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Full-Text Articles in Mathematics
Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen Bansal, Gholamhossein Hamedani, Ru Sheng
Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen Bansal, Gholamhossein Hamedani, Ru Sheng
Naveen Bansal
We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the …
Creating Composite Age Groups To Smooth Percentile Rank Distributions Of Small Samples, Francesca Lopez, Amy Olson, Naveen Bansal
Creating Composite Age Groups To Smooth Percentile Rank Distributions Of Small Samples, Francesca Lopez, Amy Olson, Naveen Bansal
Naveen Bansal
Individually administered tests are often normed on small samples, a process that may result in irregularities within and across various age or grade distributions. Test users often smooth distributions guided by Thurstone assumptions (normality and linearity) to result in norms that adhere to assumptions made about how the data should look. Test users, however, may come across particular tests or sets of data in which the Thurstone assumptions are untenable. When users expect deviations from normality within age or grade, an alternate method is desirable. The authors present a relatively simple procedure that allows the user to treat observed raw …