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The ethical needs and concerns with use and sourcing of human materials, particularly serum, in OECD in vitro test guidelines were explored in a dedicated international workshop held in 2019. The health-related aspects of the donation procedure, including tissue screening, donor health, laboratory work health protection, permission from the donor for commercial use, payment of the donors and the potential for exploitation of low-income populations and data protection of the donors; supply, availability, and competition with clinical needs; traceability of the serum and auditability/GLP needs for the Test Guideline Programme, were examined. Here we provide the recommendations of the workshop with respect to the use of human serum, and potentially other human reagents, specifically with regard to test method development for OECD Test Guideline utility as part of the Mutual Acceptance of Data requirement across all OECD member countries. These include informed donor consent terminology, a checklist of human serum information requirements to be included with the Good Laboratory Practise report, and suitable sources for human serum to ensure waste supplies are used, that can no longer be used for medical purposes, ensuring no competition of supply for essential medical use.

The aim of this work was to conduct a comprehensive study about the transport properties of NSAIDs across the blood-brain barrier (BBB) in vitro. Transport studies with celecoxib, diclofenac, ibuprofen, meloxicam, piroxicam and tenoxicam were accomplished across Transwell models based on cell line PBMEC/C1-2, ECV304 or primary rat brain endothelial cells. Single as well as group substance studies were carried out. In group studies substance group compositions, transport medium and serum content were varied, transport inhibitors verapamil and probenecid were added. Resulted permeability coefficients were compared and normalized to internal standards diazepam and carboxyfluorescein. Transport rankings of NSAIDs across each model were obtained. Single substance studies showed similar rankings as corresponding group studies across PBMEC/C1-2 or ECV304 cell layers. Serum content, glioma conditioned medium and inhibitors probenecid and verapamil influenced resulted permeability significantly. Basic differences of transport properties of the investigated NSAIDs were similar comparing all three in vitro BBB models. Different substance combinations in the group studies and addition of probenecid and verapamil suggested that transporter proteins are involved in the transport of every tested NSAID. Results especially underlined the importance of same experimental conditions (transport medium, serum content, species origin, cell line) for proper data comparison.

Merkel cells (MCs) are involved in mechanoreception, but several lines of evidence suggest that they may also participate in skin disorders through the release of neuropeptides and hormones. In addition, MC hyperplasias have been reported in inflammatory skin diseases. However, neither proliferation nor reactions to the epidermal environment have been demonstrated. We established a culture model enriched in swine MCs to analyze their proliferative capability and to discover MC survival factors and modulators of MC neuroendocrine properties. In culture, MCs reacted to bFGF by extending outgrowths. Conversely, neurotrophins failed to induce cell spreading, suggesting that they do not act as a growth factor for MCs. For the first time, we provide evidence of proliferation in culture through Ki-67 immunoreactivity. We also found that MCs reacted to histamine or activation of the proton gated/osmoreceptor TRPV4 by releasing vasoactive intestinal peptide (VIP). Since VIP is involved in many pathophysiological processes, its release suggests a putative regulatory role for MCs in skin disorders. Moreover, in contrast to mechanotransduction, neuropeptide exocytosis was Ca(2+)-independent, as inhibition of Ca(2+) channels or culture in the absence of Ca(2+) failed to decrease the amount of VIP released. We conclude that neuropeptide release and neurotransmitter exocytosis may be two distinct pathways that are differentially regulated.

A new extracorporeal bioartificial liver using alginate-entrapped hepatocytes was developed and evaluated for its ability to correct the lack of bilirubin conjugation in the Gunn rat. Hepatocytes were harvested from Sprague-Dawley rats by the two-step collagenase perfusion method and then immobilized in Ca++-alginate beads. The ability of immobilized hepatocytes to conjugate bilirubin was investigated in vitro by comparison with hepatocyte monolayer cultures. The bioartificial liver consisted of a cylindric bioreactor containing either alginate beads with hepatocytes (test group) or alginate beads alone (control group). Gunn rats were connected to this bioreactor via an extracorporeal circulation and bile fractions were collected at hourly intervals. Both bilirubin monoconjugales and bilirubin diconjugates were measured in the bile by high pressure liquid chromatography. Hepatocyte viability in alginate beads was determined prior to and at the end of each experiment and found to be unchanged (75%). In the test group, the concentration of bilirubin conjugates increased rapidly, attaining median values of 72.26 pM and 92.59 pM for mono and diconjugated bilirubin respectively, during a 3 h period of extracorporeal circulation. In the control group, the levels of either conjugate did not exceed 0.87 μM throughout the experiments. Statistical analysis showed a significant difference between the two groups (p < 0.0023). These results suggest that the bioartificial liver used in this study represents an effective method for the temporary correction of the Gunn rat's genetic defect. Such a system might be of therapeutic interest in acute liver failure.

In 2019, Bagul et al. posed two open problems dealing with inequalities involving trigonometric and hyperbolic functions and an adjustable parameter. This article is an attempt to solve these open problems. The results are supported by three-dimensional graphics, taking into account the variation of the parameter involved.

The importance of (probability) distributions in engineering science is undeniable. They are extensively used in this sector to carry out statistical studies and draw conclusions. In this article, we construct a new trigonometric distribution with support [0,1] called the truncated inverted arctan power (TIAP) distribution and demonstrate its use with engineering data. The corresponding probability density function is particularly flexible in the sense that it has various decreased right-skewness and unimodal forms. The associated hazard rate function shows that the TIAP distribution may adapt data with monotonic, U-shaped, and N-shaped failure rates. To reflect the interdependence of two random variables or sets of data, a bivariate variant of the TIAP distribution is also elaborated. All these distributional tools are then applied from a statistical perspective. In particular, the involved parameters are estimated using a maximum likelihood technique. Applications to engineering data indicate that the univariate and bivariate extensions for the TIAP distribution have a better fit compared to various current distributions.

In this article, we present a comprehensive class of estimators designed for population proportion estimation by leveraging auxiliary attributes within the framework of simple random sampling. The proposed class encompasses a diverse range of estimators, each of which undergoes a thorough examination. We provide numerical expressions for both bias and mean squared error, employing a first-order approximation. The significance of the introduced class of estimators is underscored through a detailed analysis of numerical results. These findings demonstrate the marked superiority of the suggested estimators over their existing counterparts in terms of mean squared error and percentage relative efficiency, as observed in both actual and simulated data scenarios. Consequently, we advocate for the adoption of the proposed class of estimators, asserting its potential to yield improved outcomes when estimating population proportions through the utilization of simple random sampling techniques.

This paper introduced and investigated the power unit inverse Lindley distribution (PUILD), a novel two-parameter generalization of the famous unit inverse Lindley distribution. Among its notable functional properties, the corresponding probability density function can be unimodal, decreasing, increasing, or right-skewed. In addition, the hazard rate function can be increasing, U-shaped, or N-shaped. The PUILD thus takes advantage of these characteristics to gain flexibility in the analysis of unit data compared to the former unit inverse Lindley distribution, among others. From a theoretical point of view, many key measures were determined under closed-form expressions, including mode, quantiles, median, Bowley's skewness, Moor's kurtosis, coefficient of variation, index of dispersion, moments of various types, and Lorenz and Bonferroni curves. Some important measures of uncertainty were also calculated, mainly through the incomplete gamma function. In the statistical part, the estimation of the parameters involved was studied using fifteen different methods, including the maximum likelihood method. The invariant property of this approach was then used to efficiently estimate different uncertainty measures. Some simulation results were presented to support this claim. The significance of the PUILD underlying model compared to several current statistical models, including the unit inverse Lindley, exponentiated Topp-Leone, Kumaraswamy, and beta and transformed gamma models, was illustrated by two applications using real datasets.

Abstract Extensive research has been conducted on poverty in developing countries using conventional regression analysis, which has limited prediction capability. This study aims to address this gap by applying advanced machine learning (ML) methods to predict poverty in Somalia. Utilizing data from the first-ever 2020 Somalia Demographic and Health Survey (SDHS), a cross-sectional study design is considered. ML methods, including random forest (RF), decision tree (DT), support vector machine (SVM), and logistic regression, are tested and applied using R software version 4.1.2, while conventional methods are analyzed using STATA version 17. Evaluation metrics, such as confusion matrix, accuracy, precision, sensitivity, specificity, recall, F1 score, and area under the receiver operating characteristic (AUROC), are employed to assess the performance of predictive models. The prevalence of poverty in Somalia is notable, with approximately seven out of ten Somalis living in poverty, making it one of the highest rates in the region. Among nomadic pastoralists, agro-pastoralists, and internally displaced persons (IDPs), the poverty average stands at 69%, while urban areas have a lower poverty rate of 60%. The accuracy of prediction ranged between 67.21% and 98.36% for the advanced ML methods, with the RF model demonstrating the best performance. The results reveal geographical region, household size, respondent age group, husband employment status, age of household head, and place of residence as the top six predictors of poverty in Somalia. The findings highlight the potential of ML methods to predict poverty and uncover hidden information that traditional statistical methods cannot detect, with the RF model identified as the best classifier for predicting poverty in Somalia.

