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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.
The density estimates are kernel density estimates using a Gaussian kernel. That is, a Gaussian density function is placed at each data point, and the sum of the density functions is computed over the range of the data. From the density of "glu" conditional on diabetes, we can obtain the probability of diabetes conditional on "glu" via Bayes ...
In probability and statistics, the generalized beta distribution [1] is a continuous probability distribution with four shape parameters, including more than thirty named distributions as limiting or special cases.
Pickands–Balkema–de Haan theorem (Pickands, 1975; Balkema and de Haan, 1974) states that for a large class of underlying distribution functions , and large , is well approximated by the generalized Pareto distribution (GPD), which motivated Peak Over Threshold (POT) methods to estimate : the GPD plays the key role in POT approach.
For k > 1, the density function tends to zero as x approaches zero from above, increases until its mode and decreases after it. The density function has infinite negative slope at x = 0 if 0 < k < 1, infinite positive slope at x = 0 if 1 < k < 2 and null slope at x = 0 if k > 2. For k = 1 the density has a finite negative slope at x = 0.
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] = ().
In probability theory and statistics, the Epanechnikov distribution, also known as the Epanechnikov kernel, is a continuous probability distribution that is defined on a finite interval. It is named after V. A. Epanechnikov, who introduced it in 1969 in the context of kernel density estimation .