A finite mixture approach to univariate data simulation with moment matching. (April 2017) - Bardsley, Earl
Abstract: Environmental data simulation is carried out for various purposes and is most simply achieved when recorded data can be regarded as a sequence of independent random variables. Simulating from such data involves generating random variables from some fitted probability distribution, preserving the main statistical characteristics. The particular case of data simulation with moment matching is revisited, with a proposal that data be simulated from many-component finite mixture distributions. The simulation procedure matches data moments while also giving greater flexibility for data approximation. In contrast, a single parametric distribution fitted to irregular data will result in data simulations more representative of the fitted distribution than the original data. The flexible finite mixture approach therefore has potential to replace parametric univariate data simulation generally. The method is illustrated with simulations from finite mixtures of generalised beta distributions with matching of data mean, variance, skewness and kurtosis. Highlights: Data simulation is from many-component finite mixture distributions. Component distributions are sequentially fitted to small random data samples. Beta mixture distributions preserve data mean, variance, skewness, and kurtosis. Simulations can be within specified upper and lower bounds.