Unimodal Shape Research Articles

DUS Topp-Leone-G Family of Distributions: Baseline Extension, Properties, Estimation, Simulation and Useful Applications.

This study introduces the DUS Topp-Leone family of distributions, a novel extension of the Topp-Leone distribution enhanced by the DUS transformer. We derive the cumulative distribution function (CDF) and probability density function (PDF), demonstrating the distribution's flexibility in modeling various lifetime phenomena. The DUS-TL exponential distribution was studied as a sub-model, with analytical and graphical evidence revealing that it exhibits a unique unimodal shape, along with fat-tail characteristics, making it suitable for time-to-event data analysis. We evaluate parameter estimation methods, revealing that non-Bayesian approaches, particularly Maximum Likelihood and Least Squares, outperform Bayesian techniques in terms of bias and root mean square error. Additionally, the distribution effectively models datasets with varying skewness and kurtosis values, as illustrated by its application to total factor productivity data across African countries and the mortality rate of people who injected drugs. Overall, the DUS Topp-Leone family represents a significant advancement in statistical modeling, offering robust tools for researchers in diverse fields.

A new extended Fréchet model with different estimation methods and applications

In this study, we introduce a new extension of the Fréchet distribution known as the new extended Fréchet (NE_Fr) model. The NE_Fr is created by combining the new extended X family of distributions and the Fréchet distribution. The NE_Fr has more flexibility than the classical Fréchet distribution and some generalizations of the Fréchet distribution. The probability density function of the NE_Fr can be decreasing, unimodal and right skewed shape but it's hazard rate function can be decreasing or up-side-down shape. Several mathematical properties of the new model were derived by calculating the quantile function, the ordinary moments, the incomplete moments, the moment generating function, the conditional moment, the Bonferroni curve and the Lorenz curve. Several entropy measures were developed for this purpose. The inferences from the NE_Fr distribution were investigated using several established methods such as maximum likelihood estimation, least squares and weighted least squares estimation, and Anderson-Darling estimation. The simulation results demonstrated the computational efficiency of these techniques. The proposed NE_Fr distribution was demonstrated to be useful by examining three actual data sets.

Mathematical model of ion chronogram from in-tube solid-phase microextraction device coupled with mass spectrometry and optimization framework

A mathematical description and experimental outputs exhibited that an ion chronogram from an in-tube solid-phase microextraction (SPME) device linked with mass spectrometry (in-tube-SPME-MS) generally appears as a right-skew unimodal signal with a heavy right tail. Analogous to liquid chromatography coupled with mass spectrometry (LC-MS), in-tube-SPME-MS can utilize the area under its produced ion chronogram for regression analysis and has been shown to be a potential approach for fast quantification of analyte. Different level of unimodity of signal in the ion chronogram could positively or negatively affect the choice of the area used for quantification and finally impact on analysis sensitivity and time efficiency of in-tube-SPME-MS. In the paper, we showed that different in-tube SPME design choices and elution experimental setups produce ion chronograms with controllable varying unimodal peak shape patterns. An improved mathematical model was built based on the plate theory of chromatography and the Van Deemter equation to quantitatively describe the elution process from in-tube-SPME device. A computer simulation was implemented to predict ion chronograms and the results were compared with experimental ion chronograms to show the effectiveness of the model. An optimization framework was further presented based on the model to identify optimal device designs (length and diameter of device) and experimental parameters (flow rate) to track targeted ion chronograms with “desired” peak shape patterns. Empirical elution experiments with the in-tube SPME devices adopting optimized geometric parameters and optimal experimental setups confirmed the consistency between the experimental ion chronograms and the numerical simulations to a certain level.

The complex association between drinking water consumption and endemic gastrointestinal illness as shown by Swedish cohort studies

ABSTRACT It is well known that municipal drinking water may be the cause of gastrointestinal illness (GII) outbreaks, but it is still unclear to what extent drinking water contributes to endemic GII. To explore this, we conducted a prospective cohort study among 6,955 adults in five municipalities in Sweden, collecting monthly GII episodes and mean daily cold drinking water consumption through SMS (Short Message Service). When the association between drinking water consumption and GII (all symptoms) and acute gastrointestinal illness (AGI, vomiting and/or three loose stools during a 24-h period) were assessed, there were indications that the association departed from linearity, following a unimodal shape. Among consumers in surface water areas, the highest risk of GII and AGI was generally seen among the average consumers, while the opposite was seen among groundwater consumers. The association however also seemed to be affected by neighbouring communities. The results of the study indicate that there is indeed an association between drinking water consumption and endemic GII, but the nature of this association is complex and likely affected by multiple factors, for example, water source type in the home and degree of exposure to drinking water from additional sources.

