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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. 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

  4. Chi-squared distribution - Wikipedia

    en.wikipedia.org/wiki/Chi-squared_distribution

    The probability density function (pdf) ... Simple algorithm for approximating cdf and inverse cdf for the chi-squared distribution with a pocket calculator;

  5. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_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] = ().

  6. Tukey lambda distribution - Wikipedia

    en.wikipedia.org/wiki/Tukey_lambda_distribution

    However, for any value of λ both the CDF and PDF can be tabulated for any number of cumulative probabilities, p, using the quantile function Q to calculate the value x, for each cumulative probability p, with the probability density given by ⁠ 1 / q ⁠, the reciprocal of the quantile density function. As is the usual case with statistical ...

  7. Gamma distribution - Wikipedia

    en.wikipedia.org/wiki/Gamma_distribution

    The corresponding probability density function in the shape-rate parameterization is ... The Laplace transform of the gamma PDF, ... from which we calculate the log ...

  8. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    Probability density function (pdf) or probability density: 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 random variable would equal that sample.

  9. Cauchy distribution - Wikipedia

    en.wikipedia.org/wiki/Cauchy_distribution

    When the mean of a probability distribution function (PDF) is undefined, no one can compute a reliable average over the experimental data points, regardless of the sample's size. Note that the Cauchy principal value of the mean of the Cauchy distribution is lim a → ∞ ∫ − a a x f ( x ) d x {\displaystyle \lim _{a\to \infty }\int _{-a}^{a ...

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