This paper presents a method to construct and implement an Events Knowledge Graph (EventsKG) for security-related open-source intelligence gathering, focusing on event exploration for situation monitoring in India. The EventsKG is designed to process news articles, extract events of national security significance, and represent them in a consistent and intuitive manner. This method utilizes state-of-the-art natural language understanding techniques and the capabilities of graph databases to extract and organize events. A domain-specific ontology is created for effective storage and retrieval. In addition, we provide a user-friendly dashboard for querying and a complete visualization of events across India. The effectiveness of the EventsKG is assessed through a human evaluation of the information retrieval quality. Our approach contributes to rapid data availability and decision-making through a comprehensive understanding of events, including local events, from every part of India in just a few clicks. The system is evaluated against a manually annotated dataset and by involving human evaluators through a feedback survey, and it has shown good retrieval accuracy. The EventsKG can also be used for other applications such as threat intelligence, incident response, and situational awareness.

Recent innovations have focused on the creation of new families that extend well-known distributions while providing a huge amount of practical flexibility for data modeling. Weighted distributions offer an effective approach for addressing model building and data interpretation problems. The main objective of this work is to provide a novel family based on a weighted generator called the length-biased truncated Lomax-generated (LBTLo-G) family. Discussions are held about the characteristics of the LBTLo-G family, including expressions for the probability density function, moments, and incomplete moments. In addition, different measures of uncertainty are determined. We provide four new sub-distributions and investigated their functionalities. Subsequently, a statistical analysis is given. The LBTLo-G family's parameter estimation is carried out using the maximum likelihood technique on the basis of full and censored samples. Simulation research is conducted to determine the parameters of the LBTLo Weibull (LBTLoW) distribution. Four genuine data sets are considered to illustrate the fitting behavior of the LBTLoW distribution. In each case, the application outcomes demonstrate that the LBTLoW distribution can, in fact, fit the data more accurately than other rival distributions.

The subject matter described herein includes the analysis of the stress-strength reliability of the system, in which the discrete strength of the system is impacted by two random discrete stresses. The reliability function of such systems is denoted by $ R = P[Y < X < Z] $, where $ X $ is the strength of the system and $ Y $ and $ Z $ are the stresses. We look at how $ X $, $ Y $ and $ Z $ fit into a well-known discrete distribution known as the geometric distribution. The stress-strength reliability of this form is not widely studied in the current literature, and research in this area has only considered the scenario when the strength and stress variables follow a continuous distribution, although it is essentially nil in the case of discrete stress and strength. There are numerous applications wherein a system is exposed to external stress, and its functionality depends on whether its intrinsic physical strength falls within specific stress limits. Furthermore, the continuous measurement of stress and strength variables presents inherent difficulties and inconveniences in such scenarios. For the suggested distribution, we obtain the maximum likelihood estimate of the variable $ R $, as well as its asymptotic distribution and confidence interval. Additionally, in the classical setup, we find the boot-p and boot-t confidence intervals for $ R $. In the Bayesian setup, we utilize the widely recognized Markov Chain Monte Carlo technique and the Lindley approximation method to find the Bayes estimate of $ R $ under the squared error loss function. A Monte Carlo simulation study and real data analysis are demonstrated to show the applicability of the suggested model in the real world.

