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Title: Bivariate exponential distribution with atoms at zero Authors:  Clara Gardner - Technical University of Denmark (Denmark) [presenting]
Bo Friis Nielsen - Technical University of Denmark (Denmark)
Abstract: Raftery's bivariate exponential distribution, the Farlie-Gumbel-Morgenstern construction and the Kibble-distribution are three different models for bivariate exponential distributions, which all have a multivariate PH distribution of the MPH$^*$ type. The models are expanded to include atoms at 0 such that they can model non-negative data - e.g. waiting times. An advantage is that these modified models also will have an MPH$^*$ representation. For these three models, two questions are investigated: 1) How to perform parameter estimation? 2) Which types of data are most suited for each model? For the first question two estimation techniques are investigated, namely raw maximum likelihood estimation and the EM-algorithm for MPH$^*$ models. The two methods are compared both in terms of precision and computational time. The second question is not as easy to answer, and two different approaches are taken. Firstly, the stability of the models in the parameter space is investigated. Both the estimation errors and the variation in terms of the curvature are considered. Secondly, the versatility of the models is checked by fitting data stemming from one model to another model. At last, as a real-life application, the three models are tested on data of delays in public transport.