EM algorithm for an extension of the Waring distribution

Cueva-López, Valentina; Olmo-Jiménez, María José; Avi, José Rodríguez

doi:10.1002/cmm4.1046

Cited by 4 publications

(1 citation statement)

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“…This distribution belongs to the family of discrete distributions generated by the Gaussian hypergeometric function when the two first parameters are complex conjugated numbers (i.e., 2 F 1 (a + ib, a − ib; γ; 1), where i is the imaginary unit), and it has been widely studied in [11,12]. Two particular cases with two parameters have also been developed: the complex biparametric Pearson (CBP) distribution [13,14] and the extended bivariate Waring (EBW) distribution [15,16]. It is interesting to take into account the fact that the CTP and EBW models can handle both over-and underdispersion, whereas the CBP model can only handle overdispersion.…”

Section: Introductionmentioning

confidence: 99%

cpd: An R Package for Complex Pearson Distributions

2022

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The complex Pearson (CP) distributions are a family of probability models for count data generated by the Gaussian hypergeometric function with complex arguments. The complex triparametric Pearson (CTP) distribution and its biparametric versions, the complex biparametric Pearson (CBP) and the extended biparametric Waring (EBW) distributions, belong to this family. They all have explicit expressions of the probability mass function (pmf), probability generating function and moments, so they are easy to handle from a computational point of view. Moreover, the CTP and EBW distributions can model over- and underdispersed count data, whereas the CBP can only handle overdispersed data, but unlike other well-known overdispersed distributions, the overdispersion is not due to an excess of zeros but other low values of the variable. Finally, the EBW distribution allows the variance to be split into three uniquely identifiable components: randomness, liability and proneness. These properties make the CP distributions of interest in the modeling of a great variety of data. For this reason, and for trying to spread their use, we have implemented an R package called cpd that contains the pmf, distribution function, quantile function and random generation for these distributions. In addition, the package contains fitting functions according to the maximum likelihood. This package is available from the Comprehensive R Archive Network (CRAN). In this work, we describe all the functions included in the cpd package, and we illustrate their usage with several examples. Moreover, the release of a plugin in order to use the package from the interface R Commander tries to contribute to the spreading of these models among non-advanced users.

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Section: Introductionmentioning

confidence: 99%

cpd: An R Package for Complex Pearson Distributions

2022

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Pedestrian Trajectory Prediction using BiLSTM with Spatial-Temporal Attention and Sparse Motion Fields

Khel

Greaney

McAfee

et al. 2023

2023 34th Irish Signals and Systems Conference (ISSC)

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Modeling the Overdispersion of Pasteuria penetrans Endospores

Vagelas

Leontopoulos

2022

Parasitologia

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This paper discusses a process of developing the data analysis and modeling of Pasteuria penetrans spore attachment in vitro and in planta, based on the observation that the number of spores attaching to juveniles within a given time increased by increasing the time of exposure to spores and the spores dose. Based on this, the P. penetrans spore attachment in vitro was modeled using the negative binomial distribution which permits decomposing the observation’s variability into three components: randomness, internal differences between individuals, and the presence of other external factors, e.g., the soil type. Additionally, we developed case-detection methods to explain P. penetrans spores’ attachment variability. The statistical methods developed in this paper show that a nematodes invasion is significant limited when second stage juveniles (J2s) are encumbered with seven P. penetrans spores. This research study concludes that the number of spores attached in J2s, the time of exposure of J2s to P. penetrans spores, and the soil texture are important factors affecting the invasion of root-knot nematodes in tomato plants.

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EM algorithm for an extension of the Waring distribution

Cited by 4 publications

References 20 publications

cpd: An R Package for Complex Pearson Distributions

cpd: An R Package for Complex Pearson Distributions

Pedestrian Trajectory Prediction using BiLSTM with Spatial-Temporal Attention and Sparse Motion Fields

Modeling the Overdispersion of Pasteuria penetrans Endospores

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