Gamma Family Research Articles

An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences

Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter α, called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized type-2 beta family of densities, and generalized gamma family of densities, in the scalar as well as the matrix cases, also in the real and complex domains. It is shown that when the model is applied to physical situations then the current hot topics of Tsallis statistics and superstatistics in statistical mechanics become special cases of the pathway model, and the model is capable of capturing many stable situations as well as the unstable or chaotic neighborhoods of the stable situations and transitional stages. The pathway model is shown to be connected to generalized information measures or entropies, power law, likelihood ratio criterion or λ - criterion in multivariate statistical analysis, generalized Dirichlet densities, fractional calculus, Mittag-Leffler stochastic process, Krätzel integral in applied analysis, and many other topics in different disciplines. The pathway model enables one to extend the current results on quadratic and bilinear forms, when the samples come from Gaussian populations, to wider classes of populations.

An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications

Recently, probability models with thicker or thinner tails have gained more importance among statisticians and physicists because of their vast applications in random walks, Lévi flights, financial modeling, etc. In this connection, we introduce here a new family of generalized probability distributions associated with the Mittag–Leffler function. This family gives an extension to the generalized gamma family, opens up a vast area of potential applications and establishes connections to the topics of fractional calculus, nonextensive statistical mechanics, Tsallis statistics, superstatistics, the Mittag–Leffler stochastic process, the Lévi process and time series. Apart from examining the properties, the matrix-variate analogue and the connection to fractional calculus are also explained. By using the pathway model of Mathai, the model is further generalized. Connections to Mittag–Leffler distributions and corresponding autoregressive processes are also discussed.

How often should a firm modify its products? A Bayesian analysis of automobile modification cycles

In this paper, we develop and estimate a series of Bayesian generalized gamma family and mixture family models of product modification timing that take into account both firm- and industry-specific effects that are time varying. Our models are capable of capturing non-standard modification behavior such as multi-modality and non-monotonicity in the hazard rates motivated by real data. Additionally, we explore the existence of latent groups with respect to product modification timing strategies. The models are estimated using Markov chain Monte Carlo (MCMC) methods using a panel data from the automotive industry that covers 50 years and contains 6598 car model-year observations for 683 car models. The results reveal the non-monotonic modification behavior over time and the existence of three latent groups. Larger product portfolios and higher industry product proliferation lengthen the modification time. Brand and competitive modification dynamism increases the frequency of major modifications.

Influência de Estresse, Materialismo e Autoestima na Compra Compulsiva de Adolescentes

ResumoO comportamento relacionado à compra compulsiva se caracteriza por um impulso incontrolável e irracional que tende a manifestar-se quando os indivíduos vivenciam sentimentos negativos. Apesar de ser intensamente pesquisada, ainda restam dúvidas sobre os fatores influenciadores da compra compulsiva, em especial em públicos potencialmente vulneráveis, como é o caso do público adolescente. Ao considerar tal lacuna, este artigo analisa o comportamento de compra compulsiva, assim, buscando compreender os condicionantes oriundos dos níveis de autoestima, materialismo, estresse e prazer em comprar especificamente de consumidores adolescentes. A partir da revisão de literatura, foram definidas quatro hipóteses, que foram testadas a partir de dados coletados junto a uma amostra de 153 sujeitos. No teste das hipóteses, foi utilizada a técnica de regressão da família gama de modelos lineares generalizados, operacionalizados no software R. Os resultados demonstraram que fatores como estresse, materialismo e prazer em comprar influenciam o comportamento de compra compulsiva dos adolescentes, tendo-se constatado ainda que a autoestima não teve influência na compulsividade dos respondentes da pesquisa. A pesquisa inova na operacionalização dos dados e avança no conhecimento acadêmico sobre compulsividade no consumo, gerando conhecimento que pode servir para formuladores de políticas públicas e organizações sociais orientadas ao interesse do consumidor.

