Pedro Puig

Count Data Distributions: Some Characterizations With Applications

In this article we characterize all two-parameter count distributions (satisfying very general conditions) that are partially closed under addition. We also find those for which the maximum likelihood estimator of the population mean is the sample mean. Mixed Poisson models satisfying these properties are completely determined. Among these models are the negative binomial, Poisson-inverse Gaussian, and other known distributions. New count distributions can also be constructed using these characterizations. Three examples of application are given.

Requirement for a standardized nomenclature criterium for PCBs : computer-assisted assignment of correct congener denomination and numbering

Abstract Due to the great number of congeners, the use of the correct nomenclature for PCBs is a difficult task, and unfortunately errors in the assignment of chemical denominations are not unusual. We suggest in this paper to correctly apply the rules initially introduced by Ballschmiter and Zell in 1980, which differ from those of the IUPAC. A simple algorithm in BASIC was created to help researchers in this field to denominate all the 209 congeners by their correct Ballschmiter and Zell and/or IUPAC systematic names.

Tests of Fit for the Laplace Distribution, With Applications

Tests are given for the Laplace or double exponential distribution. The test statistics are based on the empirical distribution function and include the families of Cramér-von Mises and Kolmogorov-Smirnov. Asymptotic theory is given, and asymptotic points are calculated, for the Cramér-von Mises family, and Monte Carlo points for finite samples are given for all the statistics. Power studies suggest that the Watson statistic is the most powerful for the common problem of testing Laplace against other symmetric distributions. An application of the Laplace distribution is in LAD (or L1) regression. This is also discussed in the article, with two examples.

Characterizing Additively Closed Discrete Models by a Property of Their Maximum Likelihood Estimators, With an Application to Generalized Hermite Distributions

This article reports on two-parameter count distributions (satisfying very general conditions) that are closed under addition so that their maximum likelihood estimator (MLE) of the population mean is the sample mean. The most important of these in practice, the generalized Hermite distribution, is analyzed, and a necessary and sufficient condition is given to ensure that the MLE is the solution of likelihood equations. Score test to contrast the Poisson assumption is studied, and two examples of applications are given.

The Best Test of Exponentiality against Singly Truncated Normal Alternatives

Abstract We show that the likelihood ratio test of exponentiality against singly truncated normal alternatives is the uniformly most powerful unbiased test and can be expressed in terms of the sampling coefficient of variation. This test is closely related to Greenwoods statistic for testing departures from the uniform distribution. We provide a way to approximate the critical points of the test, using saddlepoint methods, that gives a high degree of accuracy.

Goodness-of-Fit Tests for the Skew-Normal Distribution When the Parameters Are Estimated from the Data

In this article, tests are developed which can be used to investigate the goodness-of-fit of the skew-normal distribution in the context most relevant to the data analyst, namely that in which the parameter values are unknown and are estimated from the data. We consider five test statistics chosen from the broad Cramér–von Mises and Kolmogorov–Smirnov families, based on measures of disparity between the distribution function of a fitted skew-normal population and the empirical distribution function. The sampling distributions of the proposed test statistics are approximated using Monte Carlo techniques and summarized in easy to use tabular form. We also present results obtained from simulation studies designed to explore the true size of the tests and their power against various asymmetric alternative distributions.

A statistical model for hospital admissions caused by seasonal diseases

We present a model based on two-order integer-valued autoregressive time series to analyze the number of hospital emergency service arrivals caused by diseases that present seasonal behavior. We also introduce a method to describe this seasonality, on the basis of Poisson innovations with monthly means. We show parameter estimation by maximum likelihood and model validation and show several methods for forecasting, on the basis of long-time means and short-time and long-time prediction regions. We analyze an application to model the number of hospital admissions per week caused by influenza.

