Probability Density Function Distribution 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 Bivariate Survival Model: The Marshall-Olkin Bivariate Exponentiated Lomax Distribution with Modeling Bivariate Football Scoring Data

This paper focuses on applying the Marshall-Olkin approach to generate a new bivariate distribution. The distribution is called the bivariate exponentiated Lomax distribution, and its marginal distribution is the exponentiated Lomax distribution. Numerous attributes are examined, including the joint reliability and hazard functions, the bivariate probability density function, and its marginals. The joint probability density function and joint cumulative distribution function can be stated analytically. Different contour plots of the joint probability density function and joint reliability and hazard rate functions of the bivariate exponentiated Lomax distribution are given. The unknown parameters and reliability and hazard rate functions of the bivariate exponentiated Lomax distribution are estimated using the maximum likelihood method. Also, the Bayesian technique is applied to derive the Bayes estimators and reliability and hazard rate functions of the bivariate exponentiated Lomax distribution. In addition, maximum likelihood and Bayesian two-sample prediction are considered to predict a future observation from a future sample of the bivariate exponentiated Lomax distribution. A simulation study is presented to investigate the theoretical findings derived in this paper and to evaluate the performance of the maximum likelihood and Bayes estimates and predictors. Furthermore, the real data set used in this paper comprises the scoring times from 42 American Football League matches that took place over three consecutive independent weekends in 1986. The results of utilizing the real data set approve the practicality and flexibility of the bivariate exponentiated Lomax distribution in real-world situations, and the bivariate exponentiated Lomax distribution is suitable for modeling this bivariate data set.

A Comprehensive Approach to Fault Classification of Helicopter Engines with Adaboost Ensemble Model

This work is based on the PHM North America 2024 Conference Data Challenge’s datasets of Helicopter turbine engine performance measurements. These datasets were large and moderately imbalanced. For dealing with these challenges, we demonstrate significant tools covering feature engineering, augmentation and selection, model exploration, visualizations, model explainability and confidence margin estimation. This work was performed in its entirety using MATLAB. All these tools will be generally applicable to data-driven modeling and prediction of health to real life applications. Initially, we explored the 742k observations in the training set, noting a 60-40 split between healthy and faulty labels, and identified two major operational clusters within the data. We enhanced the dataset by removing duplicates and engineered new features based on domain knowledge, expanding the feature set to 242 dimensions. However for the torque margin estimation, we trained a regression model on a limited subset (18 features), which includes engineered features using domain knowledge, quadratic terms and linear interaction between all the terms. For the final submission, we utilized a stepwise linear regression model to optimize feature selection. This approach achieved a perfect regression score on test data, validated by a consistent torque margin residual range of +/- 0.5%. The model's RMSE and MAE metrics were optimal for employing a normal distribution probability density function. For , we reduced the feature set to 58 using dimensionality reduction techniques and balanced the data with upsampling and down-weighing the minority class. We employed ASHA (Asynchronous Successive Halving Algorithm) in conjunction with AutoML to efficiently determine the most suitable model family, significantly saving compute time. Subsequently, we trained ensemble models, including bagged tree and AdaBoost (Adaptive Boosting), which minimized false negatives and positives, achieving robust classification performance. This was particularly critical given the high penalty for false negatives in the data challenge. The MathWorks team score on Testing Data was 0.9686 at the close of competition. This was further improved to 0.9867. Our approach demonstrates the effectiveness of combining strategic data processing, feature engineering, and model selection to enhance predictive accuracy in complex operational datasets.