A climatological study of the effect of sea-surface temperature on North Atlantic hurricane intensification

The climatic influence of sea-surface temperature (SST) on intensification is examined for North Atlantic hurricanes by averaging hourly intensity increases from best-track data over the period 1986–2013 in 4° by 4° latitude–longitude grid cells. Independent monthly SST data over the same period are averaged in the same cells. After removing cells with cold water or fast moving hurricanes, the SST effect on intensification, at the climate scale, is quantified by regressing intensification onto SST while controlling for average intensity. The regression is performed using a generalized linear model from a gamma family and a logarithmic link function. The model shows a statistically significant relationship, with higher intensification values associated with higher SST values. On average, mean intensification increases by 16% [(9, 20)% uncertainty interval] for every 1 °C increase in mean SST. A clustered region where the model underpredicts intensification is noted over the southeastern Caribbean Sea, perhaps related to the fresh water plume from the Orinoco River.

Abstract 364: Pioglitazone Inhibition of Vascular Smooth Muscle Cell Proliferation is Associated with Activation of AMP-activated Protein Kinase but not Peroxisome Proliferator-Activated Receptor Gamma

Atherosclerosis and restenosis after angioplasty are associated with exaggerated proliferation of vascular smooth muscle cells (VSMCs). Pioglitazone (PIO), an antidiabetic drug that belongs to the family of peroxisome proliferator-activated receptor gamma (PPARg) agonists, reduces intimal hyperplasia after coronary angioplasty in diabetic and nondiabetic subjects. However, the molecular mechanisms by which PIO regulates VSMC phenotype remain unclear. The objective of the current study is to determine the role of AMP-activated protein kinase (AMPK, a cellular energy sensor) versus PPARg in PIO-induced changes in VSMC phenotype. Exposure of human aortic VSMCs to PIO followed by immunoblot analysis revealed a robust increase in the phosphorylation of AMPK (Thr172) and its downstream effector, Acetyl-CoA carboxylase (p < 0.05, n = 3), as a function of concentration (3 to 30 μM) and time (1 to 48 hr). Notably, PIO (30 μM, 48 hr) activation of AMPK remained essentially the same after PPARg downregulation (~90%) by target-specific siRNA (500 pmoles), suggesting lack of dependency on PPARg. In addition, PIO activation of AMPK was accompanied by induction of mitochondrial membrane depolarization with a trend toward an increase in AMP/ATP ratio (~40%), as revealed by tetramethylrhodamine methyl ester (TMRM) fluorescent redistribution & LC-MS/MS MRM analysis, respectively. Importantly, PIO pretreatment (30 μM, 30 min) resulted in significant inhibition of PDGF (30 ng/ml, 48 hr)-induced VSMC proliferation by ~85% (cell count) and the associated increases in proliferative markers (cyclin D1 and pRb) by > 95% (p < 0.05, n = 3). Downregulation of AMPKa1 (~80%) by target-specific AMPKa1 siRNA (500 pmoles) revealed that PIO-mediated AMPK activation inhibited mTORC1 signaling by > 95% & upregulated cell cycle inhibitor p27Kip1 by ~40%, thus accounting for PIO-mediated changes in VSMC phenotype. In vivo, PIO administration (10 mg/Kg/d, oral gavage) for 3 weeks in CJ57BL6 mice mitigated neointimal growth by ~60% in guide wire-injured femoral artery (p < 0.05, n = 8). In conclusion, the present study provides the first direct evidence for VSMC-specific AMPK activation by PIO, which may in part contribute to its vasoprotective effects in nondiabetic state.

Sample size calculations for skewed distributions.

