Distribution Parameters Research Articles

Effect of Collagen Fiber Tortuosity Distribution on the Mechanical Response of Arterial Tissues.

This study investigated the effect of collagen fiber tortuosity distribution on the biomechanical failure and prefailure properties of arterial wall tissue. An in-silico model of the arterial wall was developed using data obtained from combined multiphoton microscopy imaging and uniaxial tensile testing. Layer dependent properties were prescribed for collagen, elastin, and ground substance. Collagen fibers were modeled as discrete anisotropic elements, while elastin and ground substance were modeled as homogeneous isotropic components. Our parametric analysis, using a finite element approach, revealed that different parameters of collagen fibers tortuosity distribution significantly influence both pre-failure and failure biomechanical properties. Increased fiber tortuosity improved the tissue strength whereas the dispersion in the tortuosity distribution reduced it. This study provides novel insights into the structural-mechanical interdependencies in arterial walls, offering potential targets for clinical assessments and therapeutic interventions aimed at mitigating rupture risks.

On the posterior property of the Rician distribution

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process data. In this paper, we introduce objective Bayesian inference for the Rician distribution parameters, specifically the Jeffreys rule and Jeffreys prior are derived. We proved that the obtained posterior for the first priors led to an improper posterior while the Jeffreys prior led to a proper distribution. To evaluate the effectiveness of our proposed Bayesian estimation method, we perform extensive numerical simulations and compare the results with those obtained from traditional moment-based and maximum likelihood estimators. Our simulations illustrate that the Bayesian estimators derived from the Jeffreys prior provide nearly unbiased estimates, showcasing the advantages of our approach over classical techniques. Additionally, our framework incorporates the S.A.F.E. principles – Sustainable, Accurate, Fair, and Explainable – ensuring robustness, fairness, and transparency in predictive modelling.

Gumbel–Logistic Unit Distribution with Application in Telecommunications Data Modeling

The manuscript deals with a new unit distribution that depends on two positive parameters. The distribution itself was obtained from the Gumbel distribution, i.e., by its transformation, using generalized logistic mapping, into a unit interval. In this way, the so-called Gumbel-logistic unit (abbr. GLU) distribution is obtained, and its key properties, such as cumulative distribution function, modality, hazard and quantile function, moment-based characteristics, Bayesian inferences and entropy, have been investigated in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. An estimation of the parameters of the GLU distribution, based on its quantiles, is also performed, together with asymptotic properties of the estimates thus obtained and their numerical simulation. Finally, the GLU distribution has been applied in modeling the empirical distributions of some real-world data related to telecommunications.

Exploring statistical and machine learning methods for modeling probability distribution parameters in downtime length analysis: a paper manufacturing machine case study

Manufacturing companies focus on improving productivity, reducing costs, and aligning performance metrics with strategic objectives. In industries like paper manufacturing, minimizing equipment downtime is essential for maintaining high throughput. Leveraging the extensive data generated by these facilities offers opportunities for gaining competitive advantages through data-driven insights, revealing trends, patterns, and predicting future performance indicators like unplanned downtime length, which is essential in optimizing maintenance and minimizing potential losses. This paper explores statistical and machine learning techniques for modeling downtime length probability distributions and correlation with machine vibration measurements. We proposed a novel framework, employing advanced data-driven techniques like artificial neural networks (ANNs) to estimate parameters of probability distributions governing downtime lengths. Our approach specifically focuses on modeling parameters of these distribution, rather than directly modeling probability density function (PDF) values, as is common in other approaches. Experimental results indicate a significant performance boost, with the proposed method achieving up to 30% superior performance in modeling the distribution of downtime lengths compared to alternative methods. Moreover, this method facilitates unsupervised training, making it suitable for big data repositories of unlabelled data. The framework allows for potential expansion by incorporating additional input variables. In this study, machine vibration velocity measurements are selected for further investigation. The study underscores the potential of advanced data-driven techniques to enables companies to make better-informed decisions regarding their current maintenance practices and to direct improvement programs in industrial settings.

From particles to pixels: How many particles do I really need to construct stellar kinematic mock observational measurements?

