Title: On the computation of discrete mixtures of continuous distributions: Theoretical stability of algorithms
Authors: Jose Carlos Dias - ISCTE-IUL and UNIDE-IUL (Portugal)
Joao Pedro Nunes - ISCTE-IUL and UNIDE-IUL (Portugal)
Joana Leite - Coimbra Business School | ISCAC - IPC and CMUC (Portugal) [presenting]
Abstract: The importance of having good algorithms to compute certain values of interest in statistics and in other areas of knowledge cannot be disputed. Algorithms implemented in many software are usually unknown to the users and can subsist for many years, even though some problems arise with their use, either CPU time or accuracy and precision. This is the case of some cumulative distribution functions (cdf), namely discrete mixtures of continuous distributions, as noncentral $t$ and chi-square distributions. For the latter, the benchmark is the previous algorithms, based on the use of recurrence relations of special functions. The theoretical stability of these relations is not guaranteed when applied in both directions. In this setting and reporting new developments, the necessary adjustments in the algorithms are made and accuracy tests are carried out.