Assumption Of Gamma Distribution Research Articles

HIV models with non‐exponential probability distributed infection progression

Existing HIV infection dynamics models are based on the classical target cell‐infected cell‐free virus compartment model. In fact, in order to facilitate modeling and dynamical analysis, these models assume that the probability of infected cells staying in different infection stages obeys an exponential distribution. However, this does not accurately describe the process of HIV infection from target cells to budding of virus, that is, fusion‐reverse transcription‐reproductivity formation‐budding process. Therefore, to expand the idea of HIV modeling, in this paper, we first establish the HIV integral‐differential equation model that obeys the general distribution, and then degenerate the model into a subclass ODEs model under the assumption of gamma distribution. Finally, an equivalent age structure model is given, and numerical simulations are conducted to describe the integral‐differential equations model. It is worth mentioning that ODEs models with subclasses can provide good numerical implementations for age structure as well as other PDEs HIV models. This is another important purpose of our work.

IRS-Assisted Full Duplex Systems Over Rician and Nakagami Fading Channels

Intelligent reflecting surface (IRS) has been deemed as an energy and spectral-efficient technology, that can potentially enhance network coverage and transmission reliability, with minimum impact on transceivers' complexity. Motivated by this, we develop a comprehensive analysis on the performance of integrating IRS into full-duplex (FD) cellular or Internet of Things (IoT) networks in both realistic Rician and Nakagami fadings. Firstly, in the context of reciprocal channels in Rician fadings, we derive the closed-form approximations of the users' outage probability (OP) and ergodic capacity (EC), under the non-central Chi-square distribution assumption on the signal-to-interference-plus-noise ratio (SINR). Further following by the Gamma distribution assumption on the SINR, we derive the cumulative distribution function (CDF) expression of the user's SINR, which is then leveraged to obtain simple yet effective closed-form expressions in terms of OP and EC. Subsequently, in Nakagami fading scenarios with the reciprocal and non-reciprocal channels, the closed forms of both users' OP and EC are obtained. Finally, the correctness of all the theoretical expressions is verified through substantial Monte Carlo simulations. The results indicate that the OP and EC deduced from Gamma distribution exhibit the fairly precise results for the arbitrary number of IRS elements, especially in Nakagami fadings.

A Simulation Study on The Simulated Annealing Algorithm in Estimating The Parameters of Generalized Gamma Distribution

The gamma distribution is one of the most widely used statistical distribution in fitting various real life data set in the field of the reliability to fit failure data, because it is sufficiently flexible to deal with decreasing, constant, and increasing failure rates. In this article, the stock investment valuation model has been presented on the assumption of Gamma distribution. The purpose is to analysis profitability of investment in the property development sector in Malaysia based on the investment rate of return on investment. The flow of the investment cash and the accumulation of the share units over the investment period have been presented. it demonstrated the computing of MIRR by the case of a company which experienceed distributing a treasury share dividend, which increases the small portion of investor’s share units instead of receiving the dividend in cash. As the MIRR might exhibit negative values, the Gamma distribution of the transformed MIRR for certain investment periods is developed and the method of moment is applied to estimate the parameters. The study revealed that the transformed MIRR is well fitted with Gamma distribution for four years to eight years investment periods. It is shown that this approach has a better performance return on investment in Malaysia property sector from 2008 to 2018.

A flexible Bayesian nonconfounding spatial model for analysis of dispersed count data.

In employing spatial regression models for counts, we usually meet two issues. First, the possible inherent collinearity between covariates and the spatial effect could lead to misleading inferences. Second, real count data usually reveal over- or under-dispersion where the classical Poisson model is not appropriate to use. We propose a flexible Bayesian hierarchical modeling approach by joining nonconfounding spatial methodology and a newly reconsidered dispersed count modeling from the renewal theory to control the issues. Specifically, we extend the methodology for analyzing spatial count data based on the gamma distribution assumption for waiting times. The model can be formulated as a latent Gaussian model, and consequently, we can carry out the fast computation by using the integrated nested Laplace approximation method. We examine different popular approaches for handling spatial confounding and compare their performances in the presence of dispersion. Two real applications from a crime study against women in India as well as stomach cancer incidences in Slovenia motivate the suggested methods. We also perform a simulation study to understand the proposed approach's merits better. Supplementary Materials for this article areavailable.

