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  2. Poisson regression - Wikipedia

    en.wikipedia.org/wiki/Poisson_regression

    In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. [1] Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters.

  3. Fixed-effect Poisson model - Wikipedia

    en.wikipedia.org/wiki/Fixed-effect_Poisson_model

    Linear panel data models use the linear additivity of the fixed effects to difference them out and circumvent the incidental parameter problem. Even though Poisson models are inherently nonlinear, the use of the linear index and the exponential link function lead to multiplicative separability, more specifically [2] E[y it ∨ x i1...

  4. Poisson distribution - Wikipedia

    en.wikipedia.org/wiki/Poisson_distribution

    In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]

  5. Regression analysis - Wikipedia

    en.wikipedia.org/wiki/Regression_analysis

    In practice, researchers first select a model they would like to estimate and then use their chosen method (e.g., ordinary least squares) to estimate the parameters of that model. Regression models involve the following components: The unknown parameters, often denoted as a scalar or vector.

  6. Overdispersion - Wikipedia

    en.wikipedia.org/wiki/Overdispersion

    The Poisson distribution has one free parameter and does not allow for the variance to be adjusted independently of the mean. The choice of a distribution from the Poisson family is often dictated by the nature of the empirical data. For example, Poisson regression analysis is commonly used to model count data. If overdispersion is a feature ...

  7. Prediction interval - Wikipedia

    en.wikipedia.org/wiki/Prediction_interval

    Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".

  8. Zero-inflated model - Wikipedia

    en.wikipedia.org/wiki/Zero-inflated_model

    Hilbe [3] notes that "Poisson regression is traditionally conceived of as the basic count model upon which a variety of other count models are based." In a Poisson model, "… the random variable y {\displaystyle y} is the count response and parameter λ {\displaystyle \lambda } (lambda) is the mean.

  9. Conway–Maxwell–Poisson distribution - Wikipedia

    en.wikipedia.org/wiki/Conway–Maxwell–Poisson...

    In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion.