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  2. Wilks' theorem - Wikipedia

    en.wikipedia.org/wiki/Wilks'_theorem

    However, in another test of a factor with 15 levels, they found a reasonable match to () – 4 more degrees of freedom than the 14 that one would get from a naïve (inappropriate) application of Wilks’ theorem, and the simulated p-value was several times the naïve ().

  3. Likelihood function - Wikipedia

    en.wikipedia.org/wiki/Likelihood_function

    A partial likelihood is an adaption of the full likelihood such that only a part of the parameters (the parameters of interest) occur in it. [33] It is a key component of the proportional hazards model: using a restriction on the hazard function, the likelihood does not contain the shape of the hazard over time.

  4. Total variation distance of probability measures - Wikipedia

    en.wikipedia.org/wiki/Total_variation_distance...

    Total variation distance is half the absolute area between the two curves: Half the shaded area above. In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.

  5. 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 ...

  6. Law of total variance - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_variance

    The following formula shows how to apply the general, measure theoretic variance decomposition formula [4] to stochastic dynamic systems. Let Y ( t ) {\displaystyle Y(t)} be the value of a system variable at time t . {\displaystyle t.}

  7. Law of total expectation - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_expectation

    The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value ⁡ is defined, and is any random variable on the same probability space, then

  8. PERT distribution - Wikipedia

    en.wikipedia.org/wiki/PERT_distribution

    In probability and statistics, the PERT distributions are a family of continuous probability distributions defined by the minimum (a), most likely (b) and maximum (c) values that a variable can take. It is a transformation of the four-parameter beta distribution with an additional assumption that its expected value is

  9. Cochran's theorem - Wikipedia

    en.wikipedia.org/wiki/Cochran's_theorem

    The following version is often seen when considering linear regression. [4] Suppose that Y ∼ N n ( 0 , σ 2 I n ) {\displaystyle Y\sim N_{n}(0,\sigma ^{2}I_{n})} is a standard multivariate normal random vector (here I n {\displaystyle I_{n}} denotes the n -by- n identity matrix ), and if A 1 , … , A k {\displaystyle A_{1},\ldots ,A_{k}} are ...