Gamma Distribution Research Articles

Bivariate Pareto–Feller Distribution Based on Appell Hypergeometric Function

The Pareto–Feller distribution has been widely used across various disciplines to model “heavy-tailed” phenomena, where extreme events such as high incomes or large losses are of interest. In this paper, we present a new bivariate distribution based on the Appell hypergeometric function with marginal Pareto–Feller distributions obtained from two independent gamma random variables. The proposed distribution has the beta prime marginal distributions as special case, which were obtained using a Kibble-type bivariate gamma distribution, and the stochastic representation was obtained by the quotient of a scale mixture of two gamma random variables. This result can be viewed as a generalization of the standard bivariate beta I (or inverted bivariate beta distribution). Moreover, the obtained bivariate density is based on two confluent hypergeometric functions. Then, we derive the probability distribution function, the cumulative distribution function, the moment-generating function, the characteristic function, the approximated differential entropy, and the approximated mutual information index. Based on numerical examples, the exact and approximated expressions are shown.

Healthcare Cost of Multiple Sclerosis and in Relation to Disability Level in Alberta.

We aimed to (1) report updated estimates of direct healthcare costs for people living with MS (pwMS), (2) contrast costs to a control population and (3) explore differences between disability levels among pwMS. Administrative data were used to identify adult pwMS (MS cohort) and without (control cohort) in Alberta, Canada; disability level (based on the Expanded Disability Status Scale) among pwMS was estimated. One- and two-part generalized linear models with gamma distribution were used to estimate the incremental direct healthcare cost (2021 $CDN) of MS during a 1-year observation period. Adjusting for confounders, the total healthcare cost ratio was higher in the MS cohort (n = 13,089) versus control (n = 150,080) (5.24 [95% CI: 5.08, 5.41]) with a predicted incremental cost of $15,016 (95% CI: $14,497, $15,535) per person-year. Among the MS cohort, total predicted direct healthcare costs were higher with greater disability, $14,430 (95% CI: $13,980, $14,880) to $58,697 ($51,514, $65,879) per person-year in mild and severe disability, respectively. The primary health resource cost component shifted from disease-modifying therapies in mild disability to supportive care in moderate and severe disability. Adult pwMS had greater direct healthcare costs than those without. Extrapolating to the population level (where 14,485 adult pwMS were identified in the study), it is estimated that $218 million per year in healthcare costs may be attributable to MS in Alberta. The significantly larger economic impact associated with greater disability underscores the importance of preventing or delaying disease progression and functional impairment in MS.

Fokker-Planck equation for the crystal-size probability density in progressive nucleation and growth with application to lognormal, Gaussian and gamma distributions

The Fokker Planck (FP) equation for the probability density function (PDF) of crystal size in phase transformations ruled by progressive nucleation and growth, has been derived. Crystals are grouped in sub-sets, we refer to as τ-crystals, where τ is the birth time of the set. It is shown that the size PDF is the superposition of the PDF of the crystal sub-sets (τ-PDFs), with weight given by the nucleation rate. The growth and diffusion coefficients entering the FP equations are estimated as a function of both τ-PDFs and nucleation rate. The functional form of these coefficients is studied for solutions of the FP equation for τ-crystals given by the lognormal, Gaussian and gamma distributions. For the first two distributions, the effect of fluctuations, nucleation rate and growth rate, on the shape of the distribution has been investigated. It is shown that for an exponential decay of the fluctuation term, the shape of the PDF is mainly governed by both the time constant for nucleation and the strength of the fluctuation. It is found that τ-PDFs given by the one-parameter gamma distributions are suitable to deal with KJMA (Kolmogorov Johnson Mehl Avrami) compliant phase transformations, where the fluctuation term is proportional to crystal size. The connection between the FP equation for the size PDF and the evolution equation for the density of crystal populations is also discussed.

