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  2. 68–95–99.7 rule - Wikipedia

    en.wikipedia.org/wiki/68–95–99.7_rule

    In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean ...

  3. Chebyshev's inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_inequality

    The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics. The inequality has great utility because it can be applied to any probability distribution in which the mean and variance are defined. For example, it can be used to prove the weak law of large numbers.

  4. Concentration inequality - Wikipedia

    en.wikipedia.org/wiki/Concentration_inequality

    The Dvoretzky–Kiefer–Wolfowitz inequality bounds the difference between the real and the empirical cumulative distribution function. Given a natural number n {\displaystyle n} , let X 1 , X 2 , … , X n {\displaystyle X_{1},X_{2},\dots ,X_{n}} be real-valued independent and identically distributed random variables with cumulative ...

  5. Chebyshev's theorem - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_theorem

    Chebyshev's theorem is any of several theorems proven by Russian mathematician Pafnuty Chebyshev. Bertrand's postulate, that for every n there is a prime between n and 2n. Chebyshev's inequality, on the range of standard deviations around the mean, in statistics; Chebyshev's sum inequality, about sums and products of decreasing sequences

  6. Chernoff bound - Wikipedia

    en.wikipedia.org/wiki/Chernoff_bound

    It is a sharper bound than the first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, when applied to sums the Chernoff bound requires the random variables to be independent, a condition that is not required by either Markov's inequality or ...

  7. Empirical statistical laws - Wikipedia

    en.wikipedia.org/wiki/Empirical_statistical_laws

    There are several such popular "laws of statistics". The Pareto principle is a popular example of such a "law". It states that roughly 80% of the effects come from 20% of the causes, and is thus also known as the 80/20 rule. [2] In business, the 80/20 rule says that 80% of your business comes from just 20% of your customers. [3]

  8. Multidimensional Chebyshev's inequality - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_Chebyshev...

    In probability theory, the multidimensional Chebyshev's inequality [1] is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount.

  9. Empirical probability - Wikipedia

    en.wikipedia.org/wiki/Empirical_probability

    More generally, empirical probability estimates probabilities from experience and observation. [ 2 ] Given an event A in a sample space, the relative frequency of A is the ratio ⁠ m n , {\displaystyle {\tfrac {m}{n}},} ⁠ m being the number of outcomes in which the event A occurs, and n being the total number of outcomes of the experiment.

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