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Three competing patterns
Rita Abraham, Jan Vrbik
Assuming repeated independent sampling from a Bernoulli distribution with two possible outcomes S and F, there are formulas for computing the probability of one specific pattern of…
Accurate distribution of X^{T}X with singular, idempotent variance-covariance matrix
Hao Yuan Zhang, Jan Vrbik
Assume that X is a set of sample statistics which follow a special case Central Limit Theorem, namely: as the sample size n increases the corresponding distribution becomes multiva…
Improving Accuracy of Goodness-of-fit Test
Kris Duszak, Jan Vrbik
It is well known that the approximate distribution of the usual test statistic of a goodness-of-fit test is chi-square, with degrees of freedom equal to the number of categories mi…
Finding an ARMA(p,q) model given its spectral density or its correlogram
Jan Vrbik
An ARMA model can be fully determined based on either its spectral density, or its correlogram, i.e. a formula for computing the corresponding k th serial correlation for any integ…