Comparing direct medical care costs of patients with bladder cancer who received an ileal conduit vs. neobladder in the year following cystectomy

PurposeBladder cancer is 1 of the most costly cancers, however there is limited research on medical care costs by type of urinary diversion. The objective of our study was to compare medical care costs of the 2 most common urinary diversions in the year following radical cystectomy. MethodsThe Bladder Cancer Quality of Life Study included patients diagnosed with bladder cancer who underwent radical cystectomy and received an ileal conduit (IC, n = 821) or neobladder (NB, n = 181) in 3 integrated health systems. Medical care costs per patient per quarter were estimated for the year following cystectomy. Multivariable generalized linear models with a gamma distribution and log link were used to estimate mean monthly medical care costs (2022 USD$), adjusted for patient demographic and clinical characteristics. ResultsIn multivariable analysis, mean monthly costs per quarter were not significantly different between IC and NB patients in the 12 months following cystectomy. Overall, mean monthly costs in IC and NB patients were highest during the first quarter and decreased thereafter. Factors associated with higher mean costs across all quarters included presence of any complications and advanced tumor stage at cystectomy (all P < 0.001). ConclusionOur study addresses an important knowledge gap by quantifying the medical costs of bladder cancer patients by urinary diversion type and comparing costs of different treatment approaches. Studies that assess patient-reported outcomes and out-of-pocket costs, by urinary diversion type, are warranted to inform treatment decision-making and cost conversations.

Comparative examinations of wind speed and energy extrapolation methods using remotely sensed data – A case study from Hungary

Exact knowledge of wind energy potential is a fundamental issue in wind energy utilization. The vertical changes in wind speeds, that is, the wind profile, have a predominant impact on the wind energy available at a location because the kinetic energy of moving air is proportional to the square of the wind speed. Roughness describes the resistance of a 3D surface to moving air. The exponent α of the power law of Hellmann and the roughness length (z0) are two parameters that describe the effects of the roughness of the surface on the wind profile. They can be used for the vertical extrapolation of wind speeds. The exponent α can be determined using multiple height level wind speed measurement data, whereas a reliable technique for the calculation of the roughness length requires detailed knowledge of the 3D geometry of the measurement site. In the present study, the exponent α was calculated based on SODAR wind speed measurements, while (z0) was determined using a combination of GIS and UAS-based aerial survey methods. Wind speeds measured at 50 m were extrapolated for height levels of 80, 90, 100, 110, and 120 m using dynamic power law exponent values. Wind power was determined using the power law (method V1), roughness length (method V2), frequency distribution (method W-RF), and gamma distribution (method W-G), and Windographer software was compared to the values calculated from the empirical (measured) wind speeds. A comparative statistical analysis of the datasets of the power law and roughness length methods on monthly/diurnal, annual/diurnal, and month/direction contexts showed no significant differences at all height levels. Differences can be detected in the distribution of the signs of the differences at heights of 80 and 120 m for the entire dataset. Underestimation was dominant with a significant frequency (over 70 %) in the case of both methods and heights. There were no significant differences between the wind power estimations provided by the different methods, and all the methods involved in the study underestimated the wind speeds and wind energy potential for each height level. Methods V1 and V2 can be used alternatively, depending on the input data available for analysis. The major advantage of method V2 is that it provides the same accuracy as V1, which requires a UAS-based aerial survey at the beginning, but continuous wind measurements must be performed at a lower height only. This means that there is no need for a high measurement tower, which makes the measurements simpler, more cost-effective, and causes much less disturbance to the environment. Another important advantage of the methods presented here is that they use a dynamic approach of power law exponent values that provide a more realistic estimation of wind speed and energy on a diurnal scale.

Periodontitis adversely affects lipoprotein subfractions – results from the cohort study SHIP-TREND: Periodontitis adversely affects lipoprotein subfractions