In this article, the Lagrange expansion of the second kind is used to generate a novel zero-truncated Katz distribution; we refer to it as the Lagrangian zero-truncated Katz distribution (LZTKD). Notably, the zero-truncated Katz distribution is a special case of this distribution. Along with the closed form expression of all its statistical characteristics, the LZTKD is proven to provide an adequate model for both underdispersed and overdispersed zero-truncated count datasets. Specifically, we show that the associated hazard rate function has increasing, decreasing, bathtub, or upside-down bathtub shapes. Moreover, we demonstrate that the LZTKD belongs to the Lagrangian distribution of the first kind. Then, applications of the LZTKD in statistical scenarios are explored. The unknown parameters are estimated using the well-reputed method of the maximum likelihood. In addition, the generalized likelihood ratio test procedure is applied to test the significance of the additional parameter. In order to evaluate the performance of the maximum likelihood estimates, simulation studies are also conducted. The use of real-life datasets further highlights the relevance and applicability of the proposed model.

This paper introduces a new probability distribution called the mixture symmetric gamma (MSG) distribution, which is defined as a mixture of two symmetric gamma distributions. Its statistical properties and applications are explored. We first examine its mathematical properties, including the possible shapes of the corresponding probability density function, as well as the moments, and the moment-generating function. We then look at parameter estimation using various frequentist and Bayesian methods, such as moment estimation, maximum likelihood method, least-squares method, and Bayesian approaches. In addition, the prediction of future observations under the MSG model is extensively covered, considering both frequentist and Bayesian perspectives, including median prediction, best unbiased prediction, and Bayesian prediction. A comprehensive simulation study is conducted to evaluate the performance of the proposed estimation and prediction techniques. Finally, the practical applicability of the MSG model is demonstrated through the analysis of four real-world datasets. It is shown to outperform several well-known competing models in terms of goodness-of-fit. The results highlight the inherent simplicity, efficiency, robustness, and intuitive interpretability of the MSG distribution, making it a compelling choice for modeling data with a symmetric pattern, with potential applications in diverse domains.

In this study, we propose a new zero-inflated regression model as an alternative to zero-inflated regression models, such as the zero-inflated Poisson, zero-inflated negative binomial, zero-inflated hurdle-Poisson, and zero-inflated hurdle negative binomial models. In this regard, we take benefit of the flexibility of the Poisson–Bilal distribution and some of its notable properties. More concretely, it is employed as the baseline distribution to generate a new regression model called the zero-inflated Poisson-Bilal regression model. It is designed to be a good alternative for modeling overdispersed data quite effectively. This aspect is emphasized using two real-world data sets from the medicine and education fields. Furthermore, these data sets are analyzed to compare the goodness-of-fit of the suggested zero-inflated regression model with some of its direct competitors.

The circular Fermatean fuzzy (CFF) set is an advancement of the Fermatean fuzzy (FF) set and the interval-valued Fermatean fuzzy (IVFF) set which deals with uncertainty. The CFF set is represented as a circle of radius ranging from 0 to 2 with the center at the degree of association (DA) and degree of nonassociation (DNA). If multiple people are involved in making decisions, the CFF set, as an alternative to the FF and IVFF sets, can deal with ambiguity more effectively by encircling the decision values within a circle rather than taking an average. Using algorithms, a pattern can be observed computationally or visually. Machine learning algorithm utilizes pattern recognition as an instrument for identifying patterns and also similarity measure (SM) is a beneficial pattern recognition tool used to classify items, discover variations, and make future predictions for decision making. In this work, we introduce the CFF cosine and Dice similarity measures (CFFDMs and CFFSMs), and their properties are studied. Unlike traditional approaches of decision making, which emphasize a single number, the proposed CFFSMs observe the pattern over the circular region to help in dealing with uncertainty more effectively. We introduce an innovative decision-making method in the FF setting. Available bank loans and applicants’ eligibility levels are represented as CFF set using their FF criteria and are taken as loan patterns and customer eligibility patterns. The loan is allocated to the applicant by measuring the CFFCSM and CFFDSM between the two patterns. Also, laptops are suggested to the customers by measuring the similarity between specification pattern and requirement pattern. The correctness and consistency of the proposed models are ensured by comparison analysis and graphical simulations of the input and similarity CFFNs.

