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  2. Probability density function - Wikipedia

    en.wikipedia.org/wiki/Probability_density_function

    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 ...

  3. Probability mass function - Wikipedia

    en.wikipedia.org/wiki/Probability_mass_function

    The graph of a probability mass function. All the values of this function must be non-negative and sum up to 1. In probability and statistics, a probability mass function (sometimes called probability function or frequency function [1]) is a function that gives the probability that a discrete random variable is exactly equal to some value. [2]

  4. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    The concept of probability function is made more rigorous by defining it as the element of a probability space (,,), where is the set of possible outcomes, is the set of all subsets whose probability can be measured, and is the probability function, or probability measure, that assigns a probability to each of these measurable subsets .

  5. Density estimation - Wikipedia

    en.wikipedia.org/wiki/Density_Estimation

    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 ...

  6. Joint probability distribution - Wikipedia

    en.wikipedia.org/wiki/Joint_probability_distribution

    One must use the "mixed" joint density when finding the cumulative distribution of this binary outcome because the input variables (,) were initially defined in such a way that one could not collectively assign it either a probability density function or a probability mass function.

  7. Convolution of probability distributions - Wikipedia

    en.wikipedia.org/wiki/Convolution_of_probability...

    The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.

  8. Logistic distribution - Wikipedia

    en.wikipedia.org/wiki/Logistic_distribution

    The probability density function is the partial derivative of the cumulative distribution function: (;,) = (;,) = / (+ /) = (() / + / ()) = ⁡ ().When the location parameter μ is 0 and the scale parameter s is 1, then the probability density function of the logistic distribution is given by

  9. Kernel (statistics) - Wikipedia

    en.wikipedia.org/wiki/Kernel_(statistics)

    The first requirement ensures that the method of kernel density estimation results in a probability density function. The second requirement ensures that the average of the corresponding distribution is equal to that of the sample used. If K is a kernel, then so is the function K* defined by K*(u) = λK(λu), where λ > 0. This can be used to ...

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