AimWe aimed to investigate the medium-term associations of periodontitis and the number of missing teeth with serum lipoproteins and their plasma subfractions using follow-up data from the population-based Study of Health in Pomerania (SHIP-TREND). MethodsA total of 2,058 participants with 7-year follow-up data underwent periodontal examinations, serum lipid panel tests, and proton nuclear magnetic resonance (1H-NMR) spectroscopy of plasma lipoproteins and their subfractions. Generalized models with gamma distribution and loglink were used to analyze associations between periodontal variables and lipoproteins and their subfractions, adjusting for confounders using propensity score weighting. ResultsPeriodontal variables were consistently associated with elevated follow-up serum levels of triglycerides, total cholesterol, and low-density lipoprotein cholesterol levels. When plasma lipoprotein subfractions were evaluated, periodontal variables were associated with elevated levels of triglycerides and cholesterol-enriched apolipoprotein B-containing lipoprotein particles, particularly small dense low-density lipoprotein, very-low-density lipoprotein and intermediate density lipoprotein. In addition, altered high-density lipoprotein particle composition was observed, suggesting potential functional changes. ConclusionThis study provides evidence for causal effects of periodontitis on conventional serum lipids and plasma lipoprotein subfractions. As the underlying biological mechanisms are not fully understood, further research is needed.

RIS-aided free-space optics communications in A2G networks over inverted Gamma–Gamma turbulent channels

Reconfigurable intelligent surfaces (RISs) have revolutionized free-space optics (FSO) communication by dynamically optimizing the propagation environment. This study proposes a framework to analyze RIS-assisted FSO communication over inverted Gamma–Gamma (IGGG) distributions. We use the IGGG distribution for air-to-ground networks, accurately modeling atmospheric turbulence. Consequently, we derived performance metrics in terms of Meijer’s G by employing an asymptotic analysis to provide deeper insights. Our results demonstrate incorporating RISs into our proposed network enhances outage performance by 52.08% at a SNR of 30 dB. Furthermore, the results highlight the importance of heterodyne detection in mitigating the adverse effects of pointing errors.

Does the application of Jensen's integral inequality and LMIs confirm exponential stability in delayed systems with gapped gamma distribution through augmented Lyapunov function?

This study is dedicated to a comprehensive exploration aimed at advancing our understanding of stability within dynamic systems. The focus is particularly on the intricate domain of delayed systems characterized by gapped gamma distributions. The primary objective of this investigation revolves around evaluating the pragmatic application and efficacy of Jensen's integral inequality in combination with the powerful analytical tools provided by Linear Matrix Inequalities (LMIs). This evaluation is crucial for rigorously assessing exponential stability within these complex systems. Central to our investigative framework is the strategic deployment of augmented Lyapunov functions. These functions play a crucial role in unraveling the intricate stability properties of delayed systems featuring gapped gamma distributions, allowing for a nuanced examination of their inherent stability characteristics under various conditions. The mathematical formulation crafted in this exploration intricately captures the interplay between the distinctive attributes of the gapped gamma distribution and the complex dynamics of the loop traffic flow model within the overarching delayed system. This interconnection serves as the fundamental basis for the stability analysis, providing insights into the interdependence of these key elements. The noteworthy contribution of this study lies in the systematic construction of a robust analytical framework explicitly tailored for stability assessment. A comprehensive investigation is undertaken to elucidate critical aspects, including the convergence rate and the attainment of asymptotic stability within the considered delayed system. Additionally, a dedicated simulation section, focusing on Vehicle Active Suspension Control, has been incorporated to further validate and showcase the applicability of the proposed methodology.

Modelling Environmental Tree Species’ Volume using some selected Skewed Distributions

Ecological requirements' knowledge in determining tree species' distributions is a precondition for sustainable forest management. Tree species in all regions are threatened by climate change but some are more vulnerable than others. Rightly skewed distributions were used to take care of the environmental data set obtained from FRIN using five species which are: Beech Wood, White Afara, Opepe, Afon and Teak. Appropriate statistical tools distributions like descriptive analysis, Akaike Information Criterion (AIC), Goodness of Fit, Probability Functions, Kolmogorov Smirnovt-test, Gamma, Weibull, Log-normal and Beta-weibull were carried out to determine the best distribution for each selected specie in this research. It was established from the distributional pattern of the tree species' volume used in this research that the Gamma distribution was a better fit for the Beech wood with the AIC of 617.21, Beta-weibull distribution was a better _t for the White Afara, Opepe and Teak Species with the AIC values of 580.772, 630.84 and 733.60 respectively while the Weibull distribution was a better fit for the Afon specie with the AIC value of 752.07. Conclusively, the implication of the analysis is that the Beta-weibull distribution described the tree species' volume best among the four distributions used. In line with the findings, it is recommended that Beta-weibull should be the appropriate distribution to model forest specie when it comes to modelling because of its four (4) parameters and its goodness when fitting.