A flexible count data model to fit the wide diversity of expression profiles arising from extensively replicated RNA-seq experiments

BackgroundHigh-throughput RNA sequencing (RNA-seq) offers unprecedented power to capture the real dynamics of gene expression. Experimental designs with extensive biological replication present a unique opportunity to exploit this feature and distinguish expression profiles with higher resolution. RNA-seq data analysis methods so far have been mostly applied to data sets with few replicates and their default settings try to provide the best performance under this constraint. These methods are based on two well-known count data distributions: the Poisson and the negative binomial. The way to properly calibrate them with large RNA-seq data sets is not trivial for the non-expert bioinformatics user.ResultsHere we show that expression profiles produced by extensively-replicated RNA-seq experiments lead to a rich diversity of count data distributions beyond the Poisson and the negative binomial, such as Poisson-Inverse Gaussian or Pólya-Aeppli, which can be captured by a more general family of count data distributions called the Poisson-Tweedie. The flexibility of the Poisson-Tweedie family enables a direct fitting of emerging features of large expression profiles, such as heavy-tails or zero-inflation, without the need to alter a single configuration parameter. We provide a software package for R called tweeDEseq implementing a new test for differential expression based on the Poisson-Tweedie family. Using simulations on synthetic and real RNA-seq data we show that tweeDEseq yields P-values that are equally or more accurate than competing methods under different configuration parameters. By surveying the tiny fraction of sex-specific gene expression changes in human lymphoblastoid cell lines, we also show that tweeDEseq accurately detects differentially expressed genes in a real large RNA-seq data set with improved performance and reproducibility over the previously compared methodologies. Finally, we compared the results with those obtained from microarrays in order to check for reproducibility.ConclusionsRNA-seq data with many replicates leads to a handful of count data distributions which can be accurately estimated with the statistical model illustrated in this paper. This method provides a better fit to the underlying biological variability; this may be critical when comparing groups of RNA-seq samples with markedly different count data distributions. The tweeDEseq package forms part of the Bioconductor project and it is available for download at http://www.bioconductor.org.

Suitability of FISH painting techniques for the detection of partial-body irradiations for biological dosimetry.

Abstract Duran, A., Barquinero, J. F., Caballín, M. R., Ribas, M., Puig, P., Egozcue, J. and Barrios, L. Suitability of FISH Painting Techniques for the Detection of Partial-Body Irradiations for Biological Dosimetry. Radiat. Res. 157, 461–468 (2002). Peripheral blood was irradiated with 2, 3, 4 or 5 Gy of X rays and was mixed with nonirradiated blood at five different dilutions to simulate partial-body irradiations. Analysis by FISH was performed using whole-chromosome painting probes for chromosomes 1, 4 and 11 in combination with a pancentromeric probe. Chromosome aberrations affecting the painted fraction were classified according to the PAINT nomenclature; other unstable aberrations affecting the unpainted material were also recorded. To evaluate the suitability of painting for dose assessment in partial-body irradiations, the ability of the u test and a proposed s test to detect the expected overdispersion and the similarity between the real doses and the doses estimated using Dolphins approach were considered. For short-term biodosimetry, compared with solid-stained dicentric analyses, the suitability of FISH painting techniques for the detection of partial-body exposures is reduced, because of the decrease in the frequency of aberrations detected by FISH and in the number of cells with two or more aberrations. For reconstruction of past doses, when only complete apparently simple translocations in cells free of unstable aberrations were considered, the detection of the overdispersion and the accuracy of dose estimations were dramatically reduced. In a partial-body exposure, as the original dose increased, the whole-body dose estimated a long time after irradiation would tend to be lower, and the difference from the original dose would tend to be greater.

Testing Departures from Gamma, Rayleigh and Truncated Normal Distributions

This paper provides necessary and sufficient conditions for a solution to likelihood equations for an exponential family of distributions, which includes Gamma, Rayleigh and singly truncated normal distributions. Furthermore, the maximum likelihood estimator is obtained as a limit case when the equations have no solution. These results provide a way to test departures from Rayleigh and singly truncated normal distributions using the likelihood ratio test. A new easy way to test departures from a Gamma distribution is also introduced.