Gamma Model Research Articles

A UK cost-effectiveness analysis of trifluridine/tipiracil for heavily pretreated metastatic gastroesophageal cancers.

Background: The current work was designed to estimate the cost-effectiveness of trifluridine/tipiracil (T/T) versus best supportive care (BSC) for patients with advanced stage or metastatic gastroesophageal cancer (mGC) from a UK perspective. Materials & methods: A partitioned survival analysis was undertaken using data from the phase III TAGS trial. A jointly fitted lognormal model was selected for overall survivaland individual generalized gamma models were chosen for progression-free survival and time-to-treatment-discontinuation. The primary outcome was the cost per quality-adjusted life year (QALY) gained. Sensitivity analyses were undertaken to investigate uncertainty. Results: Compared with BSC, T/T was associated with a cost per QALY gained of £37,907. Conclusion: T/T provides a cost-effective treatment option for mGCin the UK setting.

Indications of an Achaea sp. caterpillar outbreak disrupting fruiting of an ectomycorrhizal tropical tree in Central African rainforest

Background and aims – Where one or several tree species come to dominate patches of tropical forest, as many masting ectomycorrhizal legumes do in Central Africa, ecological theory predicts they may be prone to herbivory, which might alter their reproductive output. This was indirectly investigated in lowland rainforest in Cameroon for Tetraberlinia korupensis, whose crowns were attacked in 2008 by an outbreaking black caterpillar—identified as an Achaea sp., probably A. catocaloides—in Korup National Park. Material and methods – Field-collected data on tree-level seed and fruit (pod) production of T. korupensis in its 2008 masting event were compared with that of its two co-dominant neighbours (T. bifoliolata, Microberlinia bisulcata), whose populations masted in 2007 (and 2010). To do this, bivariate regression models (linear, polynomial, ZiG [zero-inflated gamma model]), contingency table analysis, and non-parametric measures of dispersion were used. Key results – Assuming T. korupensis is prone to Achaea caterpillar attacks, empirical data support the hypothesized lower proportion of adults participating in its masting (54% in 2008) than for either masting population of M. bisulcata (98% in 2007, 89% in 2010) or T. bifoliolata (96% in 2007, 78% in 2010). These fruiting T. korupensis trees were about one-third larger in stem diameter than conspecific non-fruiters and produced as many pods and seeds per capita as T. bifoliolata. However, regressions only modestly support the hypothesis that the positive tree size–fecundity relationship for T. korupensis was weaker (i.e. lower adj. R2) than for M. bisulcata (whose leaves are morphologically similar) or T. bifoliolata, with mostly similar dispersion about the median among these species. Conclusion – Altogether, the findings suggest a role for tolerance in nutrient-poor forests. It is postulated that instead of conferring resistance to herbivores, the ectomycorrhizas associated with these trees may enable them to more quickly recover from potential yet unpredictable insect outbreaks.

Enhancing the security of free space optical communication system by employing chaos-based modulation scheme

Abstract Security and privacy are two main dominant features of any communication system. In this paper, physical layer security of free space optical communication system using chaotic modulation scheme i.e., differential chaos shift keying (DCSK) is analyzed, where eavesdropper is actively present near the receiver and interfering between the transmission of secret messages from a transmitter to the receiver. In this manuscript, we have derived analytical expressions for the average secrecy capacity and secrecy outage probability which is used as a metric for secrecy performance analysis. The channel characterization is carried out using gamma–gamma model for weak-to-strong turbulence conditions. The effect of physical layer parameters like transmission link length, spreading length, etc. are considered for evaluating the security performance of the system. Numerical analysis is carried out and graphical results are presented. The results depicted that a very good average secrecy capacity can be achieved even in the presence of eavesdropper, however, it requires a tradeoff between high signal-to-noise ratio of main channel and large values of spreading factor. The proposed system is very promising for the future secured communication systems.