Forecasting the design maxima water discharges of floods on the Latorica river according to the data of the Mukachevo gauging station using plotting position formulas

This article presents the results of forecasting design maxima discharges on the Latorica River within Mukachevo town based on hydrological observation data at the “Mukachevo” gauging station using plotting position formulas. While solving the task, a novel non-parametric method of forecasting using observation data is applied. The method includes extrapolating the discrepancy (divergence, disagreement) between the estimates of the statistical annual probabilities of exceedance obtained by different plotting position formulas. The task is considered in the frame of the stationarity hypothesis of the maximum river flow employing a time series of maximal discharges of the Latorica River observed at the “Mukachevo” gauging station from 1947 to 1999.We involved the thirteen plotting position formulas. There was no specific criterion for choosing them to solve the task. All applied formulas were considered admissible options, and results obtained after using them – expert judgments reflecting decision-makers’ predisposition to more cautious or less expensive decision options in flood management strategies.The epistemic uncertainty of the different plotting positions was reduced by employing the Fishburn rule. According to this rule, the significance of various plotting positions was given by arranging their estimates in descending order of importance of their values under decision-making. Depending on the selected significance option assignment of the different plotting position formulas, such rank-weighted estimates of the design peak discharges (each of them for annual exceedance probability 1%, 0.5%, and 0.2%) were computed: (1) the rank-weighted upper bound estimate (sup-estimate) corresponding to the predisposition to more cautious decision options; (2) the rank-weighted lower bound estimate (inf-estimate) corresponding to the predisposition to less expensive decision options. As possible control theoretical alternatives for forecasting design maximal discharges considered were five parametric probability distributions: 1) the Kritskyi-Menkel three-parameter gamma distribution; 2) Pearson’s type III distribution; 3) the Extreme value type I distribution (Gumbell’s type I distribution); 4) the Logarithmic Pearson type III distribution; and 5) the Two-parameters logarithmic-normal distribution. The population statistical parameters for these parametric probability distributions were estimated from the sample statistics by the method of moments.

Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test.

This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.

Determination of Insurance Premium Rates with Aggregation Claims at BPJS with Exponential and Gamma Distributions

Badan Penyelenggara Jaminan Sosial (BPJS) is a legal entity that has been provided by the government for the community with the aim of providing protection for all workers in Indonesia from certain socio-economic risks. National development, marked by planned and continuous strides, embodies a commitment to engage all societal, national, and state levels in fostering progress. Encompassing political, economic, socio-cultural, and defense and security realms, the development is meticulously designed to be comprehensive, targeted, integrated, gradual, and sustainable. The overarching objective is to catalyze an augmentation of national capabilities, align the standard of living for the Indonesian people with developed nations, and elevate overall welfare. To establish premium rates, a method involves multiplying the conditional expected value of claim frequency by the size of the claim, considering observed risk characteristics. A claim, in this context, constitutes a formal request to the insurance company, seeking payment in accordance with the terms of the agreement. The primary objective of this study is to establish the insurance premium rates applicable to policyholders (the insured) through the estimation of parameters in the distribution governing aggregate claims. This involves the distribution of both the number of claims and the size of the claims, and the estimation is performed using the moment method. Premium computations are executed based on two key principles: the pure premium principle and the expected value principle. This research produces the conclusion that the Poisson-Gamma aggregate claims distribution has a premium amount of 3.61 times greater than Poisson-Exponential due to the application of the anticipated value principle, namely IDR 4,403,542.94 per month and IDR 1,219,878.45 per month, respectively.