The use of distributions to model and quantify risk is essential in risk assessment and management. In this study, the generalized unit half-logistic geometric (GUHLG) distribution is developed to model bounded insurance data on the unit interval. The corresponding probability density function plots indicate that the related distribution can handle data that exhibit left-skewed, right-skewed, symmetric, reversed-J, and bathtub shapes. The hazard rate function also suggests that the distribution can be applied to analyze data with bathtubs, N-shapes, and increasing failure rates. Subsequently, the inferential aspects of the proposed model are investigated. In particular, Monte Carlo simulation exercises are carried out to examine the performance of the estimation method by using an algorithm to generate random observations from the quantile function. The results of the simulation suggest that the considered estimation method is efficient. The univariate application of the distribution and the multivariate application of the associated regression using risk survey data reveal that the model provides a better fit than the other existing distributions and regression models. Under the multivariate application, we estimate the parameters of the regression model using both maximum likelihood and Bayesian estimations. The estimates of the parameters for the two methods are very close. Diagnostic plots of the Bayesian method using the trace, ergodic, and autocorrelation plots reveal that the chains converge to a stationary distribution.

Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a common original ratio form. All of them are defined with a single tuning parameter, and all reduce to the independence copula when this parameter is equal to zero. Wide admissible domains for this parameter are established, and the mathematical developments primarily rely on non-trivial limits, two-dimensional differentiations, suitable factorizations, and mathematical inequalities. The corresponding functions and characteristics of the proposed copulas are looked at in some important details. In particular, as common features, it is shown that they are diagonally symmetric, but not Archimedean, not radially symmetric, and without tail dependence. The theory is illustrated with numerical tables and graphics. A final part discusses the multi-dimensional variation of our original ratio form. The contributions are primarily theoretical, but they provide the framework for cutting-edge dependence models that have potential applications across a wide range of fields. Some established two-dimensional inequalities may be of interest beyond the purposes of this paper.

Copula analysis was created to explain the dependence of two or more quantitative variables. Due to the need for in-depth data analysis involving complex variable relationships, there is always a need for new copula models with original features. As a modern example, for the analysis of circular or periodic data types, trigonometric copulas are particularly attractive and recommended. This is, however, an underexploited topic. In this article, we propose a new collection of eight trigonometric and hyperbolic copulas, four based on the sine function and the others on the tangent function, all derived from the construction of the famous Farlie–Gumbel–Morgenstern copula. In addition to their original trigonometric and hyperbolic functionalities, the proposed copulas have the feature of depending on three parameters with complementary roles: one is a dependence parameter; one is a shape parameter; and the last can be viewed as an angle parameter. In our main findings, for each of the eight copulas, we determine a wide range of admissible values for these parameters. Subsequently, the capabilities, features, and functions of the new copulas are thoroughly examined. The shapes of the main functions of some copulas are illustrated graphically. Theoretically, symmetry in general, stochastic dominance, quadrant dependence, tail dependence, Archimedean nature, correlation measures, and inference on the parameters are investigated. Some copula shapes are illustrated with the help of figures. On the other hand, some two-dimensional inequalities are established and may be of separate interest.

In this research work, a new three-parameter lifetime distribution is introduced and studied. It is called the Harris extended Bilal distribution due to its construction from a mixture of the famous Bilal and Harris distributions, resulting from a branching process. The basic properties, such as the moment generating function, moments, quantile function, and Rényi entropy, are discussed. We show that the hazard rate function has ideal features for modeling increasing, upside-down bathtub, and roller-coaster data sets. In a second part, the Harris extended Bilal model is investigated from a statistical viewpoint. The maximum likelihood estimation is used to estimate the parameters, and a simulation study is carried out. The flexibility of the proposed model in a hydrological data analysis scenario is demonstrated using two practical data sets and compared with important competing models. After that, we establish an acceptance sampling plan that takes advantage of all of the features of the Harris extended Bilal model. The operating characteristic values, the minimum sample size that corresponds to the maximum possible defects, and the minimum ratios of lifetime associated with the producer’s risk are discussed.

In this article, we revisit an improved Wilker type inequality established in 2020. We fill some gaps in the existing proof and propose an alternative proof using the same mathematical ingredients. All the details are given for checking purposes.