The Retrieval of Drop Size Distribution Parameters Using a Dual-Polarimetric Radar

The raindrop size distribution (DSD) is vital for applications such as quantitative precipitation estimation, understanding microphysical processes, and validation/improvement of two-moment bulk microphysical schemes. We trace the history of the DSD representation and its linkage to polarimetric radar observables from functional forms (exponential, gamma, and generalized gamma models) and its normalization (un-normalized, single/double-moment scaling normalized). The four-parameter generalized gamma model is a good candidate for the optimal representation of the DSD variability. A radar-based disdrometer was found to describe the five archetypical shapes (from Montreal, Canada) consisting of drizzle, the larger precipitation drops and the ‘S’-shaped curvature that occurs frequently in between the drizzle and the larger-sized precipitation. Similar ‘S’-shaped DSDs were reproduced by combining the disdrometric measurements of small-sized drops from an optical array probe and large-sized drops from 2DVD. A unified theory based on the double-moment scaling normalization is described. The theory assumes the multiple power law among moments and DSDs are scaling normalized by the two characteristic parameters which are expressed as a combination of any two moments. The normalized DSDs are remarkably stable. Thus, the mean underlying shape is fitted to the generalized gamma model from which the ‘optimized’ two shape parameters are obtained. The other moments of the distribution are obtained as the product of power laws of the reference moments M3 and M6 along with the two shape parameters. These reference moments can be from dual-polarimetric measurements: M6 from the attenuation-corrected reflectivity and M3 from attenuation-corrected differential reflectivity and the specific differential propagation phase. Thus, all the moments of the distribution can be calculated, and the microphysical evolution of the DSD can be inferred. This is one of the major findings of this article.

Impact of Scintillation Effect on Clear Weather and Fog Conditions using MDM-WDM Modulation Technique

The 5th generation optical wireless communication technologies have unique features of higher data rate, scalability in bandwidth, license free spectrum, cost effectiveness, easy deplorability and secured transmission. The role of free space optical (FSO) communication becomes important as the applications of next generation technologies are evolving in almost every sector. In this work, the performance of the terrestrial FSO MDM-WDM link has been investigated through a DP-QPSK modulation scheme at a data rate of 1000 Gbps. The link attenuation has been analysed with the help of Gamma- Gamma and Lognormal scintillation models considering clear weather and varying fog conditions. The link performance has been evaluated through SNR and received optical power for a varying distance of up-to 20 Km.

Impact of integration time steps of rain drop size distribution on their double-moment normalization: a case study in northern Benin

This study analyzed the sensitivity of the double-moment normalization of rain drop size distributions (DSDs) to their integration time steps. Six DSD datasets measured at different integration time steps were modeled by the double-moment normalization method. Six couples of reference moments are used for the normalization. Three DSD models (gamma, generalized gamma and lognormal) are used for modeling. Statistical criteria are used to assess the estimation of the moments of the DSDs made by the models. As results, the analysis highlighted the dependence of the shape function parameters on the DSD integration time step. It is also noted that the three DSD models are well adapted to the data used. Nevertheless, the generalized gamma model is recommended because of the independence of the moment estimation errors with respect to the integration time step, which is not the case for the other models.

Explicit calibration of pure jump processes: the BIST-30 European option case

Purpose- The study has two main purposes. First, it aims to show the efficiency of pure jump processes, more specifically Variance Gamma (VG) and Normal Inverse Gaussian models (NIG), in option pricing by comparing with the Black Scholes (BS) option pricing mode. Second, it aims to calibrate the European options written on BIST30 index. Methodology- We introduce an alternative derivation of option pricing formulas under the VG and NIG model assumption. We analyze the VG and NIG models' pricing performance by comparing their pricing result with the classical BS model for the BIST30 index. Our data includes the BIST30 index daily price and European options written on it from 05 May 2018 to 05 May 2020 with a maturity of 90 days. In the given period, the European call options' strike prices range from 1200 to 1650, and the European put options' strike prices range from 1000 to 1400. To compare their efficiency, first, the models are calibrated by minimizing the sum of squared deviations between the historically recorded and theoretical European option prices. Second, the theoretical option prices are computed, and the results are compared with the historically recorded option prices. Findings- Our significant contribution is the calibration of pure jump processes, VG and NIG processes, with the help of characteristic functions, the BS model prices for the BIST30 index, and the computation of European options prices traded in BIST. The study showed that the NIG process outperforms both VG and BS models, and the BS model is the worst model in option pricing for BIST. Conclusion- The VG and NIG processes can be calibrated by the help of their characteristic functions, and European option price estimations with these models superior to BS model option prices for BIST. Therefore, these processes are more efficient in BIST than the classical BS model. Keywords: Variance Gamma Process, Normal Inverse Gaussian Process, Black-Scholes Model, Options Pricing; Calibration JEL Codes: C63, G12, D46