Evaluation of probability distribution methods for flood frequency analysis in the Jhelum Basin of North-Western Himalayas, India

The Kashmir Valley has frequently endured devastating floods, presenting significant challenges for flood management due to unpredictable flood magnitudes and limited pre-disaster preparedness. A major difficulty in addressing these challenges is the lack of reliable flood frequency analysis (FFA) for effective planning and mitigation. This study seeks to overcome these issues by employing a rigorous quantitative analysis of annual peak discharge data over a 51-year period (1971–2021). One key challenge was the presence of low outliers, which could compromise the integrity of the data. To address this, the Multiple Grubbs-Beck test was applied to remove these outliers before conducting FFA. The study's original achievement lies in its application of multiple distribution models which include Gumbel (EV1), Generalized Extreme Variations (GEV), Log-Normal, Log Pearson III (LP III), Gamma and Normal distribution. Goodness-of-fit tests, including Kolmogorov-Smirnov (KS), Anderson-Darling (AD), and Chi-square at the 5 % significance level, along with visualization techniques such as Probability plots (PP), Quantile plots (QQ), and Probabilistic distribution (PD) graphs, were used to identify the most suitable distribution methods. The Log Pearson Type III (LP-III) was identified as the best fit for the Sangam gauge site (Upper Jhelum), the gamma distribution for Ram Munshibagh (Middle Jhelum), and the Generalized Extreme Value (GEV) and LP-III for Asham (Lower Jhelum). For Sangam, the estimated discharges for 2, 5, 10, 50, 100, 150, 200, and 250-year return periods were 549.63, 1028.43, 1471.34, 2907.64, 3758.92, 4338.61, 4790.99, and 5167.23 cumecs, respectively, using LP-III. For Ram Munshibagh, the discharges were 602.13, 911.03, 1107.04, 1512.12, 1674.35, 1767.0, 1831.87, and 1881.74 cumecs using the gamma distribution. For Asham, the discharges were 685.8, 998.0, 1193.3, 1593.2, 1750.6, 1839.4, 1901.0, and 1948.0 cumecs using the GEV distribution. The findings indicate that the Jhelum River cannot accommodate excess discharge for return periods of 5 years or more, underscoring the need for enhanced flood management strategies.

EXPRESS: Stratified Distributional Analysis - a Novel Perspective on RT Distributions.

Response times and their distributions serve as a powerful lens into cognitive processes. We present a novel statistical methodology called Stratified Distributional Analysis (SDA) to quantitatively assess how key determinants of response times (word frequency and length) shape their distributions. Taking advantage of the availability of millions of lexical decision response times in the English Lexicon Project and the British Lexicon Project, we made important advances into the theoretical issue of linking response times and word frequency by analysing RT distributions as a function of word frequency and word length. We tested these distributions against the lognormal, Wald, and Gamma distributions and three measures of word occurrence (word form frequencies obtained from subtitles and contextual diversity as operationalized as discourse contextual diversity and user contextual diversity). We found that the RT distributions were best described by a lnorm distribution across both megastudies when word occurrence was quantified by a contextual diversity measure. The link between the lnorm distribution and its generative process highlights the power of SDA in elucidating mechanisms that govern the generation of RTs through the fitting of probability distributions. Using a hierarchical Bayesian framework, SDA yielded posterior distributions for the distributional parameters at the single-participant level, enabling probabilistic predictions of response times as a function of word frequency and word length, which has the potential to serve as a diagnostic tool to uncover idiosyncratic features of word processing. Crucially, while we applied our parsimonious methodology to lexical decision response times, it is applicable to a variety of tasks such as word-naming and eye-tracking data.

Continuity of long-term climate data series after the transition from manual to automatic weather station

