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A closed-form sample size formula based on the noncentral χ2 test statistic is derived.
Zhang and Ahn (2012) derived a closed-form sample size formula for two-sample comparisons of time-averaged responses using the generalized estimating equation (GEE) approach, which takes into account different correlation structures and missing data patterns.
Since the ν parameter does not have a closed form, parameter samples were obtained at each round of the sampler with a Metropolis step (ν | y, μ, β, σ g i 2, σ e 2 ).
The method is made adaptive by a closed form updating rule to renew the sampling parameters.
In order to explicitly identify the impacts of the node density and sampling rate on the MSE, we will first focus on the analysis of system operating in the AWGN channel, and this will allow us to express the MSE as a closed form expression of the node density and sampling rate.
For a uniformly sampled data set of impulse response type a closed form expression can be given for the Fisher information using the solution of a Lyapunov equation.
The Wald test gives a closed form expression in terms of estimated odds ratios and standard errors, and in large samples the score and Wald tests are very close.
During implementation via a Bayesian MCMC approach, threshold levels were sampled using a Metropolis step because their fully conditional posterior distributions do not have a closed form.
where is a closed form.
where c is a closed form.
A differential -form is called a closed form if in.
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