A Flexible Zero-Inflated Poisson-Gamma Model with Application to Microbiome Sequence Count Data

In microbiome studies, it is of interest to use a sample from a population of microbes, such as the gut microbiota community, to estimate the population proportion of these taxa. However, due to biases introduced in sampling and preprocessing steps, these observed taxa abundances may not reflect true taxa abundance patterns in the ecosystem. Repeated measures, including longitudinal study designs, may be potential solutions to mitigate the discrepancy between observed abundances and true underlying abundances. Yet, widely observed zero-inflation and over-dispersion issues can distort downstream statistical analyses aiming to associate taxa abundances with covariates of interest. To this end, we propose a Zero-Inflated Poisson Gamma (ZIPG) model framework to address these aforementioned challenges. From a perspective of measurement errors, we accommodate the discrepancy between observations and truths by decomposing the mean parameter in Poisson regression into a true abundance level and a multiplicative measurement of sampling variability from the microbial ecosystem. Then, we provide a flexible ZIPG model framework by connecting both the mean abundance and the variability of abundances to different covariates, and build valid statistical inference procedures for both parameter estimation and hypothesis testing. Through comprehensive simulation studies and real data applications, the proposed ZIPG method provides significant insights into distinguished differential variability and mean abundance. Supplementary materials for this article are available online.

Racial/Ethnic Differences in Association Between Medicaid Expansion and Causes and Costs of Readmission After Acute Ischemic Stroke.

The purpose of this study was to examine whether the relative frequency of leading causes and total associated costs of readmission after acute ischemic stroke changed with Medicaid expansion, and how these changes differed by racial/ethnic group. We used a difference-in-differences approach to compare changes in the relative frequency of leading causes of unplanned 30-day readmission and to examine changes in the costs associated with unplanned readmission between expansion states (AR, MD, NM, and WA) and non-expansion states (FL and GA). To estimate the differential effect of Medicaid expansion by race/ethnicity on the causes and cost of readmission, we added a time*treatment*race interaction. Multinomial logistic regression was performed to analyze the changes in readmission cause. Gamma log-link modeling was used to study changes in readmission costs for expansion compared to non-expansion states. The final multinomial model showed an association between expanded Medicaid and the relative frequency of sepsis readmission for White patients. According to predictive margins, White patients in expansion states had an estimated increase of 3.3 percentage points in the share of readmissions for sepsis but not for White patients in non-expansion states. In contrast, non-White patients in expansion states had a decrease of 1.8 percentage points in the share of readmissions for sepsis. Overall, Medicaid expansion was associated with a net increase of 6.7 percentage points in the share of readmissions for sepsis among non-Hispanic Whites relative to all other groups. In the final gamma model, Medicaid expansion was associated with a decrease in readmission costs overall. According to predictive margins, the net cost reduction in expansion versus non-expansion states was an average of $2509. Medicaid expansion is associated with an overall decrease in unplanned readmission costs and an increase among readmitted White patients in the likelihood of readmission for sepsis.