Atmospheric warming during rapid sea ice loss over the Barents–Kara seas in winter

AbstractThe atmospheric temperature change associated with rapid sea ice loss events over the Barents–Kara Seas (BKS) is explored. Rapid sea ice loss events are defined as periods with a tendency for sea ice concentration averaged over BKS to be below the fifth percentile of the probability density function distribution during the winters of 1979–2020 for at least three consecutive days. Composite analysis shows that there is a significantly positive bottom‐amplified temperature anomaly ahead of the rapid sea ice loss, which is closely associated with a wave train composed of a Ural blocking and an upstream positive phase of the North Atlantic Oscillation. This structure is favorable for the transport of warm and moist air into the BKS, and therefore, the tropospheric temperature, including the surface air temperature, increases through horizontal warm‐temperature advection, specifically through warm advection of the climatological temperature by the anomalous wind. The cooling over the BKS due to the adiabatic effect and vertical mixing opposes the horizontal warm‐temperature advection above and below about 900 hPa, respectively. However, an increase in skin temperature prominently results from enhanced downward long‐wave radiation, which is also the main contributor to the rapid sea ice loss.

Modified Generalized Chen Distribution, Estimation and Application using Econometrics Data

In this study, a variant of the generalized Chen (GC) distribution with parameters α, β, γ, δ, and λ, termed the Modified Generalized Chen (MGC) distribution, was introduced. The study evaluated several Chen distribution variants theoretically, focusing on the MGC distribution. Variants considered include the Generalized Chen (GC), Half-Cauchy Chen (HCC), New Extended Chen (NEC), and Exponentially Generalized Modified Chen (EGMC) distributions. The objectives of the study was to derive the probability density function (PDF) and cumulative density function (CDF) of the MGC distribution, determine its statistical properties and reliability characteristics, compare these properties and characteristics to existing distributions, and empirically evaluate its performance. The study developed unique expressions for the PDF, CDF, survival function, and hazard function of the MGC distribution. By evaluating PDFs and performance measures such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and mean square error (MSE) across various datasets, the MGC distribution consistently demonstrated superiority over other variants. The MGC distribution offers improved model fit, predictive accuracy, and interpretability without sacrificing simplicity. The dataset employed in this study was the secondary data, encompassing economic indicators from 1981 to 2021 and public health expenditure data for Nigeria and Ghana from 1995 to 2014. Statistical analyses revealed that on the average, the MGC distribution outperforms others, with superior average AIC (-509.95), BIC (-510.49), and MSE (499.89) measures across the datasets considered in the study. This superior performance indicates better fit and accuracy in predicting economic and public health outcomes, offering valuable insights for policymakers and researchers. The study underscores the importance of adopting flexible and interpretable distribution models like the MGC distribution to enhance empirical analyses, inform policy decisions, and advance knowledge in econometrics and related disciplines.

An augmented integral method for probability distribution evaluation of performance functions

The paper proposes an efficient augmented integral method for probability distribution evaluation of performance functions. In the proposed method, the performance function is augmented by adding an auxiliary random variable, whose probability density function (PDF) and cumulative distribution function (CDF) are formulated as the integrations of the original performance function with respect to basic random variables. The optimal auxiliary random variable is determined to provide an accurate estimation of the integrations by investigating the geometric properties of integrands and a distribution parameter optimization approach based on moment analysis. According to the convolution formula, the relationship between the PDFs of the augmented performance function and the original performance function is clarified. Then, the PDF of the original performance function is calculated by solving an unconstrained optimization problem that is established using the convolution formula. Finally, three numerical examples are investigated to demonstrate the efficiency and accuracy of the proposed method for structural reliability analysis. The results indicate that the proposed method can evaluate the probability distribution of performance functions accurately and efficiently, even when the performance functions are strongly nonlinear and implicit.

Assessing wind energy exploitation potential in several regions of Viet Nam using Kernel density estimation model

This article analyzes and assesses the potential for wind energy exploitation in six regions of Vietnam. The wind speed data are used to construct wind speed probability distributions (WSPDs) based on kernel density estimation (KDE). The KDE distribution, with six bandwidth selection methods, is implemented to generate probability density functions (PDFs) for each region's data to describe wind speed characteristics. The statistical tests Cramér-Von Mises (CvM), Anderson-Darling (A-D), and Kolmogorov-Smirnov (K-S) are applied to evaluate the PDFs' goodness-of-fit performance. The analysis results present the KDE distribution using the least-squares cross-validation (LSCV), and the Scott bandwidth selection method has outstanding fitting performance. Based on these PDF distributions, the wind turbine (WT) power curve is used to estimate and predict the amount of electricity that can be produced. This study also proposes a reliable method for wind power output planning based on wind speed that can be universally applied.