Abstract This work considers the impact of resolution in the construction of mock observations of simulated galaxies. In particular, when building mock integral field spectroscopic observations from galaxy formation models in cosmological simulations, we investigate the possible systematics that may arise given the assumption that all galaxies above some stellar mass limit will provide unbiased and meaningful observable stellar kinematics. We build a catalogue of N-body simulations to sample the range of stellar particle resolutions within the Eagle Ref0050N0752 simulation box and examine how their observable kinematics vary relative to a higher-resolution N-body control. We use these models to compile a table of the minimum number of particles-per-pixel to reach a given uncertainty in the fitted line-of-sight velocity distribution parameters. Further, we introduce a Voronoi-binning module to the mock observation code, SimSpin, in order to meet these minimum numbers. Using Eagle, we show the impact of this shot noise on the observed spin-ellipticity plane and the recovery of this space when observations are binned with increasing numbers of particles. In conclusion, we advise binning mock images to meet at least 200 particles-per-pixel to avoid systematically under-estimating the velocity dispersion along a given line-of-sight. We demonstrate that this is important for comparing galaxies extracted from the same simulation, as well as between simulations of varying mass resolution and observations of real galaxies.

Application of Odd Chen-Log-Logistic Distribution to Covid-19 Data

This article created the Odd Chen-Log-Logistic distribution from Odd Chen-G family distributions. We derive various statistical features. The parameter estimation theory focuses on selecting the best estimators. We estimate distribution parameters using maximum likelihood, moment, least squares, weighted least, L-moment, maximum product spacing, and minimal distance methods. We will examine Kolmogorov-Smirnov simulation studies that compare estimator efficiency. Finally, we analyze a genuine COVID-19 data set to demonstrate the flexibility of our model and its accuracy compared to other distributions.

Exploiting the diversity of modeling methods to probe systematic biases in strong lensing analyses

Challenges inherent to high-resolution and high signal-to-noise data as well as model degeneracies can cause systematic biases in analyses of strong lens systems. In the past decade, the number of lens modeling methods has significantly increased, from purely analytical methods, to pixelated and non-parametric ones, or ones based on deep learning. We embraced this diversity by selecting different software packages and use them to blindly model independently simulated Hubble Space Telescope (HST) imaging data. To overcome the difficulties arising from using different codes and conventions, we used the COde-independent Organized LEns STandard (COOLEST) to store, compare, and release all models in a self-consistent and human-readable manner. From an ensemble of six modeling methods, we studied the recovery of the lens potential parameters and properties of the reconstructed source. In particular, we simulated and inferred parameters of an elliptical power-law mass distribution embedded in a shear field for the lens, while each modeling method reconstructs the source differently. We find that, overall, both lens and source properties are recovered reasonably well, but systematic biases arise in all methods. Interestingly, we do not observe that a single method is significantly more accurate than others, and the amount of bias largely depends on the specific lens or source property of interest. By combining posterior distributions from individual methods using equal weights, the maximal systematic biases on lens model parameters inferred from individual models are reduced by a factor of 5.4 on average. We investigated a selection of modeling effects that partly explain the observed biases, such as the cuspy nature of the background source and the accuracy of the point spread function. This work introduces, for the first time, a generic framework to compare and ease the combination of models obtained from different codes and methods, which will be key to retain accuracy in future strong lensing analyses.

Modeling of Reversed Fréchet Distribution under Linear Normalizing

Extreme value theory (EVT) is becoming increasingly important as a suitable model of extreme events to represent phenomena in various fields of applications where extreme values may appear and have detrimental effects. In EVT, the Reversed Fréchet (RF) distribution is a special case of the Reversed generalized extreme value distribution (RGEVD) for modeling extreme data under linear normalizing. The purpose of this paper is divided into four objectives: Firstly, we discuss the practical aspects of the two methods that belong to the domain attraction of RF distribution. The second objective is to use RF distribution to model the behavior of two extreme air pollutants. The third objective is based on a diagnostics plot and hypothesis testing used to evaluate an appropriate shape of the tail distribution. Lastly, for the fourth objective, we attempt to obtain the return level period (RLP) that is expected to be exceeded. Maximum likelihood estimation (MLE) is derived and used to estimate the parameters of RF distribution. The results show that applications are significant for modeling by RF distribution in all cases of two air pollutants. Software that was used in all computations and graphics is the R statistical program with packages fExtreme and ismev.

Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications

Abstract Robust quantification of predictive uncertainty is a critical addition needed for machine learning applied to weather and climate problems to improve understanding of what is driving prediction sensitivity. Ensembles of machine learning models provide predictive uncertainty estimates in a conceptually simple way but require multiple models for training and prediction, increasing computational cost and latency. Parametric deep learning can estimate uncertainty with one model by predicting the parameters of a probability distribution but does not account for epistemic uncertainty. Evidential deep learning, a technique that extends parametric deep learning to higher-order distributions, can account for both aleatoric and epistemic uncertainty with one model. This study compares the uncertainty derived from evidential neural networks to that obtained from ensembles. Through applications of classification of winter precipitation type and regression of surface layer fluxes, we show evidential deep learning models attaining predictive accuracy rivaling standard methods, while robustly quantifying both sources of uncertainty. We evaluate the uncertainty in terms of how well the predictions are calibrated and how well the uncertainty correlates with prediction error. Analyses of uncertainty in the context of the inputs reveal sensitivities to underlying meteorological processes, facilitating interpretation of the models. The conceptual simplicity, interpretability, and computational efficiency of evidential neural networks make them highly extensible, offering a promising approach for reliable and practical uncertainty quantification in Earth system science modeling. In order to encourage broader adoption of evidential deep learning, we have developed a new Python package, MILES-GUESS (https://github.com/ai2es/miles-guess), that enables users to train and evaluate both evidential and ensemble deep learning.

<i></i>Ring width distribution as a valuable anatomical trait for predicting bending strength and rigidity in European oak wood beams

Ring width variability affects the elasticity and strength of wood members. This study was conducted to determine which dispersion statistics of annual ring width distributions measured in cross section in European oak (Quercus robur L.) wood beams are useful as covariates in models for predicting modulus of elasticity (MOE) and modulus of rupture (MOR). For this purpose, 21 European oak trees growing in north-western Spain were felled, logged and sawn. The planks obtained were air-dried and surfaced into beams (50×100×2,000 mm), which were visually graded according to the UNE 56544:2022 standard. MOE, MOR, moisture content and density (determined according to EN 408:2010 standard) and abundance of sapwood and ring widths were determined in 30 beams apt for structural purposes. MOE was significantly related to standard deviation, variance and interquartile range of the ring width distribution in the beam. MOE was also related to mean ring width (r =-0.52, p<0.01) and maximum ring width per beam (r =-0.54, p<0.01), an easy to measure variable. MOR was also related to ring width distribution parameters, although yielding lower r values. The influence of ring width evenness and maximum ring width can be considered to improve visual strength grading standards for European oak timber.

The role of refractive indices in measuring mineral dust with high-spectral-resolution infrared satellite sounders: application to the Gobi Desert

Abstract. Mineral dust significantly influences the Earth's climate system by affecting the radiative balance through the emission, absorption and scattering of solar and terrestrial radiation. Estimating the dust radiative effect remains challenging due to the lack of detailed information on the physical and chemical properties of dust. High-spectral-resolution instruments in the infrared (IR) spectrum, such as the Infrared Atmospheric Sounding Instrument (IASI), have demonstrated the ability to quantify these aerosol properties. A crucial parameter for characterizing mineral dust from space is the complex refractive index (CRI), as it links the dust's physical and chemical properties to its optical properties. This paper examines the impact of six prior laboratory CRI datasets to improve the characterization of dust microphysical properties using IASI. The CRIs include older measurements obtained through the classical pellet method, commonly employed in mineral dust applications, as well as newer datasets that incorporate the latest advancements in laboratory measurement techniques for aerosol generation. These datasets are tested on IASI measurements during a dust storm event over the Gobi Desert in May 2017. We evaluate the sensitivity of IASI to different CRI datasets using the Atmospheric Radiation Algorithm for High-Spectral Resolution Measurements from Infrared Spectrometer (ARAHMIS) radiative transfer algorithm and explore the datasets' impact on retrieving size distribution parameters by mapping their spatial distributions. The results indicate that the laboratory CRI datasets decrease the total error in the covariance matrix by 30 %. In addition, we assess the ability to accurately reconstruct IASI detections and the extent to which we can retrieve the microphysical properties of dust particles. The choice of CRI significantly impacts the accuracy of dust detection and characterization from satellite observations. Notably, datasets that incorporate recent aerosol generation techniques with higher spectral resolution and samples from the case study region show improved compatibility with IASI observations. The outcomes of this research emphasize two key points: the crucial link between chemical composition of dust and its optical properties and the importance of considering the specific composition of the CRI dataset for improved retrieval of the microphysical parameters. Furthermore, this study highlights the critical role of ongoing enhancements in CRI measurement approaches, as well as the potential of high-spectral-resolution infrared sounders for aerosol atmospheric investigation and for understanding the radiative impacts of sounders.

