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The correlated variation of a kernel density estimate is very difficult to describe mathematically, while it is simple for a histogram where each bin varies independently. An alternative to kernel density estimation is the average shifted histogram, [8] which is fast to compute and gives a smooth curve estimate of the density without using kernels.
The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem.
Figure 1: The left graph shows a probability density function. The right graph shows the cumulative distribution function. The value at a in the cumulative distribution equals the area under the probability density curve up to the point a. Absolutely continuous probability distributions can be described in several ways.
The density of the maximally dense subgraph of a graph is sometimes referred to as its subgraph density. A subgraph with maximal density can also be seen as a subgraph with maximal average degree in the graph. Subgraph density is asymptotic to the related notion of arboricity and to graph degeneracy.
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is [2] [3] = ().
Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The logistic sigmoid function is invertible, and its inverse is the logit function.
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