Research on bridge safety early warning method based on strain energy theory and health monitoring data

Bridges are technology-intensive and heavily invested permanent infrastructure. After completion and opening to traffic, bridge structures are easy to be affected by factors such as traffic load and atmospheric environment. Therefore, it is necessary to do safety warning and evaluation of bridges, especially the abnormal behavior in the early stages of bridge operation. In this research paper, a large-span continuous rigid frame bridge installed with the health monitoring system (HMS), of which a large amount of health monitoring data are collected by the HMS, is used as an example, and then a bridge safety early warning method is proposed when the bridge is during early operating period. First of all, the research finding that the internal stress of the prototype bridge obeys normal distribution through statistical analysis is used; next, we deduce that the strain energy inside the prototype bridge is subject to the Non-central Chi-square distribution combined with the strain energy and statistical theories; in the end, the key probability density distribution function of strain energy and its parameters are derived by using the key stress distribution function of the high performance concrete C50 strength grade used in the prototype bridge. The method recommended in this paper is conducive to the formulation of bridge preventive maintenance strategies.

Difference of Soil Thickness Depending on Climate Zones and Geological Classification: Based on a Survey of Mountain Slopes in Japan

There is little information which examines and compares climate zones or geology/topography in their relation to soil thickness along mountain slopes, where soil thickness is a possible contributing factor for the increase of sediment wash-off. In this study, the data obtained from handy penetration tests conducted throughout Japan are collected and attached to information on climate zones and geography/topography with the aim of clarifying the difference in soil thickness according to the climate zone and geological classification. The probability distribution of soil thickness was found to fit roughly with the probability density function of a log-normal distribution, regardless of the climate zone or geological age / lithology. A comparison of μ showed that the soil thickness at target sites in the Pacific climate zone, which have high rainfall, was large, at approximately 2.1 m. Meanwhile, the soil thickness was low, at approximately 1.5 m, at target sites in the Setouchi climate zone, which has low rainfall. A comparison of the geology showed that soil thicknesses of sites where the geology consisted of Tertiary and Quaternary sedimentary rocks were high, at approximately 2.1 m and 2.3 m, respectively. This suggests that, in high-precipitation regions, the weathering of rocks is promoted so that the soil layers tend to increase in thickness.

Annual Variations of PM10, PM2.5 and PM1.0 Fraction at an Urban Site in Ansan, Korea

This study examines particulate matter (PM) concentrations, specifically PM10, PM2.5, and PM1.0, at an urban site in Ansan, South Korea. Three BAM-1020 continuous monitors measured PM10, PM2.5, and PM1.0 hourly from January to December 2021, with data acquisition rates of 97.1%, 97.3%, and 93.4%, respectively. Average annual concentrations were 45.7±48.4 µg/m³ (PM10), 26.4±22.7 µg/m³ (PM2.5), and 18.5±14.5 µg/m³ (PM1.0). PM10 was 91% of the annual air quality standard, while PM2.5 exceeded this standard by 176%, indicating severe pollution. Statistical analyses using probability density function (PDF) and cumulative distribution function (CDF) showed 98.5% of data converged at 150 µg/m³ (PM10), 75 µg/m³ (PM2.5), and 50 µg/m³ (PM1.0), with the remaining 1.5% corresponding to approximately 131 hours, annually. In 2021, all six observed yellow dust events occurred in spring (March to May). PM10, PM2.5, and PM1.0 concentrations increased from January to March, peaked in March, decreased until September, and rose again. The coarse fraction ratio increased stepwise from February to May, likely due to yellow dust and episodes of high PM concentration in the spring. The PM1.0 concentration was higher in summer and fall compared with that in spring and winter. The PM1.0/PM2.5 ratio was highest in summer and fall even though the annual PM1.0concentration was lowest, suggesting a higher secondary formation rate of fine particles during these periods. This underscores the need for further scientific investigation on PM1.0. The study provides insights into the simultaneous observation and distribution characteristics of PM10, PM2.5, and PM1.0, highlighting the mass concentration, distribution, and ratio of PM1.0. These findings are crucial for understanding PM distribution in Ansan, an industrial complex, and can serve as essential data for chemical composition comparisons, data validation, public health strategies, and cost-benefit analyses for regional PM improvement.

