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Fisher transformation via Edgeworth expansion
Jan Vrbik
We show how to calculate individual terms of the Edgeworth series to approximate the distribution of the Pearson correlation coefficient with the help of a simple Mathematica progr…
Confidence Regions for Parameters of Negative Binomial Distribution
Emmanuel Nkingi, Jan Vrbik
We describe a general method for the construction of a confidence region for the two parameters of the Negative Binomial Distribution. This is achieved by expanding the sampling di…
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…