Incidence and seasonality of Kawasaki disease in children in the Philippines, and its association with ambient air temperature.

Despite an unknown cause, Kawasaki disease (KD) is currently the primary leading cause of acquired heart disease in developed countries in children and has been increasing in recent years. Research efforts have explored environmental factors related to KD, but they are still unclear especially in the tropics. We aimed to describe the incidence of KD in children, assess its seasonality, and determine its association with ambient air temperature in the National Capital Region (NCR), Philippines from January 2009 to December 2019. Monthly number of KD cases from the Philippine Pediatric Society (PPS) disease registry was collected to determine the incidence of KD. A generalized linear model (GLM) with quasi-Poisson regression was utilized to assess the seasonality of KD and determine its association with ambient air temperature after adjusting for the relevant confounders. The majority of KD cases (68.52%) occurred in children less than five years old, with incidence rates ranging from 14.98 to 23.20 cases per 100,000 population, and a male-to-female ratio of 1.43:1. Seasonal variation followed a unimodal shape with a rate ratio of 1.13 from the average, peaking in March and reaching the lowest in September. After adjusting for seasonality and long-term trend, every one-degree Celsius increase in the monthly mean temperature significantly increased the risk of developing KD by 8.28% (95% CI: 2.12%, 14.80%). Season-specific analysis revealed a positive association during the dry season (RR: 1.06, 95% CI: 1.01, 1.11), whereas no evidence of association was found during the wet season (RR: 1.10, 95% CI: 0.95, 1.27). We have presented the incidence of KD in the Philippines which is relatively varied from its neighboring countries. The unimodal seasonality of KD and its linear association with temperature, independent of season and secular trend, especially during dry season, may provide insights into its etiology and may support enhanced KD detection efforts in the country.

Experience transforms crossmodal object representations in the anterior temporal lobes.

Combining information from multiple senses is essential to object recognition, core to the ability to learn concepts, make new inferences, and generalize across distinct entities. Yet how the mind combines sensory input into coherent crossmodal representations - the crossmodal binding problem - remains poorly understood. Here, we applied multi-echo fMRI across a 4-day paradigm, in which participants learned three-dimensional crossmodal representations created from well-characterized unimodal visual shape and sound features. Our novel paradigm decoupled the learned crossmodal object representations from their baseline unimodal shapes and sounds, thus allowing us to track the emergence of crossmodal object representations as they were learned by healthy adults. Critically, we found that two anterior temporal lobe structures - temporal pole and perirhinal cortex - differentiated learned from non-learned crossmodal objects, even when controlling for the unimodal features that composed those objects. These results provide evidence for integrated crossmodal object representations in the anterior temporal lobes that were different from the representations for the unimodal features. Furthermore, we found that perirhinal cortex representations were by default biased toward visual shape, but this initial visual bias was attenuated by crossmodal learning. Thus, crossmodal learning transformed perirhinal representations such that they were no longer predominantly grounded in the visual modality, which may be a mechanism by which object concepts gain their abstraction.

Strain-modulated anomalous circular photogalvanic effect in p-type GaAs

The influence of spatial strain distribution on the anomalous circular photogalvanic effect (ACPGE) is investigated in the p-type GaAs material. By tuning the position of exerted stress, it is experimentally observed that the uniform strain related ACPGE behaves like the sine function, which resembles the non-strain situation. Whereas the gradient strain related ACPGE shows the unimodal function line shape. To explain the observations, a new theoretical model is constructed based on spin splitting of energy bands. It is demonstrated that the ACPGE could purely derive from the spin splitting effect. Besides, the combination effect of spin splitting and inverse spin Hall effect on the ACPGE is also investigated. This work reveals the importance of bands spin splitting on ACPGE, which has not been considered before.