BackgroundSample size calculations should correspond to the intended method of analysis. Nevertheless, for non-normal distributions, they are often done on the basis of normal approximations, even when the data are to be analysed using generalized linear models (GLMs).MethodsFor the case of comparison of two means, we use GLM theory to derive sample size formulae, with particular cases being the negative binomial, Poisson, binomial, and gamma families. By simulation we estimate the performance of normal approximations, which, via the identity link, are special cases of our approach, and for common link functions such as the log. The negative binomial and gamma scenarios are motivated by examples in hookworm vaccine trials and insecticide-treated materials, respectively.ResultsCalculations on the link function (log) scale work well for the negative binomial and gamma scenarios examined and are often superior to the normal approximations. However, they have little advantage for the Poisson and binomial distributions.ConclusionsThe proposed method is suitable for sample size calculations for comparisons of means of highly skewed outcome variables.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-015-0023-0) contains supplementary material, which is available to authorized users.

Breaking the mold: transcription factors in the anucleate platelet and platelet-derived microparticles.

Platelets are small anucleate blood cells derived from megakaryocytes. In addition to their pivotal roles in hemostasis, platelets are the smallest, yet most abundant, immune cells and regulate inflammation, immunity, and disease progression. Although platelets lack DNA, and thus no functional transcriptional activities, they are nonetheless rich sources of RNAs, possess an intact spliceosome, and are thus capable of synthesizing proteins. Previously, it was thought that platelet RNAs and translational machinery were remnants from the megakaryocyte. We now know that the initial description of platelets as “cellular fragments” is an antiquated notion, as mounting evidence suggests otherwise. Therefore, it is reasonable to hypothesize that platelet transcription factors are not vestigial remnants from megakaryocytes, but have important, if only partly understood functions. Proteins play multiple cellular roles to minimize energy expenditure for maximum cellular function; thus, the same can be expected for transcription factors. In fact, numerous transcription factors have non-genomic roles, both in platelets and in nucleated cells. Our lab and others have discovered the presence and non-genomic roles of transcription factors in platelets, such as the nuclear factor kappa β (NFκB) family of proteins and peroxisome proliferator-activated receptor gamma (PPARγ). In addition to numerous roles in regulating platelet activation, functional transcription factors can be transferred to vascular and immune cells through platelet microparticles. This method of transcellular delivery of key immune molecules may be a vital mechanism by which platelet transcription factors regulate inflammation and immunity. At the very least, platelets are an ideal model cell to dissect out the non-genomic roles of transcription factors in nucleated cells. There is abundant evidence to suggest that transcription factors in platelets play key roles in regulating inflammatory and hemostatic functions.

A note on gamma difference distributions

It is the aim of this note to point out that the double gamma difference distribution recently introduced by [Augustyniak M, and Doray, LG. Inference for a leptokurtic symmetric family of distributions represented by the difference of two gamma variables. J Statist Comput Simul. 2012;82:1621–1634] is well known in financial econometrics: it is the symmetric variance gamma family of distributions. We trace back to the various origins of this distribution. In addition, we consider in some detail the difference of two independent gamma distributed random variables with different shape parameters.

Cramér–Von Mises distance estimation for some positive infinitely divisible parametric families with actuarial applications

Cramér–Von Mises (CVM) inference techniques are developed for some positive flexible infinitely divisible parametric families generalizing the compound Poisson family. These larger families appear to be useful for parametric inference for positive data. The methods are based on inverting the characteristic functions. They are numerically implementable whenever the characteristic function has a closed form. In general, likelihood methods based on density functions are more difficult to implement. CVM methods also lead to model testing, with test statistics asymptotically following a chi-square distribution. The methods are for continuous models, but they can also handle models with a discontinuity point at the origin such as the case of compound Poisson models. Simulation studies seem to suggest that CVM estimators are more efficient than moment estimators for the common range of the compound Poisson gamma family. Actuarial applications include estimation of the stop loss premium, and estimation of the present value of cash flows when interest rates are assumed to be driven by a corresponding Lévy process.

Lens defects in Astyanax mexicanus Cavefish: evolution of crystallins and a role for alphaA-crystallin.