Inefficient star formation in high Mach number environments

Context. The star formation rate (SFR), the number of stars formed per unit of time, is a fundamental quantity in the evolution of the Universe. Aims. While turbulence is believed to play a crucial role in setting the SFR, the exact mechanism remains unclear. Turbulence promotes star formation by compressing the gas, but also slows it down by stabilizing the gas against gravity. Most widely used analytical models rely on questionable assumptions, including: i) integrating over the density PDF, a one-point statistical description that ignores spatial correlation, ii) selecting self-gravitating gas based on a density threshold that often ignores turbulent dispersion, iii) assuming the freefall time as the timescale for estimating SFR without considering the need to rejuvenate the density PDF, iv) assuming the density probability distribution function (PDF) to be log-normal. This leads to the reliance on fudge factors for rough agreement with simulations. Even more seriously, when a more accurate density PDF is being used, the classical theory predicts a SFR that is essentially 0. Methods. Improving upon the only existing model that incorporates the spatial correlation of the density field, we present a new analytical model that, in a companion paper, is rigorously compared against a large series of numerical simulations. We calculate the time needed to rejuvenate density fluctuations of a given density and spatial scale, revealing that it is generally much longer than the freefall time, rendering the latter inappropriate for use. Results. We make specific predictions regarding the role of the Mach number, ℳ, and the driving scale of turbulence divided by the mean Jeans length. At low to moderate Mach numbers, turbulence does not reduce and may even slightly promote star formation by broadening the PDF. However, at higher Mach numbers, most density fluctuations are stabilized by turbulent dispersion, leading to a steep drop in the SFR as the Mach number increases. A fundamental parameter is the exponent of the power spectrum of the natural logarithm of the density, ln ρ, characterizing the spatial distribution of the density field. In the high Mach regime, the SFR strongly depends on it, as lower values imply a paucity of massive, gravitationally unstable clumps. Conclusions. We provide a revised analytical model to calculate the SFR of a system, considering not only the mean density and Mach number but also the spatial distribution of the gas through the power spectrum of ln ρ, as well as the injection scale of turbulence. At low Mach numbers, the model predicts a relatively high SFR nearly independent of ℳ, whereas for high Mach, the SFR is a steeply decreasing function of ℳ.

Stabilization of nonhomogenous semi-Markov jump linear systems with synchronous switching delays via aperiodically intermittent control

A type of nonhomogenous semi-Markov jump linear systems with synchronous switching delays is considered in the present paper. Owing to the existence of time-varying delays and nonhomogenous semi-Markov switching process, the selection of Lyapunov functional and the transformation of some time-varying parameters become more complicated in comparison with many existing works. To overcome these difficulties, a sort of Lyapunov–Krasovskii functional related to switching delays is introduced. Simultaneously, the technique of convex combination is applied to tackle a variety of time-varying terms including transition probabilities (TPs), probability distribution function and probability density function (PDF). Then, a time-invariant stability criterion superior to many relevant works in conservativeness is obtained to ensure mean-square exponential stability (MES). Based on this result, time-invariant conditions for mean square exponential stability of the controlled system are also attained by the continuous feedback control. Subsequently, to stand on the point of cost reduction, an aperiodically intermittent control (AIC) is adopted in such a system and a stability criterion is attained as well under more relaxed restrictions on relative parameters. Finally, a numerical example is provided to verify the effectiveness and correctness of the results.

