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An Approximation to the Probability Normal Distribution and its Inverse
An Approximation to the Probability Normal Distribution and its Inverse

... are specified in terms of their maximum absolute error. The absolute errors of the approximations are small but their relative errors are significant, which becomes important in the tail of probability distribution. In the present work, this inconvenience is shown for the best mathematical function ...
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... 5. P(37.5 < x < 45.5) = .6757 The probability that between 38 and 45 (inclusive) out of 50 planes land on time at the Sacramento Airport is .6757 A lay person might if say that if 50 planes land at the Sacramento Airport there is about a 66% chance that between 38 and 45 ( inclusive ) out of 50 land ...
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... where H ; H ; : : : ; H M are independent samples from the importance sampling function Q. For appropriate choice of Q this estimator will have much smaller variance than (1). Indeed, if Q is the posterior distribution P (H j An) then the estimator (2) will have zero variance, but unfortunately thi ...
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Generalized linear model

In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation of the model parameters. Maximum-likelihood estimation remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian approaches and least squares fits to variance stabilized responses, have been developed.
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