Broadleaved trees enhance biodiversity of the understorey vegetation in boreal forests

Understorey vegetation constitutes a remarkable part of the total biodiversity of boreal forests. Mixing broadleaved trees in coniferous forests has been shown to enhance vascular plant abundance and species richness, while high stand density has a counteracting effect. However, more information is needed on how environmental factors modify these biodiversity responses.We investigated how the proportion of broadleaved trees of total basal area, tree species richness, stand density, and shrub cover were reflected in the number of vascular plant species and percentage cover of herbs and bilberry (Vaccinium myrtillus). We also studied the response of site fertility indicators, i.e. C:N ratio and extractable calcium concentration in the soil organic layer, to broadleaved species in mixed-forests.The study was based on the data of understorey vegetation, soil, and stand properties in forests on mineral soil, inventoried on a systematic sample plot network in Finland in 2006. We used a subset of 307 plots in the hemi-southern and middle boreal zones and divided the plots either to xeric or mesic types. We used generalized additive models in analysing the data.Birches (Betula sp.) were the main broadleaved species. Vascular species richness and herb cover generally increased with increasing proportions of broadleaved trees and tree species number both on mesic and xeric sites but decreased with increasing stand density on mesic sites. An increase in proportion of broadleaved trees and stand density resulted in decreased bilberry cover in the southern boreal zone, probably due to stand shading, but in increased cover in the middle boreal zone. Vegetation responses to increasing shrub cover often showed unimodal shape. As increase of proportion of broadleaved trees correlated positively with calcium and negatively with C:N of the organic layer, we suggest that nutrient input from easily decomposable birch leaf litter promotes species richness and herb cover via improved nutrient availability in the soil.Our results indicate that many stand characteristics determining understorey biodiversity can be directed by forest management regimes. Generally, slight increase of broadleaved trees benefitted the understory plant richness, given that stand density is not too high. Because site type and zone controlled many responses, we suggest that it would be beneficial to have habitat and zone-specific instructions in forest management practices that conserve understorey vegetation and its multi-purpose ecosystem services.

Noise-induced bistability in a simple mutual inhibition system.

In this study, we study noise-induced bistability in a simple bivariate mutual inhibition system with slow fluctuating responses to external signals. We give a general condition that the marginal stationary probability density of one of the two variables experiences a transition from a unimodal shape to a bimodal one. We show that the transition occurs even when the stationary probability density of the response to external signals is monotone. The mechanism for the transition is investigated in terms of the calculation of the mean first passage time. We also discuss the genericity of the transition mechanism.

A Transmuted Modified Power-Generated Family of Distributions with Practice on Submodels in Insurance and Reliability

In this article, we propose a new transmuted modified power-generalized family of distributions constructed from the transmuted-generated and modified power-generated families. The proposed approach is flexible and provides a tradeoff between the two baseline families. For a prime study, we identify the main characteristics of the new transmuted modified power family, such as the asymptotic results, quantile function, series representation, and the various kinds of moment measures. By using the exponential distribution as the baseline, a new three-parameter lifetime distribution is constructed. The associated probability functions (density and hazard rate) are flexible and have a variety of asymmetric shapes, which make them attractive for statistical purposes. In particular, for the related probability density function, reversed-J, unimodal, and right-skewed shapes are observed. Measures relating to risk theory are also computed, such as the value at risk and the expected shortfall. By using both simulation analysis and the maximum likelihood approach, the estimation of the model parameters is evaluated. The effectiveness of the proposed model is demonstrated by two real-world cases (one in insurance and the other in reliability), and we show that it yields better fits when compared to other extended models connected to the exponential model.

Alternative statistical modeling for radical prostatectomy data

Several statistical models have been proposed in recent years, among them is the semiparametric regression. In medicine, there are several situations in which it is impracticable to consider a linear regression for statistical modeling, especially when the data contain explanatory variables that present a nonlinear relationship with the response variable. Another common situation is when the response variable does not have a unimodal shape, and it is not possible to adopt distributions belonging to the symmetric or asymmetric classes. In this context, a semiparametric heteroskedastic regression is proposed based on an extension of the normal distribution. Then, we show the usefulness of this model to analyze the cost of prostate cancer surgery. The predictor variables refer to two groups of patients such that one group receives a multimodal local anesthetic solution (Preemptive Target Anesthetic Solution) and the second group is treated with neuraxial blockade (spinal anesthesia/traditional standard). The other relevant predictor variables are also evaluated, thus allowing for the in-depth interpretation of the predictor variables with a nonlinear effect on the dependent variable cost. The penalized maximum likelihood method is adopted to estimate the model parameters. The new regression is a useful statistical tool for analyzing medical data.

