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  2. Probability density function - Wikipedia

    en.wikipedia.org/wiki/Probability_density_function

    In this example, the ratio (probability of living during an interval) / (duration of the interval) is approximately constant, and equal to 2 per hour (or 2 hour −1). For example, there is 0.02 probability of dying in the 0.01-hour interval between 5 and 5.01 hours, and (0.02 probability / 0.01 hours) = 2 hour −1.

  3. Matrix normal distribution - Wikipedia

    en.wikipedia.org/wiki/Matrix_normal_distribution

    The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ⁡ ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...

  4. Fisher information - Wikipedia

    en.wikipedia.org/wiki/Fisher_information

    The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys ...

  5. Binomial proportion confidence interval - Wikipedia

    en.wikipedia.org/wiki/Binomial_proportion...

    The probability density function (PDF) for the Wilson score interval, plus PDF s at interval bounds. Tail areas are equal. Since the interval is derived by solving from the normal approximation to the binomial, the Wilson score interval ( , + ) has the property of being guaranteed to obtain the same result as the equivalent z-test or chi-squared test.

  6. Moment-generating function - Wikipedia

    en.wikipedia.org/wiki/Moment-generating_function

    In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution.Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.

  7. Design matrix - Wikipedia

    en.wikipedia.org/wiki/Design_matrix

    The design matrix contains data on the independent variables (also called explanatory variables), in a statistical model that is intended to explain observed data on a response variable (often called a dependent variable). The theory relating to such models uses the design matrix as input to some linear algebra : see for example linear regression.

  8. Fisher's exact test - Wikipedia

    en.wikipedia.org/wiki/Fisher's_exact_test

    Thus, we can calculate the exact probability of any arrangement of the 24 teenagers into the four cells of the table, but Fisher showed that to generate a significance level, we need consider only the cases where the marginal totals are the same as in the observed table, and among those, only the cases where the arrangement is as extreme as the ...

  9. Joint probability distribution - Wikipedia

    en.wikipedia.org/wiki/Joint_probability_distribution

    For example, for A the first of these cells gives the sum of the probabilities for A being red, regardless of which possibility for B in the column above the cell occurs, as ⁠ 2 / 3 ⁠. Thus the marginal probability distribution for A {\displaystyle A} gives A {\displaystyle A} 's probabilities unconditional on B {\displaystyle B} , in a ...