Seismic fragility analysis of long-span rigid-frame bridge on mountainous soft clay site

In order to assess the damage condition of bridge components for a large-span rigid bridge in a soft clay site in a mountainous area in China southwest, a finite element model of a large-span rigid bridge is established based on the OpenSees software, and the joint probability density distribution function of the ground motion strength and seismic demand and the marginal distribution function of the ground motion are introduced into the kernel density function. As a basis to get the method of calculating the fragility of the bridge members, and the method is verified for its feasibility, on this basis, the damage condition of the bridge components are analyzed, and finally the damage condition of the bridge system are analyzed by the first-order bounds method and the improved PCM method (IPCM). The results showed that: (1) Kernel density method (KDE) can effectively calculate the damage probability of each component, for example, under ground motions with PGA equal to 0.2 g, the probability of slight damage of the 1# pier is 29%, that of the intermediate consolidation pier (2# pier ~ 4# pier) is about 90%; the probability of slight damage of the 1# bearing is 48%, and that of the 2# bearing is 87%. (2) Reasonable value of the expansion joints can effectively reduce the probability of main beam collision. In this investigation, the value is taken as 0.18 m ~ 0.24 m. (3) The bridge system is more likely to be damaged than a single component in the system, and the damage probability of a single component cannot be used as a criterion for the bridge system in the actual working condition. Comparing the first-order boundary law with the IPCM method, the IPCM method has higher accuracy.

Capacity Optimization for RSMA-Based Multi-User System over Underwater Turbulence Channel

The underwater environment used for communication is harsh and complex, necessitating heightened standards for spectral efficiency and reliability in underwater wireless optical communication (UWOC) systems. The focus of this work is on the performance of multi-user UWOC systems operating in oblique channels of ocean turbulence downlink, where users are randomly distributed at a certain depth. A joint optimization scheme is proposed, which joints rate-splitting multiple access (RSMA) and power allocation so that the system’s ergodic sum capacity is optimized to improve the transmission bandwidth. Furthermore, the probability density function (PDF) and cumulative distribution function (CDF) models for the received signal-to-noise ratio (SNR) of a multi-user multiple-input multiple-output (MIMO) system operating in the turbulent underwater oblique channels are established, accounting for the avalanche photodiode (APD) shot noise and solar radiation noise. Theoretical derivations are presented to quantify the ergodic capacity and outage probability of the multi-user system utilizing the RSMA technology. Subsequently, a numerical analysis is conducted to investigate the influence of the power allocation coefficient, RSMA, and the joint optimization algorithm on the performance of a two-user MIMO system leveraging RSMA. The simulation results show that our optimization scheme effectively reduces the outage probability, thereby achieving the maximum system sum rate and validating the practical feasibility and efficacy of the proposed scheme.

On Epidemiological and Actuarial Analyses of Health Insurance Models for Communicable Diseases

This article examines an SIDRS disease model design for insurance contracts, in which the insured population is exposed to the risks of communicable diseases. For the epidemiological models, the population is structured into four demographic groups, namely: susceptibles (S), infected PHs undergoing treatment (I), infected PHs who are diseased (D), and infected PHs who recovered (R) from the disease, with part of the latter thereafter re-entering the group of susceptibles (S) and continuing with the insurer by paying premiums until he or she is infected again. The infective class is a union of the class of those undergoing treatment, deceased policy holders (PHs), and those who have recovered. The number of deceased PHs is counted as part of the insured population because the number PHs who die of the disease must be accounted for and are entitled to claims. The insurance policies are designed for the members of the susceptible group: the latter constantly face the risk of infection and death due to the disease. The probability of PHs remaining susceptible for the SIDRS disease model is formulated. The probability density function (PDF) and cumulative distribution function (CDFs) for the SIDRS disease model for an insurance policy are obtained. For the actuarial part, we used actuarial techniques and principles to determine the financial obligations of the parties and the insurance amounts for the insurer and PHs. The cumulative insurance reserve for an annuity and a lump sum plan are also considered. To ascertain the risk of insolvency, premium adjustment for the PHs is considered. Some numerical computations of the results arising from our model analyses are also considered in this article. This article has practical applications in health insurance schemes. It is also applicable in the determination of insurance premiums payable by PHs who did not have the disease and insurance claims receivable by those who are hospitalized or die of the disease. Our model can also be practically applicable in the determination of health insurance reserves for communicable diseases.