In climatology, transitioning from conventional manual weather stations (MWS) to automatic weather stations (AWS) presents challenges in maintaining the homogeneity of long-term data series. At the Skalnaté Pleso Observatory (1778 m a.s.l., High Tatras), manual meteorological measurements have been conducted since 1943 using the same methods and devices at the same location. In 2014, the AWS Physicus was installed to record meteorological data parallelly with manual measurements. This study processed six years of parallel measurements (2017–2022) to derive corrections for AWS monthly atmospheric precipitation totals and maximum (Tmax), minimum (Tmin) and mean air temperatures (Tmean) measured in 2023. Two correction approaches were proposed: monthly regressions (MR) and cumulative distribution functions (CDF), including Generalized Extreme Value (GEV) distribution, normal distribution (GAUSS), and Gamma distribution (GAMMA). Analyses of monthly data revealed an underestimation of precipitation totals in AWS data, with a mean bias error (MBE) of −6.8 mm and a root mean squared error (RMSE) of 20.0 mm. The most suitable correction method was the MR, which decreased MBE to 1.5 mm and RMSE to 11.1 mm. AWS monthly air temperature data were overestimated by 0.1 °C, 0.3 °C, and 0.1 °C for Tmax, Tmin, and Tmean, respectively. For Tmax, correction using the MR and GEV methods reduced the MBE to 0.0 °C and achieved RMSE of 0.1 °C for both. After applying GAUSS, MBE and RMSE decreased to 0.1 °C. The most appropriate correction method for Tmin was the MR resulting in MBE of 0.0 °C and RMSE of 0.3 °C. For Tmean, the MR and GEV methods reduced the MBE to 0.0 °C and the RMSE to 0.1 °C for both methods. These results demonstrate that AWS monthly data, when corrected using the presented methods, have the potential to maintain the continuity of historical climate data series at Skalnaté Pleso.

A new two-parameter mixture family of generalized distributions: Statistical properties and application

This paper introduces a novel two-parameter G-family of distributions derived through a mixing approach, where a mixture of the exponentiated G-family with parameter α follows gamma distribution. Within this new family, we focus on the mixture of gamma-exponentiated exponential distribution (MGExED) as a key sub-model. The study thoroughly investigates by determining some of the MGExED statistical properties, such as quantile function, moments, and order statistics. The MGExED's parameters are estimated using different estimation methods. Due to the complexity of obtaining explicit forms for MGExED's estimators, the accuracy of these estimates is assessed through Monte Carlo simulations. To illustrate the practical utility of the MGExED, we apply it to two distinct real datasets, demonstrating its superior flexibility and fit compared to several established distributions in the literature. This comprehensive evaluation underscores the MGExED's potential for broader statistical modeling and analysis application.

A Statewide Examination of Medical Cannabis Purchasing Patterns in Arkansas Over the Three Years Immediately Following Legalization.

Introduction: The use of medical cannabis (MC) to treat a host of conditions has expanded considerably in the United States; however, precise quantitative assessments of purchasing characteristics are unknown. This study sought to characterize the trends in MC purchases, US dollars spent, and type and amount purchased by demographic and clinical characteristics. Materials and Methods: This descriptive exploratory association study examined statewide MC registry data in Arkansas linked at the person level with statewide transaction data documenting each MC purchase. MC transaction data (May 11, 2019-August 31, 2022) were assessed to identify persons who could be linked to the registry data and made at least one purchase. Individual demographic characteristics and MC qualifying conditions (QCs) were ascertained. Product types were classified into plant cannabis, cannabis extract for inhalation (vape), edibles, and others. The average daily total delta-9-tetrahydrocannabinol (THC) purchased was calculated based on the concentration and quantity purchased. Purchasing characteristics are described and demographic and clinical factors associated with THC purchased per day and dollars spent per year were estimated by ordinary least square regression and general linear models with a gamma distribution. Results: On average, 89,057 MC purchasers spent $3343 (interquartile range [IQR], $907-$4802), had 33.34 (IQR, 8.32-46.03) transaction days per year, and purchased 162.32 mg (IQR, 30.51-237.69) of THC per day. Most persons predominantly purchased plant cannabis (68.27%), followed by edibles (14.92%) and vape (11.96%). Individuals younger than 18 years of age (β=-78.23; 95% confidence interval [CI], -116.599 to -39.863), persons 70 and older (β = -122.30; 95% CI, -128.18 to -116.422), and women (β=-33.70; 95% CI, -35.95 to -31.446) purchased less THC per day than their counterparts after multivariate adjustment. The most common QCs were pain and post-traumatic stress disorder (PTSD), and compared to those with cancer, persons with pain (β = 26.30; 95% CI, 18.636-33.96) and PTSD (β = 38.34; 95% CI, 30.467-46.222) purchased more THC per day. Conclusion: The average THC purchased per person per day exceeds typically recommended daily doses for therapeutic uses, and further research is warranted to assess the safety and benefits of MC across these conditions.