Statistical modeling and forecasting are crucial to understanding the depth of information in data from all sources. For precision purposes, researchers are always in search of ways to improve the quality of modeling and forecasting, whatever the complexity of the situation. To this end, new (probability) distributions and suitable forecasting methods are demanded. The first part of this paper contributes to this direction. Indeed, we introduce a modified version of the flexible Weibull distribution, called the modified flexible Weibull distribution. It is constructed by mixing the flexible Weibull distribution with the exponential T-X scheme. This strategy is winning; the new distribution has a larger panel of functionalities in comparison to those of the classical Weibull distribution, among other things. To check the quality of the fitting of the modified flexible Weibull distribution, two different datasets are analyzed. After analyzing these datasets, it is observed that the modified flexible Weibull distribution has improved fitting power compared to other similar distributions. Apart from this, the conventional time series model, namely, the autoregressive integrated moving average (ARIMA) model, and the modern artificial neural network (ANN) model are considered for forecasting results. Utilizing the two datasets discussed earlier, it was discovered that the ANN model is more effective than the traditional ARIMA model.

In this article, we introduce and study the truncated inverse power Lindley distribution. The aim is to transpose the remarkable flexibility of the two-parameter inverse power Lindley distribution to the interval [0,1]. The corresponding probability density function has the potential to be unimodal, decreasing, right-skewed, and heavy-tailed. On the other hand, the hazard rate function can be increasing, N-shaped, or U-shaped. These shapes’ versatility enables accurate representation and analysis of proportional or percentage data across a wide range of applications, such as survival analysis, reliability, and uncertainty modeling. Several statistical features, such as the mode, quantiles, Bowley’s skewness, Moor’s kurtosis, MacGillivray’s skewness, moments, inverse moments, incomplete moments, and probability-weighted moments, are computed. In practice, for the estimation of the model parameters from truncated data under the progressively type-II censoring scheme, the maximum likelihood, maximum product spacing, and Bayesian approaches are used. The Tierney–Kadane approximation and Markov chain Monte Carlo techniques are employed to produce the Bayesian estimates under the squared error loss function. We present some simulation results to evaluate these approaches. Four applications based on real-world datasets—one of them is on times of infection, the second is on failure times, and the other two are on the rate of inflation in Asia and Africa—explain the significance of the new truncated model in comparison to some reputed comparable models, such as the inverse power Lindley, Kumaraswamy, truncated power Lomax, beta, truncated Weibull, unit-Weibull, Kumaraswamy Kumaraswamy, and exponentiated Kumaraswamy models.

This study makes a significant contribution to the creation of a versatile trigonometric extension of the well-known truncated Lomax distribution. Specifically, we construct a novel one-parameter distribution known as the sine truncated Lomax (STLo) distribution using characteristics from the sine generalized family of distributions. Quantiles, moments, stress–strength reliability, some information measures, residual moments, and reversed residual moments are a few of the crucial elements and characteristics we explored in our research. The flexibility of the STLo distribution in terms of the forms of the hazard rate and probability density functions illustrates how effectively it is able to match many types of data. Maximum likelihood and Bayesian estimation techniques are used to estimate the model parameter. The squared error loss function is employed in the Bayesian approach. To evaluate how various estimates behave, a Monte Carlo simulation study is carried out with the aid of a useful algorithm. Additionally, the STLo distribution has a good fit, making it a viable option when compared to certain other competing models using specific criteria to describe the given dataset.

The half-logistic (HL) distribution is a widely considered statistical model for studying lifetime phenomena arising in science, engineering, finance, and biomedical sciences. One of its weaknesses is that it has a decreasing probability density function and an increasing hazard rate function only. Due to that, researchers have been modifying the HL distribution to have more functional ability. This article provides an extensive overview of the HL distribution and its generalization (or extensions). The recent advancements regarding the HL distribution have led to numerous results in modern theory and statistical computing techniques across science and engineering. This work extended the body of literature in a summarized way to clarify some of the states of knowledge, potentials, and important roles played by the HL distribution and related models in probability theory and statistical studies in various areas and applications. In particular, at least sixty-seven flexible extensions of the HL distribution have been proposed in the past few years. We give a brief introduction to these distributions, emphasizing model parameters, properties derived, and the estimation method. Conclusively, there is no doubt that this summary could create a consensus between various related results in both theory and applications of the HL-related models to develop an interest in future studies.

In this research, we design the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, a bivariate analogue of the moment exponential distribution, using the Farlie–Gumbel–Morgenstern approach. With the analysis of real-life data, the competitiveness of the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution in comparison with the other Farlie–Gumbel–Morgenstern distributions is discussed. Based on the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, we develop the distribution theory of concomitants of order statistics and derive the best linear unbiased estimator of the parameter associated with the variable of primary interest (study variable). Evaluations are also conducted regarding the efficiency comparison of the best linear unbiased estimator relative to the respective unbiased estimator. Additionally, empirical illustrations of the best linear unbiased estimator with respect to the unbiased estimator are performed.