MHD Mixed Convection Boundary Layer Casson Nanofluid Flow over an Exponential Stretching Sheet

This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach.

Structure–Tissue Exposure/Selectivity Relationship (STR) on Carbamates of Cannabidiol

The structure–tissue exposure/selectivity relationship (STR) aids in lead optimization to improve drug candidate selection and balance clinical dose, efficacy, and toxicity. In this work, butyrocholinesterase (BuChE)-targeted cannabidiol (CBD) carbamates were used to study the STR in correlation with observed efficacy/toxicity. CBD carbamates with similar structures and same molecular target showed similar/different pharmacokinetics. L2 and L4 had almost same plasma exposure, which was not correlated with their exposure in the brain, while tissue exposure/selectivity was correlated with efficacy/safety. Structural modifications of CBD carbamates not only changed drug plasma exposure, but also altered drug tissue exposure/selectivity. The secondary amine of carbamate can be metabolized into CBD, while the tertiary amine is more stable. Absorption, distribution, metabolism, excretion, and toxicity (ADMET) parameters can be used to predict STR. Therefore, STR can alter drug tissue exposure/selectivity in normal tissues, impacting efficacy/toxicity. The drug optimization process should balance the structure–activity relationship (SAR) and STR of drug candidates for improving clinical trials.

Bayesian estimation under different loss functions for the case of inverse Rayleigh distribution

In this study, the best parameter estimator for the scale parameter of the inverse Rayleigh distribution was determined based on a comparison of the maximum likelihood estimator (MLE) method, the Bayesian generalized squared error loss function (SELF), the Bayesian linear exponential loss function (LINEX LF), and the Bayesian entropy loss function (ELF). The prior distribution chosen was the non-informative prior, namely the Jeffrey prior, and the informative prior using the exponential distribution. The estimator evaluation method used was based on the smallest value of the Akaike information criterion (AIC), corrected Akaike information criterion (AICc), and Bayesian information criterion (BIC). Based on simulation studies and real data, it was found that the best parameter estimator on the data for the scale parameter of the inverse Rayleigh distribution is the Bayes ELF prior exponential .

Multi-target Phenylpropanoids Against Epilepsy.

Epilepsy is a neurological disease with no defined cause, characterized by recurrent epileptic seizures. These occur due to the dysregulation of excitatory and inhibitory neurotransmitters in the central nervous system (CNS). Psychopharmaceuticals have undesirable side effects; many patients require more than one pharmacotherapy to control crises. With this in mind, this work emphasizes the discovery of new substances from natural products that can combat epileptic seizures. Using in silico techniques, this review aims to evaluate the antiepileptic and multi-target activity of phenylpropanoid derivatives. Initially, ligand-based virtual screening models (LBVS) were performed with 468 phenylpropanoid compounds to predict biological activities. The LBVS were developed for the targets alpha- amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA), voltage-gated calcium channel Ttype (CaV), gamma-aminobutyric acid A (GABAA), gamma-aminobutyric acid transporter type 1 (GAT-1), voltage-gated potassium channel of the Q family (KCNQ), voltage-gated sodium channel (NaV), and N-methyl D-aspartate (NMDA). The compounds that had good results in the LBVS were analyzed for the absorption, distribution, metabolism, excretion, and toxicity (ADMET) parameters, and later, the best molecules were evaluated in the molecular docking consensus. The TR430 compound showed the best results in pharmacokinetic parameters; its oral absorption was 99.03%, it did not violate any Lipinski rule, it showed good bioavailability, and no cytotoxicity was observed either from the molecule or from the metabolites in the evaluated parameters. TR430 was able to bind with GABAA (activation) and AMPA (inhibition) targets and demonstrated good binding energy and significant interactions with both targets. The studied compound showed to be a promising molecule with a possible multi-target activity in both fundamental pharmacological targets for the treatment of epilepsy.