Diversity and composition of plants species along elevational gradient: research trends

Studies on species richness patterns along elevation gradients are fascinating and gaining attention. We compiled data from 118 studies of elevational gradients in a broad range of organisms of plant species throughout the world between 2001 and 2021 to estimate the patterns of species richness and their determinants. The present study showed that more than half (57%) of studies had found unimodal hump-shaped richness patterns (maximum diversity at the middle and lower edges), followed by a monotonic decline (26%), in different taxa of the plant. Nearly one-fifth of studies (17.5%) followed either monotonic incline, reverse hump-shaped, or non-distinct patterns. A more uniform model as a unimodal hump shape was present in extensive studies in mountainous regions. Despite the latitudinal and elevational variation, both hemispheres showed similar patterns of species richness for all plant taxa. Some taxa showed bimodality, and some others showed multi-model patterns of elevation-species richness patterns with peak diversity due to topographical and climatic factors. Upper and lower elevational ranges may provide temperature and rainfall extremes, reducing species diversity. The mid-domain effect may explain this species richness pattern. However, the current study confirmed the presence of a hump-shaped species richness pattern as a result of the size of the midpoint elevation or elevation range considered for an individual species. The higher the midpoint value, the longer the elevation range that favors a unimodal pattern. Due to inclusion of limited number of species, universal pattern of species richness along elevational gradient and their determinants could not be anticipated. We need more succinct and regional researches focusing specific taxa and delimiting factors.

Epidemiological investigation of a food-borne outbreak in a kindergarten, Jeju Province, Korea.

On Monday, September 6, 2021, at a kindergarten in Jeju Province, a large number of children vomited and developed food poisoning symptoms, and this necessitated an epidemiological investigation. The team surveyed symptoms and food intake history of kindergarten children, teachers, and workers who ate lunch between September 2 (Thursday) and September 6 (Monday), excluding weekends. In addition to rectal swabs, environmental samples from preserved foods, cooking utensils, drinking water, and refrigerator handles were collected. Pulsed field gel electrophoresis (PFGE) for genetic fingerprint analysis was also performed. There were 19 cases among 176 subjects, which indicated an attack rate of 10.8%. The epidemic curve showed a unimodal shape, and the average incubation period was 2.6 hours. While no food was statistically significant in food intake history, the analysis of 35 rectal smear samples detected Bacillus cereus in 7 children, 4 teachers, and 1 cooking staff. Enterotoxins were also detected in 12 samples. Out of 38 environmental samples, B. cereus and enterotoxins were detected in the morning snack cereal, lunch bean sprouts, and afternoon snack steamed potatoes on Monday, September 6th. The result of the PFGE test on 10 isolates of B. cereus showed that there was no genetic homology. Our results indicated that this outbreak was simultaneously caused by various strains of B. cereus from the environment.

A New Three-Parameter Mixed Poisson Transmuted Weighted Exponential Distribution with Applications to Insurance Data

The classical Poisson distribution assumes equidispersion and this is hardly the case when given count observations. To improve efficiency and general applicability for dispersed data, this paper obtains a new mixing probability distribution using quadratic transmutation map on the weighed exponential distribution. The mixing distribution is used to obtain a new three parameter mixed Poisson distribution. The new distribution has unimodal shape with positive skewness and tends to zero speedily. Basic properties of the new distribution like the distribution function, moments, and dispersion index are obtained. Maximum likelihood estimates of the parameters of the distribution are obtained. Applications are made using four claims frequencies from different insurance companies. Results show that the new distribution gives a good fit in comparisons with some referred discrete distributions.

Molecular weight distribution shape approach for simultaneously enhancing the stiffness, ductility and strength of isotropic semicrystalline polymers based on linear unimodal and bimodal polyethylenes

Bimodal polyethylenes (PEs) have captured broad attention in recent years, while little is known about the contribution of bimodal molecular weight distribution (MWD) shape on their properties compared with unimodal MWD shape. In this work, a comparative investigation of MWD shape-mechanical property relationship of isotropic semicrystalline polymers based on linear unimodal and bimodal PEs has been carried out. This first systematic study indicates that MWD shape influences the chain arrangements in crystalline and amorphous phases which affect their mechanical performance. PEs with bimodal shape exhibit higher crystallinity, lower entanglements and higher fraction of tie molecules than unimodal shape, contributing to simultaneously enhanced Young's modulus, yield strength, elongation at break and tensile strength. This work demonstrates that the modulation of MWD from unimodal to bimodal shape could overcome the trade-off among stiffness, strength and ductility of semicrystalline polymers without altering chain structure, chemical composition or average molecular weight.

