Latent GLM Tweedie Distribution in Butterflies Species Counts

Political scientists often study dollar-denominated outcomes that are zero for some observations. These zeros can arise because the data-generating process is granular: The observed outcome results from aggregation of a small number of discrete projects or grants, each of varying dollar size. This article describes the use of a compound distribution in which each observed outcome is the sum of a Poisson—distributed number of gamma distributed quantities, a special case of the Tweedie distribution. Regression models based on this distribution estimate loglinear marginal effects without either the ad hoc treatment of zeros necessary to use a log-dependent variable regression or the change in quantity of interest necessary to use a tobit or selection model. The compound Poisson—gamma regression is compared with commonly applied approaches in an application to data on high-speed rail grants from the United States federal government to the states, and against simulated data from several data-generating processes.

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Dividend payout ratio follows a Tweedie distribution: international evidence

Economics The Open-Access Open-Assessment E-Journal ◽

10.5018/economics-ejournal.ja.2019-45 ◽

2019 ◽

Cited By ~ 2

Author(s):

Victor Dragotă ◽

Daniel Traian Pele ◽

Hanaan Yaseen

Keyword(s):

Dividend Payout ◽

International Evidence ◽

Tweedie Distribution

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The Investigation of a Forward-Rate Mortality Framework

Risks ◽

10.3390/risks7020061 ◽

2019 ◽

Vol 7 (2) ◽

pp. 61

Author(s):

Daniel H. Alai ◽

Katja Ignatieva ◽

Michael Sherris

Keyword(s):

Interest Rates ◽

Financial Management ◽

Financial Risk ◽

Covariance Structure ◽

Forward Rate ◽

Longevity Risk ◽

Demographic Projections ◽

Stochastic Mortality Models ◽

Tweedie Distribution ◽

Insurance Funds

Stochastic mortality models have been developed for a range of applications from demographic projections to financial management. Financial risk based models built on methods used for interest rates and apply these to mortality rates. They have the advantage of being applied to financial pricing and the management of longevity risk. Olivier and Jeffery (2004) and Smith (2005) proposed a model based on a forward-rate mortality framework with stochastic factors driven by univariate gamma random variables irrespective of age or duration. We assess and further develop this model. We generalize random shocks from a univariate gamma to a univariate Tweedie distribution and allow for the distributions to vary by age. Furthermore, since dependence between ages is an observed characteristic of mortality rate improvements, we formulate a multivariate framework using copulas. We find that dependence increases with age and introduce a suitable covariance structure, one that is related to the notion of ax minimum. The resulting model provides a more realistic basis for capturing the risk of mortality improvements and serves to enhance longevity risk management for pension and insurance funds.

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Differences in Household size, Employment Status and Ability to pay for the service, are Associated with Distance Travelled for Inpatient Care in Kenya

10.20944/preprints202009.0412.v1 ◽

2020 ◽

Author(s):

Ngugi Mwenda ◽

Ruth Nduati ◽

Mathew Kosgey ◽

Gregory Kerich

Keyword(s):

Health Facility ◽

Rural Areas ◽

Inpatient Care ◽

Economic Status ◽

Continuous Variable ◽

Household Size ◽

Poor People ◽

Long Distance ◽

Ability To Pay ◽

Tweedie Distribution

Background: Distance to a health facility for inpatient care in developing countries has been a huge hindrance towards the achievement of the Sustainable Development Goal three. The United Nation encourages countries to research on access to inpatient care, so as to form health policies based on data. Methods: Data on four hundred and eighty-one participants of all ages from forty-seven counties in Kenya who sought inpatient care in Kenya in 2018 were analyzed. Distance to a health facility was captured as a continuous variable and was self-reported by the respondent. The response exhibited a discrete mass at zero and continuous characteristic, therefore a Tweedie distribution was adopted for modelling. Due to the correlation nature of clustered data, we embraced the Generalized Estimating Equations approach with an exchangeable correlation. Since no standard software was available to analyze this problem, we developed an R functions. We assessed the best model fit using the QICu and criteria, in which the lowest value for the former and the highest for the later are preferred.Findings: Differences in employment, ability to pay for the service and household size are associated with the distance covered to access government facilities. Interpretation: Poor people tend to have large households and are more likely to live in rural areas and slums, thus are forced to travel for long distance to access inpatient care. Compared to unemployed, the employed could have better socio-economic status and possibly live within reach of the inpatient health facilities, therefore travel less distances to access. Longer distances are associated with high payments, signifying some form of specialized treatment care due to the complexity of the medical cases, that are expensive to treat.

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Differential expression of single-cell RNA-seq data using Tweedie models

10.1101/2021.03.28.437378 ◽

2021 ◽

Author(s):

Himel Mallick ◽

Suvo Chatterjee ◽

Shrabanti Chowdhury ◽

Saptarshi Chatterjee ◽

Ali Rahnavard ◽

...