The fish Astyanax mexicanus presents, within the same species, populations of river-dwelling surface fish (SF) and blind cave-living fish. In cavefish (CF), the eyes develop almost normally during embryogenesis. But 40 h after fertilization, the lens enters apoptosis, triggering the progressive degeneration of the entire eye. Before apoptosis, the CF lens expresses early differentiation factors correctly. Here, we searched for possible late differentiation defects that would be causal in CF lens degeneration. We reasoned that crystallins, the major lens structural proteins, could be defective or misregulated. We surveyed the CF and SF transcriptomes and uncovered 14 Astyanax crystallins from the beta, gamma, lambda, mu, and zeta families. These proteins are less polymorphic and accumulate more fixed mutations, some at highly conserved positions, in CF than in SF, suggesting relaxed selection at these loci in CF. In situ hybridizations and qPCR show that crybb1c, crybgx, crygm5 are expressed at much lower levels or are not expressed in the CF lens. For the best crystallin candidates, we tested a potential causal role in CF lens apoptosis. Crybgx, crybb1c (not expressed in CF from very early on), and cryaa (previously shown to be faintly expressed in CF) failed to induce any defect when knocked-down in zebrafish embryos. However, the anti-apoptotic cryaa protected lens cells from apoptosis when reexpressed by transgenesis in CF, suggesting a cell-autonomous effect of cryaa on lens cell survival. Altogether, these data suggest that crystallin sequence evolution and expression defects may contribute to the loss of eyes in CF.

Small Sample Tests for Shape Parameters of Gamma Distributions

The introduction of shape parameters into statistical distributions provided flexible models that produced better fit to experimental data. The Weibull and gamma families are prime examples wherein shape parameters produce more reliable statistical models than standard exponential models in lifetime studies. In the presence of many independent gamma populations, one may test equality (or homogeneity) of shape parameters. In this article, we develop two tests for testing shape parameters of gamma distributions using chi-square distributions, stochastic majorization, and Schur convexity. The first one tests hypotheses on the shape parameter of a single gamma distribution. We numerically examine the performance of this test and find that it controls Type I error rate for small samples. To compare shape parameters of a set of independent gamma populations, we develop a test that is unbiased in the sense of Schur convexity. These tests are motivated by the need to have simple, easy to use tests and accurate procedures in case of small samples. We illustrate the new tests using three real datasets taken from engineering and environmental science. In addition, we investigate the Bayes’ factor in this context and conclude that for small samples, the frequentist approach performs better than the Bayesian approach.

Does hospital academic status impact colon cancer care value?

6 Background: Given the high cost of cancer care, delivery of high-value care is crucial. The effect of hospital academic status on value of care for patients with stage II and III colon cancer is unknown. Methods: SEER-Medicare cohort study of 20,118 patients age 66+ with stage II or III colon cancer diagnosed 2000-2005 and followed through December 31, 2007. Patients were assigned to a treating hospital based on hospital affiliation of the primary oncologist. We constructed Kaplan-Meier curves to assess unadjusted overall survival. We estimated a Cox proportional hazards model to assess adjusted overall survival. To examine associations between hospital academic status and mean cost of care we estimated a generalized linear model (GLM) with log link and gamma family. We estimated quantile regression models to examine associations between hospital teaching status and cost at various quantiles (25th, 50th, 75th, 90th, 95th, 99th, 99.5th, 99.9th). Standard errors were adjusted to account for clustering of patients within hospitals. Results: 4449/20,118 (22%) patients received care from providers affiliated with academic hospitals. There was no significant difference in unadjusted median survival based on hospital academic status for patients with stage II (academic 6.4 yrs vs. non-academic 6.3 yrs, p=0.711) or stage III disease (academic 4.2 yrs vs. non-academic 4.2 yrs, p=0.81). After adjustment, treatment at academic hospitals was not associated with significantly reduced risk of death from colon cancer (stage II HR 1.05, 95% CI: 0.97 - 1.13; p=0.23; stage III HR 0.99, 95% CI: 0.94-1.07; p=0.98). Excepting stage III patients at the 99.9th percentile of costs, there were no significant differences in adjusted costs between academic and non-academic hospitals. Conclusions: We find no difference in overall survival for patients with stage II or stage III colon cancer based on academic status of the treating hospital. Furthermore, costs of care are similar between academic and non-academic hospitals across virtually the full range of the cost distribution. Most colon cancer patients do not receive cancer care at academic hospitals. Our findings indicate that for patients with stage II or III disease, this inequity does not impact the value of care.