Modeling insurance loss data using novel approach of moment exponential model: Inference, actuarial measures and application

Asymmetrical probability models are helpful for analyzing skewed data sets since they allow you to describe the form of the distribution and anticipate the chance of extreme events. This article defines a novel approach to continuous moment exponential distribution called the exponentiated generalized moment exponential model. The extension has two additional parameters accounting for the distribution’s shape. We extend this distribution probability density, cumulative distribution, hazard rate, and survival functions and establish different key statistical properties. Parameter estimation is obtained using different procedures, notably maximum likelihood estimation, least square, and Bayesian methods. A Monte Carlo simulation experiment is conducted to assess parameter performance and indicator risk measures. This article examines two distinct actual data sets in order to highlight the significance of the proposed model as well as its application in a variety of settings. The new model is compared to a large number of well-known extensions that were developed by other businesses.

Physical layer security in SWIPT-based cooperative vehicular relaying networks

The future of autonomous transportation systems depends on energy sustainability and secure information exchange from low-power vehicular sensors, hence the increased interest in vehicular sensor charging using simultaneous wireless information and power transfer (SWIPT). This study investigates the physical layer security of a SWIPT-based radio frequency energy harvesting cooperative vehicular relaying network subjected to cascade Nakagami-m and double Nakagami-m (DN) fading channels. In the considered system model, a stationary source communicates with a mobile destination through a power-splitting-based decode-and-forward relay in the presence of a mobile passive eavesdropper. Based on the Gamma-distributed first term of the Laguerre series, new statistical probability density function (PDF) and cumulative distribution function (CDF) expressions for the DN are derived to accurately model the complex cascaded fading scenario. The secrecy performance metrics analyzed are the secrecy outage probability (SOP), the probability of non-zero secrecy capacity (PNZSC), and the intercept probability (IP). In addition, the asymptotic SOP (ASOP) is investigated in the high signal-to-noise ratio (SNR) to enhance the comprehension of the secrecy performance. Based on the derived ASOP, the secrecy diversity order (SDO) of the proposed system is determined and examined. Particularly, we present analytical closed-form expressions for the secrecy performance metrics and provide a detailed understanding of the impact of the system parameters under the cascade fading scenario. Then, a power splitting (PS) optimization problem is formulated to minimize the SOP. The results demonstrate a reduction in the SOP with the proposed PS scheme compared to the equal PS scheme. The obtained analytical findings are validated using Monte Carlo simulations.

Testing for Markovian character of transfer of fluctuations in solar wind turbulence on kinetic scales.

We apply statistical analysis to search for processes responsible for turbulence in physical systems. In our previous studies, we have shown that solar wind turbulence in the inertial range of large magnetohydrodynamic scales exhibits Markov properties. We have recently extended this approach on much smaller kinetic scales. Here we are testing for the Markovian character of stochastic processes in a kinetic regime based on magnetic field and velocity fluctuations in the solar wind, measured onboard the Magnetospheric Multiscale (MMS) mission: behind the bow shock, inside the magnetosheath, and near the magnetopause. We have verified that the Chapman-Kolmogorov necessary conditions for Markov processes is satisfied for local transfer of energy between the magnetic and velocity fields also on kinetic scales. We have confirmed that for magnetic fluctuations, the first Kramers-Moyal coefficient is linear, while the second term is quadratic, corresponding to drift and diffusion processes in the resulting Fokker-Planck equation. It means that magnetic self-similar turbulence is described by generalized Ornstein-Uhlenbeck processes. We show that for the magnetic case, the Fokker-Planck equationleads to the probability density functions of the kappa distributions, which exhibit global universal scale invariance with a linear scaling and lack of intermittency. On the contrary, for velocity fluctuations, higher order Kramers-Moyal coefficients should be taken into account and hence scale invariance is not observed. However, the nonextensity parameter in Tsallis entropy provides a robust measure of the departure of the system from equilibrium. The obtained results are important for a better understanding of the physical mechanism governing turbulent systems in space and laboratory.