Fat Distribution and Urolithiasis Risk Parameters in Uric Acid Stone Formers and Patients with Type 2 Diabetes Mellitus.

Key Points Under a controlled diet, uric acid stone formers (UASFs) and diabetic patients have higher endogenous net acid production.Under a controlled diet, UASFs have lower ammonium-to-net acid excretion ratio.Body fat inversely correlates with urine buffer capacity in normal individuals, but this relationship is lost in diabetic patients and UASFs. Background Uric acid (UA) nephrolithiasis affects approximately 10% of kidney stones, with a greater preponderance among patients with obesity and diabetes mellitus (DM). UA lithogenicity is driven by abnormally acidic urine pH. Distinguishing the contribution of intrinsic (e.g., body adiposity) versus external (e.g., dietary) factors to UA stone propensity is challenging because of uncontrolled diets in outpatients in previously published studies. Methods This compilation of metabolic studies with body composition examined by dual-energy x-ray absorptiometry scan and blood and urine biochemistry collected under a controlled metabolic diet was conducted across three distinct populations: 74 UA stone formers (UASF group), 13 patients with type 2 DM without kidney stones (DM group), and 51 healthy volunteers (HV group). Results Compared with HVs, both UASFs and patients with DM exhibited higher levels of net acid excretion (NAE) and significantly lower urine pH and lower proportion of NAE excreted as ammonium (NH4 +/NAE), all under controlled diets. UASFs exhibited significantly lower NH4 +/NAE compared with patients with DM. UASFs also showed higher total body and truncal fat compared with HVs. Among the HVs, lower NH4 +/NAE ratio correlated with higher truncal and total fat. However, this association was abolished in the UASF and DM groups who exhibit a fixed low NH4 +/NAE ratio across a range of body and truncal fat. Conclusions The findings suggest a dual defect of diet-independent increase in acid production and impaired kidney NH4 + excretion as major contributors to the risk of UA stone formation. There is an inverse physiologic association between body fat content and NH4 +/NAE in HVs, whereas NH4 +/NAE is persistently low in UASFs and patients with DM, regardless of body fat, representing pathophysiology.

Design, synthesis of antipyrine-based Schiff bases and investigation of their cholinesterase and carbonic anhydrase activities by in vitro and in silico approaches

In this study, a series of antipyrine-based Schiff bases (1-10) was designed, synthesized, and evaluated as potential inhibitors of various metabolic enzymes, including acetylcholinesterase (AChE), butyrylcholinesterase (BChE), and human erythrocyte carbonic anhydrase I and II (hCA I and hCA II). The target molecules were characterized by UV-Vis, FT-IR, 1H NMR, 13CNMR, LC-HRMS, and elemental analysis. All tested derivatives demonstrated low nanomolar inhibition with Ki values of in the range of 20.58 ± 0.35 to 53.11 ± 1.02 nM against AChE, 21.84 ± 0.40 to 54.41 ± 1.05 nM against BChE, 27.45 ± 0.41 to 48.22 ± 0.91 nM against cytosolic hCA I isoform associated with epilepsy, and 6.02 ± 0.11 to 29.32 ± 0.54 nM against cytosolic hCA II isoform associated with glaucoma. In general, most these molecules, except for a few, inhibited these enzymes more than acetazolamide (AZA) and neostigmine. Among them, compounds 5, 7, 8, and 9 showed the best inhibitory activities against AChE, BChE, hCA I, and hCA II, respectively. Docking results were calculated for the compounds that showed the best inhibitory activity against these enzymes and for reference compounds. Based on the molecular docking results, they were determined to have high binding energies, including hydrogen bonds, electrostatic interactions, and hydrophobic interactions. Absorption, distribution, metabolism, and excretion (ADME) parameters determined that all the synthesized pyrazolone ring-bearing Schif base derivatives (1-10) have the expected physicochemical properties in terms of drug-likeness and can be evaluated as orally active potential. Properties such as the electrophilicity index and chemical hardness were also investigated by density functional theory (DFT) at the B3LYP/6-311G** level of theory.

