g., each bar might be for a different population), so altogether the bar chart can be used to compare different categories.
The distribution was independently rediscovered by the English mathematician Karl Pearson in the context of goodness of fit, for which he developed his Pearson's chi-squared test, published in 1900, with computed table of values published in (Elderton 1902), collected in (Pearson 1914, pp. xxxi–xxxiii, 26–28, Table XII).
Therefore, the Poisson distribution with parameter λ = np can be used as an approximation to B(n, p) of the binomial distribution if n is sufficiently large and p is sufficiently small. According to rules of thumb, this approximation is good if n ≥ 20 and p ≤ 0.05 [ 36 ] such that np ≤ 1 , or if n > 50 and p < 0.1 such that np < 5 , [ 37 ...
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).
The t distribution is often used as an alternative to the normal distribution as a model for data, which often has heavier tails than the normal distribution allows for; see e.g. Lange et al. [14] The classical approach was to identify outliers (e.g., using Grubbs's test) and exclude or downweight them in some way.