A Comparative Study of Shared Frailty Models for Kidney Infection Data with Generalized Exponential Baseline Distribution

Shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and baseline hazard function which is common to all individuals. There are certain as sumptions about the baseline distribution and distribution of frailty. Mostly assumption of gamma distribution is considered for frailty distribution. To compare the results with gamma frailty model, we introduce three shared frailty models with generalized exponential as baseline distribution. The other three shared frailty models are inverse Gaussian shared frailty model, compound Poisson shared frailty model and compound negative binomial shared frailty model. We fit these models to a real life bivariate survival data set of McGilchrist and Aisbett (1991) related to kidney infection using Markov Chain Monte Carlo (MCMC) technique. Model comparison is made using Bayesian model selection criteria and a better model is suggested for the data.

Pricing of Rainfall Derivatives Using Generalized Linear Modelling of Daily Rainfall Process

The structure of a typical rainfall insurance is complex; insurance payoffs are based on many parameters such as the rainfall volume, the rainfall distribution (the number of consecutive dry days), the number of days with excess rainfall etc. Such a complex insurance structure is essential to minimize the basis risk and to amply compensate a farmer for the loss of the crop yield due to the rainfall weather event. A rainfall derivative could always be brokered as a rainfall insurance or a traded option. To price complex rainfall insurances or to trade complex financial instrument based on the rainfall index on the capital markets, the underlying daily rainfall process needs to be modelled. The daily rainfall modelling is essential because the trading of any financial instrument based on the rainfall index requires the pricing of the instrument contingent on the daily rainfall information as it becomes available. In this work, we price a rainfall derivative by modelling the underlying daily rainfall process using generalized linear models (GLMs). The rainfall occurrence process is modelled using a binomial GLM and the rainfall intensity process is modelled using a quasi-likelihood GLM with the gamma, the Pareto and the lognormal distribution assumptions. Our models estimate the average annual monsoon rainfall correctly but overestimate the standard deviation, the skewness and the excess kurtosis of the annual monsoon rainfall distribution. The expected total derivative payoff obtained using only the models with the gamma distribution assumption is comparable to that obtained from Burn analysis. There was no significant gain from using a model with two auto-regressive rainfall intensity terms.

Skewness of cloud droplet spectrum and an improved estimation for its relative dispersion

The relative dispersion of the cloud droplet spectrum is a very important parameter in describing and modeling cloud microphysical processes. Based on the definition of skewness as well as theoretical and data analyses, a linear fitting relationship (α = 2.91ε−0.59) between skewness (α) and relative dispersion (ε) is established and a new method is developed to estimate the relative dispersion of the cloud droplet spectrum. The new method does not depend on any assumption of a particular distribution for the cloud droplet spectrum and has broader applicability than the previous methods. Comparisons of the three methods for the relative dispersion with the observed data supported the following conclusions. (1) The skewness of the cloud droplet spectrum is asymmetrically distributed. An assumption of zero skewness in quantifying the relative dispersion inevitably results in relatively large deviations from the observations. Errors of the estimated relative dispersion due to the omission of the skewness term are not solely related to the skewness, but rather to the product of the skewness and relative dispersion. (2) The use of the assumption that the cloud droplet spectrum takes a gamma distribution is similar to the assumption that the skewness is twice the relative dispersion. This leads to a better accuracy in estimating the relative dispersion than that with zero skewness assumption. (3) Comparisons with observations show that the new method is more accurate than the one under gamma distribution assumption and is the best among all the three methods. (4) It is believed that finding a better correlation between the skewness and the relative dispersion would further reduce the deviations for the estimated relative dispersion.

Bayesian estimation and inference for log-ACD models

This paper adapts Bayesian Markov chain Monte Carlo methods for application to some auto-regressive conditional duration models. Subsequently, the properties of these estimators are examined and assessed across a range of possible conditional error distributions and dynamic specifications, including under error mis-specification. A novel model error distribution, employing a truncated skewed Student-t distribution is proposed and the Bayesian estimator assessed for it. The results of an extensive simulation study reveal that favourable estimation properties are achieved under a range of possible error distributions, but that the generalised gamma distribution assumption is most robust and best preserves these properties, including when it is incorrectly specified. The results indicate that the powerful numerical methods underlying the Bayesian estimator allow more efficiency than the (quasi-) maximum likelihood estimator for the cases considered.