On E-Bayesian analysis of the hierarchical normal and inverse gamma model using different loss functions and its application

This paper introduces the idea of hierarchical modelling to derive the variance (i.e. squared scale) parameter of the hierarchical normal and inverse gamma model using E-Bayesian estimation. We propose the idea of a hierarchical probability density function instead of the traditional hierarchical prior density function. We aim to derive E-Bayesian estimators with respect to the conjugate prior distribution IG(a,b) on the basis of the Balanced squared error loss function (BSELF) and Stein's loss function (STLF) for the unknown squared scale parameter. We use E-Posterior Risk as an evaluation standard. This study also intends to reveal the relationship among the E-Bayesian estimates under three distinct bivariate independent prior distributions of hyperparameters. The asymptotic properties of the E-Bayesian estimators are also evaluated. Monte Carlo simulations are prosecuted to study the efficiency of E-Bayesian estimators empirically and also, a real data application is analysed for exemplifying purposes.

Insights into the streamwater age in the headwater catchments covered by glaciers and permafrost, Central Tibetan Plateau

Improving our understanding of streamwater age knowledge is critical for revealing the complex hydrological processes in alpine cryosphere catchments. However, few studies on water age have been conducted in alpine cryosphere catchments due to the complicated and inclement environment. In this study, the Buqu catchment, a typical alpine catchment covered by glaciers and permafrost on the central Tibetan Plateau (TP), was selected as the study area. Using the sine-wave approach and a gamma model based on the seasonal cycle of stable isotopes in water, the young water fraction (Fyw) and mean transit time (MTT) of the Buqu catchment outlet and 23 sub-catchments was estimated to comprehensively reveal the potential driving mechanism of water age variability. The streamwater MTT for the entire catchment was 107 days, and 15.1 % of the streamwater was younger than 41 days on average. The estimated water age showed significant spatial heterogeneity with shorter water ages in high-elevation and glacier catchments and longer water ages in low-elevation and non-glacier catchments. Precipitation was the primary driver for spatial variations in water age, while the thickness of the permafrost active layer may function as an intermediate hub to drive water age variability. Mechanically, the thickness of the permafrost active layer controls the water ages by modifying the flow direction and length of water flow path. Spatially, this control mechanism is indirectly driven by the elevation gradient. The TDS concentration in streamwater is significantly related to water age, thus revealing a close link between water quality and hydrology. Our findings suggest that cryosphere retreats likely alter water age, thereby slowing water circulation rates and affecting water quality security under global warming. This study provides insights into the evolution of water ages, thereby deepening our understanding of the hydrological processes and guiding the protection of water resources in alpine headwater catchments.

Meta-analysis of the experimental coefficient of variation in wheat using the Bayesian and Frequentist approaches

A large set of variables is assessed for progeny selection in a plant-breeding program and other agronomic fields. The meta-analysis of the coefficient of variation (CVe) produces information for researchers and breeders on the experimental quality of trials. This analysis can also be applied in the decision-making process of the experimental plan regarding the experimental design, the number of repetitions, and the treatments and plants/progenies to be measured. In this study, we evaluated the dataset distribution and the descriptive statistics of CVe through the Frequentist and Bayesian approaches, aiming to establish the credibility and confidence intervals. We submitted CVe data of ten wheat (Triticum aestivum L.) traits reported in 1,068 articles published to the Bayesian and Frequentist analyses. Sample data were analyzed via Gamma and normal models. We selected the model with the lowest Akaike Information Criterion (AIC) value, and then we tested three link functions. In the Bayesian analysis, uniform distributions were used as non-informative priors for the Gamma distribution parameters with three ranges of q~U (a,b,). Thus, the prior probability density function was given by: pθ =1β-α, θ ∈ α,β. The Bayesian and Frequentist approaches with the Gamma model presented similar results for CVe; however, the range Bayesian credible intervals was narrower than the Frequentist confidence intervals. Gamma distribution fitted the CVe data better than the normal distribution. The credible and confidence intervals of CVe were successfully applied to wheat traits and could be used as experimental accuracy measurements in other experiments.