Molecular cloud matching in CO and dust in M33

This study is aimed to contribute to a more comprehensive understanding of the molecular hydrogen distribution in the galaxy M33 by introducing novel methods for generating high angular resolution (18.2″, equivalent to 75 pc for a distance of 847 kpc) column density maps of molecular hydrogen (NH2). M33 is a local group galaxy that has been observed with Herschel in the far-infrared (FIR) wavelength range from 70 to 500 μm. Previous studies have presented total hydrogen column density maps (NH), using these FIR data (partly combined with mid-IR maps), employing various methods. We first performed a spectral energy distribution (SED) fit to the 160, 250, 350, and 500 μm continuum data obtain NH, using a technique similar to one previously reported in the literature. We also use a second method which involves translating only the 250 μm map into a NH map at the same angular resolution of 18.2″. An NH2 map via each method is then obtained by subtracting the H I component. Distinguishing our study from previous ones, we adopt a more versatile approach by considering a variable emissivity index, β, and dust absorption coefficient, κ0. This choice enables us to construct a κ0 map, thereby enhancing the depth and accuracy of our investigation of the hydrogen column density. We address the inherent biases and challenges within both methods (which give similar results) and compare them with existing maps available in the literature. Moreover, we calculate a map of the carbon monoxide CO(1 − 0)-to-molecular hydrogen (H2) conversion factor (XCO factor), which shows a strong dispersion around an average value of 1.8 × 1020 cm−2/(K km s−1) throughout the disk. We obtain column density probability distribution functions (N-PDFs) from the NH, NH2, and NH I maps and discuss their shape, consisting of several log-normal and power-law tail components.

Defining a clinically meaningful within-patient change threshold for the Cohen-Mansfield Agitation Inventory in Alzheimer's dementia.

The Cohen-Mansfield Agitation Inventory (CMAI) quantifies the frequency of agitation behaviors in elderly persons. This post hoc analysis of data from the brexpiprazole clinical program aimed to determine a meaningful within-patient change (MWPC) threshold for CMAI Total score among patients with agitation associated with dementia due to Alzheimer's disease. Data were included from three 12-week, multicenter, randomized, double-blind, placebo-controlled, parallel-arm trials of brexpiprazole for the treatment of agitation associated with dementia due to Alzheimer's disease (ClinicalTrials.gov identifiers: NCT01862640, NCT01922258, NCT03548584). Change in CMAI Total score (range 29-203; higher scores indicate higher frequency of agitation behaviors) from baseline to Week 12 was the primary endpoint in each trial. MWPC thresholds were estimated from anchor-based mean change analyses and receiver operating characteristic (ROC) curves. The Clinical Global Impression-Severity of illness (CGI-S) and Clinical Global Impression-Improvement (CGI-I) scales, both as related to agitation, were used as anchors. Empirical cumulative distribution functions (eCDFs) and probability density functions (PDFs) were plotted as supportive evidence. Distribution-based methods were also employed. Data from 898 patients were analyzed (mean age, 73.7 years; mean baseline CMAI Total score, 73.8). The mean CMAI Total score change corresponding to a difference of small improvement vs. stable (CGI-S one-point decrease vs. no change), or minimally improved vs. no change (CGI-I rating of 3 vs. 4), ranged from -10.6 to -13.5 points. The mean CMAI Total score change corresponding to a difference of moderate improvement vs. stable (CGI-S two-point decrease vs. no change), or much improved vs. no change (CGI-I rating of 2 vs. 4), ranged from -20.2 to -25.7 points. ROC curve analyses generally produced smaller estimates of meaningful change. eCDFs and PDFs showed good distribution and separation of CMAI Total score change between CGI-S/CGI-I categories. In distribution-based analyses, the minimal detectable change for CMAI Total score (10.5-11.8 points) was generally lower than anchor-suggested thresholds. Triangulation of evidence from anchor- and distribution-based analyses supports an MWPC threshold for CMAI Total score of -20 points, with a threshold range of -15 to -25 points, in patients with agitation associated with dementia due to Alzheimer's disease.