Sebaran probabilitas

Sababaraha sebaran probabiliti kacida pentingna dina téori atawa pamakéan dibéré ngaran nu husus:

• Sebaran diskrit
  • Dina kaayaan terhingga
    • Sebaran degenerate dina x₀, nu mana X mangrupa nilai penting dicokot jadi nilai x₀. This does not look random, but it satisfies the definition of variabel acak. This is useful because it puts deterministic variables and random variables in the same formalism.
    • The discrete uniform distribution, where all elements of a finite set are equally likely. This is supposed to be the distribution of a balanced coin, an unbiased die, a casino roulette or a well-shuffled deck. Also, one can use méasurements of quantum states to generate uniform random variables. All these are "physical" or "mechanical" devices, subject to design flaws or perturbations, so the uniform distribution is only an approximation of their behaviour. In digital computers, pseudo-random number generators are used to produced a statistically random discrete uniform distribution.
    • The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q=1-p.
    • Sebaran binomial, nu ngajelaskeun jumlah kasuksesan dina deret tina percobaan bébas Enya/Henteu.
    • The hypergeometric distribution, which describes the number of successes in the first m of a series of n independent Yes/No experiments, if the total number of successes is known.
  • With infinite support
    • The geometric distribution, a discrete distribution which describes the number of attempts needed to get the first success in a series of independent Yes/No experiments.
    • The negative binomial distribution, a generalization of the géometric distribution to the nth success.
    • The Poisson distribution, which describes the number of rare events that happen in a certain time interval.
    • The Boltzmann distribution, a discrete distribution important in statistical physics which describes the probabilities of the various discrete energy levels of a system in thermal equilibrium. It has a contiuous analogue. Special cases include
      • The Gibbs distribution
      • The Maxwell-Boltzmann distribution
      • The Bose-Einstein distribution
      • The Fermi-Dirac distribution
    • The zeta distribution has uses in applied statistics and statistical mechanics, and perhaps may be of interest to number théorists.
• Continuous distributions
  • Supported on a finite interval
    • sebaran seragam dina [a,b], nu mana sakabéh titik dina interval nu kawengku mibanda ajén nu ampir sarua.
    • Sebaran beta dina [0,1], mangrupa sebaran seragam dina kasus husus, nu dipaké dina estimasi probabiliti sukses.
    • The Triangular distribution on [a, b]
  • Supported on semi-infinite intervals, usually [0,∞)
    • Sebaran eksponensial, which describes the time between consecutive rare random events in a process with no memory.
    • Sebaran gamma, nu ngajelaskeun waktu salila n consecutive rare random events occur in a process with no memory.
    • The Erlang distribution, which is a special case of the gamma distribution with integral shape paraméter, developed to predict waiting times in queuing systems.
    • The Log-normal distribution, describing variables which can be modélled as the product of many small independent positive variables.
    • The Weibull distribution, of which the exponential distribution is a special case, is used to modél the lifetime of technical devices.
    • Sebaran chi-kuadrat, nu mangrupa jumlah kuadrat n variabel random Gauss bébas. Ieu mangrupa kasus husus dina sebaran Gamma, sarta dipaké dina tes goodness-of-fit dina statistik.
    • Sebaran-F, nu mana sebaran rasio dua sebaran variabel normal, dipaké dina analisa varian.
  • Supported on the whole réal line
    • Sebaran normal, disebut ogé Gaussian atawa kurva bel. It is ubiquitous in nature and statistics due to the central limit theorem: every variable that can be modélled as a sum of many small independent variables is approximately normal.
    • Sebaran-t student, dipaké keur nga-estimasi méan nu teu dipikanyaho dina populasi Gaussian.
    • Sebaran Cauchy, conto sebaran nu teu mibanda nilai ekspektasi atawa varian. Dina fisika biasana disebut Lorentzian, sarta ieu sebaran tina tetapan énérgi teu stabil dina mekanika kuantum. Dina fisika partikel, the extremely short-lived particles associated to such unstable states are called resonances.
• Joint distributions
  • Two or more random variables on the same sample space
    • Bivariate distribution
    • Conditional distribution
    • Multivariate distribution
    • Multinomial distribution, a generalization of the sebaran binomial.
• Sebaran nilai-matrix
  • sebaran Wishart
  • Matrix normal distribution
  • Matrix T distribution
  • Normal-inverse Wishart distribution

daptar jejer statistis -- variabel acak -- cumulative distribution function -- probability density function -- likelihood

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