The overlooked potential of Generalized Linear Models in astronomy-II: Gamma regression and photometric redshifts

Machine learning techniques offer a precious tool box for use within astronomy to solve problems involving so-called big data. They provide a means to make accurate predictions about a particular system without prior knowledge of the underlying physical processes of the data. In this article, and the companion papers of this series, we present the set of Generalized Linear Models (GLMs) as a fast alternative method for tackling general astronomical problems, including the ones related to the machine learning paradigm. To demonstrate the applicability of GLMs to inherently positive and continuous physical observables, we explore their use in estimating the photometric redshifts of galaxies from their multi-wavelength photometry. Using the gamma family with a log link function we predict redshifts from the PHoto-z Accuracy Testing simulated catalogue and a subset of the Sloan Digital Sky Survey from Data Release 10. We obtain fits that result in catastrophic outlier rates as low as ~1% for simulated and ~2% for real data. Moreover, we can easily obtain such levels of precision within a matter of seconds on a normal desktop computer and with training sets that contain merely thousands of galaxies. Our software is made publicly available as an user-friendly package developed in Python, R and via an interactive web application (https://cosmostatisticsinitiative.shinyapps.io/CosmoPhotoz). This software allows users to apply a set of GLMs to their own photometric catalogues and generates publication quality plots with minimum effort from the user. By facilitating their ease of use to the astronomical community, this paper series aims to make GLMs widely known and to encourage their implementation in future large-scale projects, such as the Large Synoptic Survey Telescope.

An EM algorithm for the estimation of parameters of a flexible cure rate model with generalized gamma lifetime and model discrimination using likelihood- and information-based methods

In this paper, we consider the Conway---Maxwell Poisson (COM-Poisson) cure rate model based on a competing risks scenario. This model includes, as special cases, some of the well-known cure rate models discussed in the literature. By assuming the time-to-event to follow the generalized gamma distribution, which contains some of the commonly used lifetime distributions as special cases, we develop exact likelihood inference based on the expectation maximization algorithm. The standard errors of the maximum likelihood estimates are obtained by inverting the observed information matrix. An extensive Monte Carlo simulation study is performed to examine the method of inference developed here. Model discrimination within the generalized gamma family is also carried out by means of likelihood- and information-based methods to select the particular lifetime distribution that provides an adequate fit to the data. Finally, a data on cancer recurrence is analyzed to illustrate the flexibility of the COM-Poisson family and the generalized gamma family so as to select a parsimonious competing cause distribution and a lifetime distribution that jointly provide an adequate fit to the data.

TRIM68 negatively regulates IFN-β production by degrading TRK fused gene, a novel driver of IFN-β downstream of anti-viral detection systems.