Modeling Egg Curves In Partridges

In this study, a modeling study was carried out on the weekly average values of henna partridge egg production. For this purpose, weekly average of henna partridge egg yields of 148 days from the herd consisting of 320 breeders were taken and cubic spline, Gompertz, Logistic, Richard, Schunute, Quadratic Spline, McNally and Gamma equations were used in the modeling. In the comparison of the goodness of fit of the equations, Determination Coefficient〖(R〗^2), Mean Square Error (MSE), Durbin-Watson (DW) and Akaike Information Criteria (AIC) values were taken into account. As a result of the study, Logistic (MSE= 12.4, R^2= 0.994, AIC= 43.56, DW= 2.09), Cubic Spline (MSE= 10.56, R^2= 0.996, AIC= 46.55, DW= 1.95) and McNally (MSE= 11.02, R^2= 0.996, AIC= 48.67, DW= 2.11) models were found to have the best results with similar results. It was concluded that the Schnute (MSE= 11.24, R^2= 0.990, AIC= 136.51, DW= 0.49), Gamma (MSE= 24.67, R^2= 0.991, AIC= 69.89, DW= 2.95) and Quadratic Spline (MSE= 10.43, R^2= 0.946, AIC= 149.34, DW= 2.97) models had the worst results.

A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries.

The aim of this paper is to introduce a discrete mixture model from the point of view of reliability and ordered statistics theoretically and practically for modeling extreme and outliers' observations. The base distribution can be expressed as a mixture of gamma and Lindley models. A wide range of the reported model structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, reversed hazard rate function, min-max models, mean residual life, mean past life, moments, order statistics and L-moment statistics. These properties can be formulated as closed forms. It is found that the proposed model can be used effectively to evaluate over- and under-dispersed phenomena. Moreover, it can be applied to analyze asymmetric data under extreme and outliers' notes. To get the competent estimators for modeling observations, the maximum likelihood approach is utilized under conditions of the Newton-Raphson numerical technique. A simulation study is carried out to examine the bias and mean squared error of the estimators. Finally, the flexibility of the discrete mixture model is explained by discussing three COVID-19 data sets.

A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique. We refer to the new model as modified alpha power transformed Weibull distribution. The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions, which are quite familiar in environmental investigations. Its hazard rate function can be decreasing, increasing, bathtub and upside-down then bathtub shaped. Diverse structural properties of the proposed model are acquired including quantile function, moments, entropies, order statistics, residual life and reversed failure rate function. The parameters of the distribution were estimated using the maximum likelihood function. The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed. Via a simulation study, the performance of the point and interval estimates are compared using different criteria. Employing real lifetime data sets, we verify that the offered model furnishes a better fit than some other lifetime models including Weibull, gamma and alpha power Weibull models.

Polarization-Enabled MIMO Bidirectional Device-to-Device Communications via RIS

In future wireless networks, device-to-device (D2D) communications are expected to play an important role to support a plethora of applications. To meet the target quality of service while ensuring high reliability, and high spectral and energy efficiencies, manipulation of the radio waves by reconfigurable intelligent surfaces (RIS) will be critical. In this context, leveraging concepts of polarization, this paper proposes a framework for bidirectional D2D communications, where the data exchange between a central node and devices operating in distinct polarization states, is multiple-input multiple-output in nature and takes place via a dual-polarized RIS, in the presence of hardware impairments and imperfect interference cancellation, as well as impairments caused by the spatial correlation and cross-polarization. Performance evaluation of such a framework is conducted in terms of key metrics, namely, bit error rate, outage probability, channel capacity, and energy efficiency, for which closed-form expressions are obtained considering transmissions over Nakagami fading channels. An asymptotic analysis is also conducted to evaluate the achievable diversity gains, by approximating the Nakagami model with a tractable Gamma model. Further, the impact of imperfect channel estimation on performance is also investigated. Comparative numerical results are provided, and the effects of the main system parameters on performance are analyzed. The proposed framework is shown to provide significant performance improvements as compared to D2D communications via non-polarized RIS.

