Abstract: The standard birth-death process with intensities of moderate growth generates stationary skewed distributions suitable for modelling frequency distributions of events arising in large-scale biomolecular systems.
We study a large class of such distributions that can be used to model, for instance, frequency distributions of the number of expressed genes in the transcriptome, the number of protein domain occurrences in the proteomes, etc.
In the present paper a new dediscretization approach is suggested, discussed and applied to the chosen class. This approach conserves the qualitative properties of the original class of distributions.
The advantages of the approach consist in following:
The deviations of the dediscretized continuous distribution functions from the original distribution functions is estimated.
Several typical examples are considered which illustrate the possibilities of the dediscretization approach.
The reverse procedure to dediscretization, i.e. the procedure of discretization, back to discrete distributions is described.
Keywords: Dediscretization, distribution, distribution function, regular variation, skewness, convexity, biomolecular systems.