In recent years members of the tripartite motif-containing (TRIM) family of E3 ubiquitin ligases have been shown to both positively and negatively regulate viral defence and as such are emerging as compelling targets for modulating the anti-viral immune response. In this study we identify TRIM68, a close homologue of TRIM21, as a novel regulator of Toll-like receptor (TLR)- and RIG-I-like receptor (RLR)-driven type I IFN production. Proteomic analysis of TRIM68-containing complexes identified TRK-fused gene (TFG) as a potential TRIM68 target. Overexpression of TRIM68 and TFG confirmed their ability to associate, with TLR3 stimulation appearing to enhance the interaction. TFG is a known activator of NF-κB via its ability to interact with inhibitor of NF-κB kinase subunit gamma (IKK-γ) and TRAF family member-associated NF-κB activator (TANK). Our data identifies a novel role for TFG as a positive regulator of type I IFN production and suggests that TRIM68 targets TFG for lysosomal degradation, thus turning off TFG-mediated IFN-β production. Knockdown of TRIM68 in primary human monocytes resulted in enhanced levels of type I IFN and TFG following poly(I:C) treatment. Thus TRIM68 targets TFG, a novel regulator of IFN production, and in doing so turns off and limits type I IFN production in response to anti-viral detection systems.

Kullback–Leibler life time testing

The paper deals with testing the hypotheses for homogeneity and point null value of the scale parameter in the gamma family. Tests suggested here are based upon the Kullback–Leibler divergence from an observed vector to the canonical parameter (see Pázman, 1993 [14]), and upon its decomposition. The latter is used to derive the exact distribution of the test statistic by convolution. A geometric integration method is used alternatively to derive the distribution directly. Because it is observed by simulation, that the test’s performance is poor when the shape parameter is estimated from the data, an interval method is developed and its use is demonstrated in an analysis of real data.

A time-varying shared frailty model with application to infectious diseases

We propose a new parametric time-varying shared frailty model to represent changes over time in population heterogeneity, for use with bivariate current status data. The model uses a power transformation of a time-invariant frailty $U$, and is particularly convenient when $U$ is a member of the generalized gamma family. This model avoids some shortcomings of a previously suggested time-varying frailty model, notably time-dependent support. We describe some key properties of the model, including its relative frailty variance function in different settings and how the model can be fitted to data. We describe several applications to shared frailty modeling of bivariate current status data on infectious diseases, in which the frailty represents age-dependent heterogeneity in contact rates or susceptibility to infection.

Chi-Square Mixture of Transformed/Inverse Transformed Gamma Family

In this study, we define the chi-square mixture of transformed gamma distribution which contained some special submodels namely, the chi-square mixture of gamma, Weibull, and exponential mixture distributions. Also, the chi-square mixture of inverse transformed gamma distribution is defined and a class of submodels are deduced, that is, the chi-square mixture of inverse gamma, inverse Weibull, and inverse exponential mixture distributions. For both classes, statistical properties are investigated, that is, mean, variance, skewness and kurtosis using $r$th raw moment. The limiting behavior and special cases are also given to established relationships.

Maximum likelihood estimation of gamma parameters for coarsely binned and truncated raindrop size data

AbstractThe gamma family of probability densities has recently been used to model raindrop size. However, the traditional approach of using the method of moments to estimate the gamma distribution parameters is known to be biased and can have substantial errors. A recently developed approach combining moment information and a weighted least‐squares analysis generally produces substantially better results. Other procedures superior to the method of moments approach include maximum likelihood. In particular, maximum likelihood estimates have been shown to outperform method of moments estimators, both for the case in which the full range of drop sizes are observed and for the case in which small drop sizes fail to be observed because of the inability of disdrometers to record observations below a threshold.The foregoing comments on maximum likelihood concern the situation in which drop sizes are measured on a continuous scale. In this work we consider drop sizes from gamma distributions which are classified into broad size bins, as would be the case with data obtained from many disdrometers; this requires some modification of the maximum likelihood procedure. We also allow for the possibility of drop sizes below a threshold, or above another threshold, not being observed. Maximum likelihood performance in this case is investigated through simulation of volume sampling from gamma distributions with known parameters. We compare the performance of the maximum likelihood estimates with those of method of moments (only a truncated‐data version is viable) and the recently developed weighted least‐squares procedure, and also apply the three estimation procedures to some experimental data. Since the experimental data are surface data, we indicate how drop fall velocity may be incorporated to obtain parameters for the volume distributions from the surface data.