The Determination of the Most Appropriate Probability Distribution Models for the Meteorological Variables

Every component of the hydrological cycle is essential for controlling water supplies and assessing the potential catastrophic events like floods and droughts. The variables of hydrological system are unexpected and unique to each place. In this paper, the most crucial variables including precipitation, temperature, relative humidity, and evaporation are examined for Ankara province. For meteorological parameters, the Lognormal, Log-logistic, Gamma, Weibull, Normal, and Gumbel models are used to find the best suitable distributions. Kolmogorov-Smirnov, Cramers-von Mises, Akaike's Information Criterion, Bayesian Information Criterion, Anderson-Darling, and Maximum Loglikelihood methods are utilized to test these models. Results shows that there is a distinct distribution model for each parameter. In particular, it has been determined that the Gumbel distribution is a better model for annual total precipitation, whereas the Normal distribution is a better model for annual minimum temperature. At stations 17130 and 17664, the gamma distribution is observed to be the best fit distribution at annual total precipitation, but station 17128 is found to be the most appropriate Log-logistic and normal distribution. Stations 17128, 17130, and 17664 for annual maximum temperature series are fitted with the Normal, Log-logistic, and Lognormal, respectively. Gamma is found to be the best fit when analyzing annual mean temperature for stations 17128 and 17130, whereas Lognormal is selected for station 17664. It is expected that these results will contribute to the planning of water resources projects in the region.

Option pricing in emerging markets using pure jump processes: explicit calibration of IST30 European option

Purpose- This study aims to illustrate the efficiency of pure jump processes, more specifically Variance Gamma (VG) and Normal Inverse Gaussian models (NIG), in option pricing by comparing with the Black Scholes (BS) option pricing model for emerging markets. Methodology- This study presents an alternative derivation of option pricing formulas for VG and NIG models. Then, it investigates the VG and NIG models' option pricing performance with the help of new derivation by comparing them with the BS option pricing model for emerging markets for an emerging country, Turkey. The data consists of the BIST30 index daily price and European options written on this index extend from 05 May 2018 to 05 May 2020 for given exercise prices with a maturity of 90 days. In this period, the European call options' strike prices range from 1200 to 1650, and the European put options' strike prices range from 1000 to 1400. To compare the models' efficiency, first, we calibrate the models by minimizing the sum of squared deviations between the observed and theoretical option prices. Second, we compute the option prices and compare the results with the observed option prices. Findings- The significant contribution to the literature is the calibration of the pure jump processes (VG and NIG processes) using the characteristic functions, the continuous BS prices for an emerging market, and the computation of European options prices in BIST. We find that while the NIG process performs better than VG and BS models, the BS model is the worst in option pricing. Conclusion- The pure jump processes (VG and NIG processes) can be calibrated using the characteristic functions, and option price estimations with them are better than the continuous BS prices for an emerging market. Thus, the pure jump processes are more efficient in market modeling than the BS model.

Standardized maximin D- and c-optimal designs for the Poisson–Gamma model

Standardized maximin D- and c-optimal designs for the Poisson–Gamma model

An Application of Exponential-Lindley Distribution in Modelling Cancer Survival Data

Objective: To explore multiple myeloma cancer survival data using the Exponential-Lindley model and compare the performance with other related models. Methods: In this article both simulated and real data sets were used for comparison. The model parameters are estimated for real and simulated data sets using the maximum likelihood method. The real data sets consist of 48 Cancer patients with multiple myeloma with 25% of them was censored observations. We consider both type I and type II censoring mechanism with 5%, 10% and 20% censoring. The performance was compared using three measures Deviance, AIC and BIC. Findings: The performance of Exponential-Lindley model was compared with related models Exponential, Lindley, Power Lindley, Gamma, and Burr-XII models. Simulated and real data sets are applied in the underlying models. The Exponential-Lindley model outperformed compared to other models. Novelty: The new model is novel alternative for modelling censored survival data for different levels and types of censoring. Keywords: Cancer survival; Censoring; Simulation; ExpG family; Exponential Lindley Model