Marta Pérez-Casany

Weighted Poisson Distributions for Overdispersion and Underdispersion Situations

The main goal of this paper is to introduce new exponential families, that come from the concept of weighted distribution, that include and generalize the Poisson distribution. In these families there are distributions with index of dispersion greater than, equal to or smaller than one. This property makes them suitable to fit discrete data in overdispersion or underdispersion situations. We study the statistical properties of the families and we provide a useful interpretation of the parameters. Two classical examples are considered in order to compare the fits with some other distributions. To obtain the fits with the new family, the study of the profile log-likelihood is required.

Extended truncated Inverse Gaussian–Poisson model

The inverse Gaussian–Poisson mixture model is very useful when modelling highly skewed non-negative integer data in fields as diverse as linguistics, ecology, market research, bibliometry, engineering and insurance. When using this statistical model on the frequency of word or species frequency data, one typically truncates its sample space at zero to accommodate for the ignorance about the number of words or species that are not observed. In this paper, we show that by truncating the sample space of the inverse Gaussian–Poisson model, one is allowed to extend its parameter space and in that way improve its fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. By fitting the extended model to word frequency count data, we find many instances where the maximum likelihood estimates fall in the extension of the parameter space.

On zero-truncating and mixing Poisson distributions

The distributions that result from zero-truncating mixed Poisson (ZTMP) distributions and those obtained from mixing zero-truncated Poisson (MZTP) distributions are characterised based on their probability generating functions. One consequence is that every ZTMP distribution is an MZTP distribution, but not vice versa. These characterisations also indicate that the size-biased version of a Poisson mixture and, under certain regularity conditions, the shifted version of a Poisson mixture are neither ZTMP distributions nor MZTP distributions.

On left-truncating and mixing Poisson distributions

ABSTRACT The distributions obtained by left-truncating at k a mixed Poisson distribution, denoted kT-MP, and those obtained by mixing previously left-truncated Poisson distributions, denoted M-kTP, are characterized by means of their probability generating function. The main consequence is that every kT-MP distribution is a M-kTP distribution, but not the other way around.

Parameterizing a genetic optimizer

Genetic programming has been proposed as a possible although still intriguing approach for query optimization. There exist two main aspects which are still unclear and need further investigation, namely, the quality of the results and the speed to converge to an optimum solution. In this paper we tackle the first aspect and present and validate a statistical model that, for the first time in the literature, lets us state that the average cost of the best query execution plan (QEP) obtained by a genetic optimizer is predictable. Also, it allows us to analyze the parameters that are most important in order to obtain the best possible costed QEP. As a consequence of this analysis, we demonstrate that it is possible to extract general rules in order to parameterize a genetic optimizer independently from the random effects of the initial population.

IOAgent: a parallel I/O workload generator

The purpose of this paper is twofold. First, we present IOAgent, a tool that allows to generate synthetic workloads for parallel environments in a simple way. IOAgent has been implemented for Linux and takes into account different I/O characteristics like synchronous and asynchronous calls, buffered and unbuffered accesses, as well as different numbers of disks, intermediate buffers and number of agents simulating the workload. Second, we propose statistical models that help us to analyze the I/O behaviour of an IBM e-server OpenPower 710, with 4 SCSI drives. The observations used to build the model have been obtained using IOAgent.

Using the Marshall-Olkin Extended Zipf Distribution in Graph Generation

Being able to generate large synthetic graphs resembling those found in the real world, is of high importance for the design of new graph algorithms and benchmarks. In this paper, we first compare several probability models in terms of goodness-of-fit, when used to model the degree distribution of real graphs. Second, after confirming that the MOEZipf model is the one that gives better fits, we present a method to generate MOEZipf distributions. The method is shown to work well in practice when implemented in a scalable synthetic graph generator.Being able to generate large synthetic graphs resembling those found in the real world, is of high importance for the design of new graph algorithms and benchmarks. In this paper, we first compare several probability models in terms of goodness-of-fit, when used to model the degree distribution of real graphs. Second, after confirming that the MOEZipf model is the one that gives better fits, we present a method to generate MOEZipf distributions. The method is shown to work well in practice when implemented in a scalable synthetic graph generator.Being able to generate large synthetic graphs resembling those found in the real world, is of high importance for the design of new graph algorithms and benchmarks. In this paper, we first compare several probability models in terms of goodness-of-fit, when used to model the degree distribution of real graphs. Second, after confirming that the MOEZipf model is the one that gives better fits, we present a method to generate MOEZipf distributions. The method is shown to work well in practice when implemented in a scalable synthetic graph generator.