Convolution and sampling theory of the binormal distribution as a prerequisite to its application in statistical process control

Various researchers in the past have shown the suitability of the binormal (also known as the joined half-Gaussian or the two-piece normal) distribution for modelling natural phenomena which exhibit skewness. There is considerable scope for extending the application of this distribution to problems encountered in business and management, particularly in statistical process control using small samples. However, a prerequisite for use in an area such as this is that the consequences of convolution, or adding together independent random variables with known distribution, is predictable. This paper describes an investigation into the convolution of binormal distributions, which verifies their reproductive properties, and derives expressions for the parameters of the resulting distribution. Sampling from the binormal distribution is examined, a theory proposed and the results verified empirically.