We consider input deterministic finite state transducers with infinite inputs and outputs, we the property of Borel normality on words. When these are given by a strongly connected set states, when is normal sequence, output an word such that every has frequency weighted automaton over rationals. prove there algorithm decides in cubic time whether transducer preserves normality.

Functional mapping has been a powerful tool in mapping quantitative trait loci (QTL) underlying dynamic traits of agricultural or biomedical interest. In functional mapping, multivariate normality is often assumed for the underlying data distribution, partially due to the ease of parameter estimation. The normality assumption however could be easily violated in real applications due to various ...

Various parametric tests make assumptions of the normal distribution, including t-test, analysis of variance (ANOVA), correlation, and regression. Different from some researcher’s understanding, tests of normality are not for the normality of observed data but for normality of the population distribution of a random characteristic; e.g. assuming normality for the population distribution of the ...