Estimate non-Gaussian road roughness from international roughness index

Gaussian model is commonly used to characterize road roughness, while field measured data is usually non-Gaussian. A new method based on the amplitude modulation and International Roughness Index is proposed in this paper to estimate non-Gaussian road roughness. A modified Gamma distribution is proposed to describe the International Roughness Index and to create the amplitude modulation signal. To ensure that the high kurtosis of the amplitude-modulated non-Gaussian profile is correctly transferred to the vehicle response, the method is further developed to fulfill the specifications for the fatigue damage spectrum by controlling the spectral content of the amplitude modulation signal. Herein, a Gaussian amplitude modulation signal with a cutoff frequency is firstly generated, and then converted to a modified Gamma distribution amplitude modulation signal based on the cumulative distribution function transform. Field data are used to verify the proposed method. The results show that a good match is obtained between the estimated and measured non-Gaussian road roughness. The estimated International Roughness Index and fatigue damage potential of vehicle response are well represented using the proposed method.

Molecular characterization, genetic divergence, expression of encapsidiation and synergism by a bipartite begomovirus; Tomato leaf curl Palampur virus (ToLCPMV) infecting bitter gourd (Momordica charantia)

The Tomato leaf curl Palampur virus (ToLCPMV) is a bipartite begomovirus that poses a substantial risk to agriculture by infecting a variety of crops, including cucurbitaceous group. This study examines the manifestation of encapsidation and synergism by ToLCPMV in bitter gourd (Momordica charantia) and focuses on its epidemiological approaches and implications of managing this virus in tomatoes growing areas. Through the utilization of molecular and biological techniques, we have successfully ascertained the epidemiology of this highly destructive virus, highlighting the vital roles played by its two genetic components. An analysis was conducted to identify the mechanism by which the virus clusters its DNA into virions, known as the encapsidation process. Additionally, the impact of synergism with other viral or environmental factors over the degree of infection was examined. The evolutionary rate differences among sites were modeled deploying a discrete Gamma distribution with 5 categories and a [+G] parameter. The results of this study provide important and unique information about synergism, encapsidiation and host-virus interactions. Sequencing study revealed that the bipartite ToLCPMV is linked to the occurrence of leaf curl disease in bitter gourd. The DNA-A and DNA-B of the ToLCPMV isolates infecting bitter gourd (SP1-4) showed 89 %, 93 %, 95 %, and 98 % similarity respectively. Mean evolutionary rates in these categories were 0.19, 0.47, 0.79, 1.24, 2.31 substitutions per site. Unexpectedly, the DNA-A sequences of ToLCPMV that infect this particular host seemed to be an amalgamation of sequences that are closely associated with tomato leaf curl New Delhi virus (ToLCNDV). Additionally, reiterate cropping of tomatoes with vegetables expanded the virus's host geographic region. This understanding will create some specific ways to regulate the dissemination of ToLCPMV and minimize its adverse impacts in tomato growing regions. Through the implementation of these strategies, the ability of crops to withstand and recover from adverse conditions can be enhanced, so encouraging the adoption of sustainable farming practices in affected regions.

Coalescence time of ellipsoidal-wobbling bubbles at surfactant-free interface: Experimental analysis and collision criteria

This work experimentally analyzed bubbles' coalescence with an air-water interface in the ellipsoidal-wobbling regime for different bubble approach velocities, encompassing the ranges of Eötvös, Weber, and Reynolds numbers of 2-3, 1-4, and 500-1100, respectively. We employed high-speed imaging to measure the bubbles' size, shape, velocity, coalescence time, and number of bounces at the interface. We investigated two criteria to determine the beginning of bubble-interface interaction (“collision”): the physical criterion, based on the distance between the bubble top surface and the interface, and the hydrodynamic criterion, based on the bubble velocity. Gamma distributions represented the coalescence times of bubbles at their terminal velocities well. We found a linear relationship between the coalescence time and the number of bounces. The hydrodynamic criterion was more consistent in representing our data on coalescence time.