Approximation of the inverse normal distribution function

Linear regression, the normal distribution of error values or normal distribution of the dependent variable?

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Approximation of Posterior Means and Variances of the Digitised Normal Distribution using Continuous Normal Approximation

Abstract All statistical measurements which represent the values of useful unknown quantities have a realm that is both finite and discrete. Thus our uncertainties about any measurement can be represented by discrete probability mass functions. Nonetheless, common statistical practice treats probability distributions as representable by continuous densities or mixture densities. Many statistica...

A Formula for the Approximation of Definite Integrals of the Normal Distribution Function

The Ellipsoid Normal Distribution Function

The Ellipsoid NDF is a new normal distribution function (NDF) that we introduce and use in the accompanying paper. It can be used with micro-facet BRDF to model the reflection and refraction of light from surfaces. This new distribution is a generalization of the widely used isotropic GGX/Trowbridge-Reitz distribution. The Ellipsoid model is based on the surface statistics of an arbitrary 3D el...

A New Approximation for the Null Distribution of the Likelihood Ratio Test Statistics for k Outliers in a Normal Sample

Usually when performing a statistical test or estimation procedure, we assume the data are all observations of i.i.d. random variables, often from a normal distribution. Sometimes, however, we notice in a sample one or more observations that stand out from the crowd. These observation(s) are commonly called outlier(s). Outlier tests are more formal procedures which have been developed for detec...