Comparison of Frailty Models for Acute Leukemia Data under Gompertz Baseline Distribution

In this article, we consider two different shared frailty regression models under the assumption of Gompertz as baseline distribution. Mostly assumption of gamma distribution is considered for frailty distribution. To compare the results with gamma frailty model, we consider the inverse Gaussian shared frailty model also. We compare these two models to a real life bivariate survival data set of acute leukemia remission times (Freireich et al., 1963). Analysis is performed using Markov Chain Monte Carlo methods. Model comparison is made using Bayesian model selection criterion and a well-fitted model is suggested for the acute leukemia data.

PRM48 - Diagnostics for checking the gamma distribution assumption in generalized linear models used for modeling health care costs

PRM48 - Diagnostics for checking the gamma distribution assumption in generalized linear models used for modeling health care costs

Qualitative study of a quarantine/isolation model with multiple disease stages

Recent studies suggest that, for disease transmission models with latent and infectious periods, the use of gamma distribution assumption seems to provide a better fit for the associated epidemiological data in comparison to the use of exponential distribution assumption. The objective of this study is to carry out a rigorous mathematical analysis of a communicable disease transmission model with quarantine (of latent cases) and isolation (of symptomatic cases), in which the waiting periods in the infected classes are assumed to have gamma distributions. Rigorous analysis of the model reveals that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique endemic equilibrium when the threshold quantity exceeds unity. The endemic equilibrium is shown to be locally and globally-asymptotically stable for special cases. Numerical simulations, using data related to the 2003 SARS outbreaks, show that the cumulative number of disease-related mortality increases with increasing number of disease stages. Furthermore, the cumulative number of new cases is higher if the asymptomatic period is distributed such that most of the period is spent in the early stages of the asymptomatic compartments in comparison to the cases where the average time period is equally distributed among the associated stages or if most of the time period is spent in the later (final) stages of the asymptomatic compartments. Finally, it is shown that distributing the average sojourn time in the infectious (asymptomatic) classes equally or unequally does not effect the cumulative number of new cases.

Assessing erectile neurogenic dysfunction from heart rate variability through a Generalized Linear Mixed Model framework

Background The low (LF) vs. high (HF) frequency energy ratio, computed from the spectral decomposition of heart beat intervals, has become a major tool in cardiac autonomic system control and sympatho–vagal balance studies. The (statistical) distributions of response variables designed from ratios of two quantities, such as the LF/HF ratio, are likely to non-normal, hence preventing e.g., from a relevant use of the t-test. Even using a non-parametric formulation, the solution may be not appropriate as the test statistics do not account for correlation and heteroskedasticity, such as those that can be observed when several measures are taken from the same patient. Objectives The analyses for such type of data require the application of statistical models which do not assume a priori independence. In this spirit, the present contribution proposes the use of the Generalized Linear Mixed Models (GLMMs) framework to assess differences between groups of measures performed over classes of patients. Methods Statistical linear mixed models allow the inclusion of at least one random effect, besides the error term, which induces correlation between observations from the same subject. Moreover, by using GLMM, practitioners could assume any probability distribution, within the exponential family, for the data, and naturally model heteroskedasticity. Here, the sympatho–vagal balance expressed as LF/HF ratio of patients suffering neurogenic erectile dysfunction under three different body positions was analyzed in a case–control protocol by means of a GLMM under gamma and Gaussian distributed responses assumptions. Results The gamma GLMM model was compared with the normal linear mixed model (LMM) approach conducted using raw and log transformed data. Both raw GLMM gamma and log transformed LMM allow better inference for factor effects, including correlations between observations from the same patient under different body position compared to the raw LMM. The gamma GLMM provides a more natural distribution assumption of a response expressed as a ratio. Conclusions A gamma distribution assumption intrinsically models quadratic relationships between the expected value and the variance of the data avoiding prior data transformation. SAS and R source code are available on request.

