List of Probability Topics - Properties of Probability Distributions

Properties of Probability Distributions

  • Central limit theorem
    • Illustration of the central limit theorem
    • Concrete illustration of the central limit theorem
    • Berry-Esséen theorem
    • Berry–Esséen theorem
    • De Moivre–Laplace theorem
    • Lyapunov's central limit theorem
    • Martingale central limit theorem
    • Infinite divisibility (probability)
    • Method of moments (probability theory)
    • Stability (probability)
    • Stein's lemma
  • Characteristic function (probability theory)
    • Lévy continuity theorem
  • Edgeworth series
  • Helly-Bray theorem
  • Location parameter
  • Maxwell's theorem
  • Moment-generating function
    • Factorial moment generating function
  • Negative probability
  • Probability-generating function
  • Vysochanskiï-Petunin inequality
  • Mutual information
  • Kullback-Leibler divergence
  • Normally distributed and uncorrelated does not imply independent
  • Le Cam's theorem
  • Large deviations theory
    • Contraction principle (large deviations theory)
    • Varadhan's lemma
    • Tilted large deviation principle
    • Rate function
    • Laplace principle (large deviations theory)
    • Exponentially equivalent measures
    • Cramér's theorem (second part)

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    A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.
    Ralph Waldo Emerson (1803–1882)

    The probability of learning something unusual from a newspaper is far greater than that of experiencing it; in other words, it is in the realm of the abstract that the more important things happen in these times, and it is the unimportant that happens in real life.
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