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The issue of sample size for Mokken scaling is largely unresolved. Work using simulated samples and varying the item quality in the scales (Loevinger's coefficient and the correlation between scales) suggests that, where the quality of the items is high that lower samples sizes in the region of 250–500 are required compared with sample sizes ...
The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain Jacobi series. [ 6 ]
In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible.
Consider a finite state irreducible aperiodic Markov chain with state space and (unique) stationary distribution (is a probability vector). Suppose that we come up with a probability distribution on the set of maps : with the property that for every fixed , its image () is distributed according to the transition probability of from state .
Some tests perform univariate analysis on a single sample with a single variable. Others compare two or more paired or unpaired samples. Unpaired samples are also called independent samples. Paired samples are also called dependent. Finally, there are some statistical tests that perform analysis of relationship between multiple variables like ...
For a -approximation of the optimal expected revenue, when the bidders are i.i.d OR when there is an unlimited supply of items (digital goods), the sample-complexity is (/) when the agents' distributions have monotone hazard rate, and (/) when the agents' distributions are regular but do not have monotone-hazard-rate.