Validation of an STR peak area model

In analyzing a DNA mixture sample, the measured peak areas of alleles of STR markers amplified using the polymerase chain-reaction (PCR) technique provide valuable information concerning the relative amounts of DNA originating from each contributor to the mixture. This information can be exploited for the purpose of trying to predict the genetic profiles of those contributors whose genetic profiles are not known. The task is non-trivial, in part due to the need to take into account the stochastic nature of peak area values. Various methods have been proposed suggesting ways in which this may be done. One recent suggestion is a probabilistic expert system model that uses gamma distributions to model the size and stochastic variation in peak area values. In this paper we carry out a statistical analysis of the gamma distribution assumption, testing the assumption against synthetic peak area values computer generated using an independent model that simulates the PCR amplification process. Our analysis shows the gamma assumption works very well when allelic dropout is not present, but performs less and less well as dropout becomes more and more of an issue, such as occurs, for example, in Low Copy Template amplifications.

GAMMA OTOREGRESİF MODELLER VE KIZILIRMAK HAVZASINA UYGULAMA

Gamma Autoregressive Models and Application on Kizilirmak Basin Stochastic models are required to generate synthetic values of flows statistically similar to observed ones to use in the simulation studies of water related structures. Such models are extremely important for generation of flows of streams with short record length. Autoregressive time series (AR) models are the most used models in this area. In recent years, AR models valid for gamma distribution are developed. In these studies, method of moments and modified maximum likelihood methods are used to estimate the model parameters. The aim of this study are comparing two AR models under gamma distribution assumption and applying these models for monthly data set of EIE 1501 and EIE 1517 streamflow gauging stations located in Kizilirmak Basin. The results of each model are interpreted for researchers using these models in their further studies.

Outage Performance of Single/dual Polarized Fixed Wireless Access Links in Heavy Rain Climatic Regions

The outage performance of line-of-sight fixed wireless access channels operating above 10 GHz is predominantly controlled by rain attenuation. In this paper, a prediction model, appropriate for heavy rain climatic regions based on gamma distribution assumption for the rainfall rate and the rain attenuation is being reviewed to incorporate the recently released ITU-R rainmaps. The model exhibits a very good performance, as validated by tests against the ITU-R databank Moreover, the above model is extended to evaluate the outage performance of a dual-polarized mm-wave fixed wireless access link located in heavy rain climatic regions. The obtained numerical results focus on the investigation of the effects of various operational parameters upon the outage performance of the microwave communication link.

Adjacent satellite interference effects as applied to the outage performance of an earth- space system located in a heavy rain climatic region

Interference effects are of utmost importance to the reliable design of modern satellite communication systems operating at Ku and Ka bands. In these frequencies rain attenuation is the dominant fading mechanism particularly for Earth-space systems located in subtropical and tropical regions. On the other hand, the main propagation effect on interference between two adjacent satellite systems is considered to be the differential rain attenuation. The subject of the paper is the development of a procedure for the prediction of carrier-to-noise plus interference ratio (cnir) statistics, under the presence of rain fading conditions, applied to heavy rain climatic regions. The method is based on a model of convective raincells and the gamma distribution assumption for point rainfall rate statistics, which fits better than lognormal distribution in subtropical and tropical regions. A tropical raindrop size distribution is also adopted for the calculation of the power-law parameters of specific rain attenuation. The numerical results are concentrated on the analytical examination of various operational parameters upon the CNIR statistics and the subsequent outage performance of the system. Comparison of the proposed model with an already existing one is attempted and the necessity of the present procedure for application to locations belonging to subtropical/tropical zones becomes obvious.

Assessing gamma frailty models for clustered failure time data.

Proportional hazards frailty models use a random effect, so called frailty, to construct association for clustered failure time data. It is customary to assume that the random frailty follows a gamma distribution. In this paper, we propose a graphical method for assessing adequacy of the proportional hazards frailty models. In particular, we focus on the assessment of the gamma distribution assumption for the frailties. We calculate the average of the posterior expected frailties at several followup time points and compare it at these time points to 1, the known mean frailty. Large discrepancies indicate lack of fit. To aid in assessing the goodness of fit, we derive and estimate the standard error of the mean of the posterior expected frailties at each time point examined. We give an example to illustrate the proposed methodology and perform sensitivity analysis by simulations.