Half Logistic Inverted Nadarajah–Haghighi Distribution under Ranked Set Sampling with Applications

In this paper, we present the half logistic inverted Nadarajah–Haghigh (HL-INH) distribution, a novel extension of the inverted Nadarajah–Haghigh (INH) distribution. The probability density function (PDF) for the HL-INH distribution might have a unimodal, right skewness, or heavy-tailed shape for numerous parameter values; however, the shape forms of the hazard rate function (HRF) for the HL-INH distribution may be decreasing. Four specific entropy measurements were investigated. Some useful expansions for the HL-INH distribution were investigated. Several statistical and computational features of the HL-INH distribution were calculated. Using simple (SRS) and ranked set sampling (RSS), the parameters for the HL-INH distribution were estimated using the maximum likelihood (ML) technique. A simulation analysis was executed in order to determine the model parameters of the HL-INH distribution using the SRS and RSS methods, and RSS was shown to be more efficient than SRS. We demonstrate that the HL-INH distribution is more adaptable than the INH distribution and other statistical distributions when utilizing three real-world datasets.

A Modified Gamma Model: Properties, Estimation, and Applications

Statistical methods are essential for describing, predicting, and modeling natural phenomena in numerous application areas. These methods are helpful for modeling and predicting data in medicine, reliability engineering, actuarial science, and other fields. This paper presents a novel, simple, and fully flexible modified gamma model. The new model provides various forms of densities, including symmetric, asymmetric, unimodal, and reversed-J shapes, as well as a bathtub-shaped failure rate, which is suitable for modeling the lifespan of patients with an increased risk of death. Some basic and dynamic properties of the model are examined. Four methods for estimating its parameters are discussed, and a simulation study is used to examine the consistency and efficiency of these estimators. Finally, the usefulness of the proposed model is demonstrated in the analysis of some data sets.

Molecular Weight Distribution Shape Dependence of the Crystallization Kinetics of Semicrystalline Polymers Based on Linear Unimodal and Bimodal Polyethylenes

The manipulation of the crystallization kinetics and crystallinity of polymers without altering their chemical composition, chain structure, or average molecular weight is challenging, while little attention is paid to the role of molecular weight distribution (MWD) shape. In this work, a series of well-defined linear unimodal and bimodal polyethylenes (PEs) with molecular weights ranging from 300 k to 1200 k g/mol were synthesized to serve as a model system to study the impact of bimodal MWD shape on the crystallization kinetics of semicrystalline polymers in comparison with unimodal MWD shape at the same weight-average molecular weight (Mw). It is shown that PEs with a bimodal shape exhibit a faster nucleation rate and crystallization rate with a smaller lamellar width at low isothermal temperatures. A higher crystallization enthalpy of bimodal PEs is shown in non-isothermal experiments. The mechanism behind this is elucidated, which suggests that MWD shapes mainly affect the small-scale nucleation process without altering the large-scale growth process. This first systematic comparative study on the crystallization kinetics of linear unimodal and bimodal PEs gives insight into tailoring the crystallization behavior of semicrystalline polymers from an MWD shape perspective.

An Alternative Lambert-Type Distribution for Bounded Data

In this article, we propose a new two-parameter distribution for bounded data such as rates, proportions, or percentages. The density function of the proposed distribution, presenting monotonic, unimodal, and inverse-unimodal shapes, tends to a positive finite value at the lower end of its support, which can lead to a better fit of the lower empirical quantiles. We derive some of the main structural properties of the new distribution. We make a description of the skewness and kurtosis of the distribution. We discuss the parameter estimation under the maximum likelihood method. We developed a simulation study to evaluate the behavior of the estimators. Finally, we present two applications to real data providing evidence that the proposed distribution can perform better than the popular beta and Kumaraswamy distributions.

Foreground segmentation and location of coal and gangue under complex similar background

To improve the foreground segmentation and location accuracy of complex coal gangue images with gray histogram distribution close to the unimodal shape, a contour detection algorithm of the grayscale fluctuation matrix is proposed. The contour and non-contour pixels of coal and gangue images are investigated, and the result indicates that the gray values of the pixels around the contour exhibit the non-uniform distribution, and the gray value changes in different directions are significantly different. Accordingly, a grayscale fluctuation matrix is built by calculating the change amplitude of pixels in different directions, and multiple features are extracted from the grayscale fluctuation matrix to realize the target contour segmentation. Furthermore, the contour is optimized using the historical and future information of the contour image, thus effectively removing numerous false contours, reproducing some hidden contours and increasing segmentation accuracy. This method has high accuracy, and the maximum error rates of the pixel area and center coordinate of contour detection are 4.404% and 3.18% respectively. This study provides a feasible solution to the edge detection and segmentation of images with similar and complex backgrounds.