Probing Populations of Dark Stellar Remnants in the Globular Clusters 47 Tuc and Terzan 5 Using Pulsar Timing

We present a new method to combine multimass equilibrium dynamical models and pulsar timing data to constrain the mass distribution and remnant populations of Milky Way globular clusters (GCs). We first apply this method to 47 Tuc, a cluster for which there exists an abundance of stellar kinematic data and which is also host to a large population of millisecond pulsars. We demonstrate that the pulsar timing data allow us to place strong constraints on the overall mass distribution and remnant populations even without fitting on stellar kinematics. Our models favor a small population of stellar-mass black holes (BHs) in this cluster (with a total mass of 446−72+75M⊙ ), arguing against the need for a large (>2000 M ⊙) central intermediate-mass BH. We then apply the method to Terzan 5, a heavily obscured bulge cluster that hosts the largest population of millisecond pulsars of any Milky Way GC and for which the collection of conventional stellar kinematic data is very limited. We improve existing constraints on the mass distribution and structural parameters of this cluster and place stringent constraints on its black hole content, finding an upper limit on the mass in BHs of ∼4000 M ⊙. This method allows us to probe the central dynamics of GCs even in the absence of stellar kinematic data and can be easily applied to other GCs with pulsar timing data, for which data sets will continue to grow with the next generation of radio telescopes.

An empirical model of the kinetics of hydrogen-induced cracking in pipeline steel, using statistical distribution models and considering microstructural characteristics and hydrogen diffusion parameters

This study proposes an empirical model to predict the kinetics of hydrogen-induced cracking (HIC) growth rate in pipeline steels based on experimentally measured hydrogen diffusion parameters and spatial distribution of microstructural features previously identified to have a role on HIC kinetics. In the experimental work, the HIC was induced by electrochemical cathodic charging and the crack growth was monitored by ultrasonic inspection. Optical and scanning electron microscopy were used to determine the spatial distribution parameters of non-metallic inclusions, and the ferrite grain and second phase characteristics. The hydrogen microprint technique used to visualize hydrogen diffusion path in the microstructure and the hydrogen diffusion parameters were determined by hydrogen permeation tests. Results show that NMI shape affects HIC nucleation sites, using student's t-distribution, while ferrite grain characteristics affect HIC growth rates, with X70–2 and X56 steel plates recorded highest HIC growth rate. The Log-Normal distribution model, supported by statistical analysis, effectively predicts HIC growth rates compared with Weibull and Gamma distribution models.

Evaluation of the cross sections and photoelectron angular distribution parameters following atomic photoionization under extreme conditions

In this manuscript, we report on a theoretical study of the atomic structures, cross sections, and photoelectron angular distribution parameters following the atomic photoionization under extreme conditions. To achieve this goal, a relativistic approach using the Dirac-Coulomb Hamiltonian within the framework of relativistic configuration interaction, taking advantage of independent particle basis wave functions, is proposed. To describe the interaction of charged particles in the ideal and non-ideal plasmas, the Debye potential and the pseudopotential are implemented, the latter being derived from a progressive resolution of the Bogolyubov chain equations. Both bound and continuous state wave functions, essential for a comprehensive understanding of quantum systems, are determined from the modified local central potential, which is obtained in a self-consistent manner to represent the electronic shielding effect on the nuclear potential. The photoionization processes are evaluated using the relativistic distorted wave approach, which is consistent with the principles of relativistic Dirac theory and thus provides an accurate description of the dynamics. As a test desk, the present method is applied to the evaluation of the energies, ionization potentials, wave functions, cross sections, and photoelectron angular distribution parameters, using the single photon ionization of the Li-like Fe XXIV ions as the basis for analysis. Our results demonstrate that the plasma environment effect not only decreases the ionization potentials and increases the cross sections but also affects the photoelectron angular distribution parameters across different shells, leading to a more balanced and symmetrical photoelectron distribution pattern. A detailed comparison is made between our results, and the available well-established theoretical predictions and experimental data of the unshielded case in the literature shows a good agreement. The present work provides novel insights and theoretical models that not only help us to better understand the fundamental properties of the complex systems but are also beneficial for innovative applications in the study of astrophysical and laboratory plasmas.