Keyword(s):

Single Cell ◽

Differential Expression ◽

Statistical Power ◽

Heavy Tails ◽

Linear Models ◽

Dynamic Range ◽

Expression Profiles ◽

R Package ◽

Tweedie Distribution ◽

Probability Mass

SummaryThe performance of computational methods and software to identify differentially expressed genes in single-cell RNA-sequencing (scRNA-seq) has been shown to be influenced by several factors, including the choice of the normalization method used and the choice of the experimental platform (or library preparation protocol) to profile gene expression in individual cells. Currently, it is up to the practitioner to choose the most appropriate differential expression (DE) method out of over 100 DE tools available to date, each relying on their own assumptions to model scRNA-seq data. Here, we propose to use generalized linear models with the Tweedie distribution that can flexibly capture a large dynamic range of observed scRNA-seq data across experimental platforms induced by heavy tails, sparsity, or different count distributions to model the technological variability in scRNA-seq expression profiles. We also propose a zero-inflated Tweedie model that allows zero probability mass to exceed a traditional Tweedie distribution to model zero-inflated scRNA-seq data with excessive zero counts. Using both synthetic and published plate- and droplet-based scRNA-seq datasets, we performed a systematic benchmark evaluation of more than 10 representative DE methods and demonstrate that our method (Tweedieverse) outperforms the state-of-the-art DE approaches across experimental platforms in terms of statistical power and false discovery rate control. Our open-source software (R package) is available at https://github.com/himelmallick/Tweedieverse.

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Testing for the Poisson–Tweedie distribution

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2018.08.001 ◽

2019 ◽

Vol 164 ◽

pp. 146-162 ◽

Cited By ~ 1

Author(s):

M.D. Jiménez-Gamero ◽

M.V. Alba-Fernández

Keyword(s):

Tweedie Distribution

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Standardizing blue ling landings per unit effort from industry haul-by-haul data using generalized additive models

ICES Journal of Marine Science ◽

10.1093/icesjms/fsq048 ◽

2010 ◽

Vol 67 (8) ◽

pp. 1650-1658 ◽

Cited By ~ 15

Author(s):

Pascal Lorance ◽

Lionel Pawlowski ◽

Verena M. Trenkel

Keyword(s):

Deep Water ◽

Generalized Additive Models ◽

Additive Models ◽

Spawning Season ◽

The West ◽

Explanatory Variables ◽

Unit Effort ◽

Abundance Indices ◽

Tweedie Distribution ◽

Logbook Data

Abstract Lorance, P., Pawlowski, L., and Trenkel, V. M. 2010. Standardizing blue ling landings per unit effort from industry haul-by-haul data using generalized additive models. – ICES Journal of Marine Science, 67: 1650–1658. Haul-by-haul data derived from skippers' personal logbooks, from the French deep-water fishery to the west of the British Isles, were used to calculate standardized blue ling (Molva dypterygia) landings per unit effort (lpue) for the period 2000–2008. Lpue values were estimated using generalized additive models with depth, vessel, statistical rectangle, area, and year as explanatory variables. Because of their statistical distribution, landings were modelled by a Tweedie distribution, which allows datasets to contain many zeros. To investigate how to track stock trends reliably, lpue values were estimated in five areas for different subsets of the data. The subsets consisted of hauls during the spawning season (when blue ling aggregate), outside the spawning season, and hauls in which blue ling was only a bycatch. The results suggest that blue ling lpue values have been stable over the period 2000–2008, and that the declining trend previously observed for the stock has been halted. This finding is consistent with stable mean lengths in the landings during the same period. The study demonstrates the greater suitability of haul-by-haul data than EC logbook data for deriving abundance indices for deep-water stocks.

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1/ f Noise and multifractality from bristlecone pine growth explained by the statistical convergence of random data

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2016.0586 ◽

2017 ◽

Vol 473 (2198) ◽

pp. 20160586 ◽

Cited By ~ 3

Author(s):

Wayne S. Kendal

Keyword(s):

Power Law ◽

Random Systems ◽

Mean Power ◽

Random Data ◽

Pine Tree ◽

Self Organized ◽

Bristlecone Pine ◽

Tweedie Distribution ◽

Self Organized Criticality ◽

Non Gaussian

Tree-ring growth records from bristlecone pines reveal an irregular pattern of fluctuations that have been linked to climatic change but otherwise have remained poorly understood. We find within these records evidence for a temporally related variance to mean power law, 1/ f noise and multifractality that empirically resembles a fractal stochastic process and could be attributed to self-organized criticality. These growth records, however, also conformed to a non-Gaussian statistical distribution (the Tweedie compound Poisson distribution) characterized by an inherent variance to mean power law, that by itself implies 1/ f noise. This distribution has a fundamental role in statistical theory as a focus of convergence for many types of random data, much like the Gaussian distribution has with the central limit theorem. The growth records were also multifractal, with the dimensional exponent of the Tweedie distribution critically balanced near the transition point between fractal stochastic processes and gamma distributed data, possibly consequent to a related convergence effect. Non-Gaussian random systems, like those related to bristlecone pine tree growth, may express 1/ f noise and multifractality through mathematical convergence effects alone, without the dynamical assumptions of self-organized criticality.

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