The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare events. These two zero-truncated distributions exhibit underdispersion (i.e., their variance is less than their mean). In this research, we offer an alternative solution for dealing with intervention problems by proposing a generalization of the IPD by a Lagrangian approach called the Lagrangian intervened Poisson distribution (LIPD), which in fact generalizes both the ZTPD and the IPD. As a notable feature, it has the ability to analyze both overdispersed and underdispersed datasets. In addition, the LIPD has a closed-form expression of all of its statistical characteristics, as well as an increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function. A consequent part is devoted to its statistical application. The maximum likelihood estimation method is considered, and the effectiveness of the estimates is demonstrated through a simulated study. To evaluate the significance of the new parameter in the LIPD, a generalized likelihood ratio test is performed. Subsequently, we present a new count regression model that is suitable for both overdispersed and underdispersed datasets using the mean-parametrized form of the LIPD. Additionally, the LIPD’s relevance and application are shown using real-world datasets.

Copulas are probabilistic functions that are being used more and more frequently to describe, examine, and model the interdependence of continuous random variables. Among the numerous proposed copulas, renewed interest has recently been shown in the so-called Celebioglu–Cuadras copula. It is mainly because of its simplicity, exploitable dependence properties, and potential for applicability. In this article, we contribute to the development of this copula by proposing three generalized versions of it, each involving three tuning parameters. The main results are theoretical: they consist of determining wide and manageable intervals of admissible values for the involved parameters. The proofs are mainly based on limit, differentiation, and factorization techniques as well as mathematical inequalities. Some of the configuration parameters are new in the literature, and original phenomena are revealed. Subsequently, the basic properties of the proposed copulas are studied, such as symmetry, quadrant dependence, various expansions, concordance ordering, tail dependences, medial correlation, and Spearman correlation. Detailed examples, numerical tables, and graphics are used to support the theory.

In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely Rényi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cramér von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained.

The importance of Lagrangian distributions and their applicability in real-world events have been highlighted in several studies. In light of this, we create a new zero-truncated Lagrangian distribution. It is presented as a generalization of the zero-truncated binomial distribution (ZTBD) and hence named the Lagrangian zero-truncated binomial distribution (LZTBD). The moments, probability generating function, factorial moments, as well as skewness and kurtosis measures of the LZTBD are discussed. We also show that the new model’s finite mixture is identifiable. The unknown parameters of the LZTBD are estimated using the maximum likelihood method. A broad simulation study is executed as an evaluation of the well-established performance of the maximum likelihood estimates. The likelihood ratio test is used to assess the effectiveness of the third parameter in the new model. Six COVID-19 datasets are used to demonstrate the LZTBD’s applicability, and we conclude that the LZTBD is very competitive on the fitting objective.

The generalized unit half-logistic geometric distribution (GUHLGD) is a modern two-parameter unit distribution with attractive shape flexibility for the corresponding probability density and hazard rate functions. Due to its versatility, it may be used to model a variety of current bounded real-world datasets. On the other hand, an effective sampling strategy for both parametric and non-parametric inferences is the ranked set sampling (RSS) method. This article focuses on estimating the parameters of the GUHLGD based on the RSS method as well as the simple random sampling (SRS) method. Eleven traditional estimation methods are taken into consideration, including the percentile, Cramér–von Mises, maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, least squares, weighted least squares, minimum spacing absolute-log distance, maximum product of spacing, and minimum spacing absolute distance methods. A Monte Carlo simulation is employed to compare the performance of the resultant estimates based on some accuracy measures. We draw the conclusion that, for both sampling procedures, the maximum likelihood estimation methodology is the best option among the rest based on the partial and total ranking measures. The estimates based on the RSS method are more efficient than the others based on the SRS method. Results from actual data further support the advantage of the RSS design over the SRS design.

Abstract Background Accessibility to the immense collection of studies on noncommunicable diseases related to coronavirus disease of 2019 (COVID‐19) and severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) is an immediate focus of researchers. However, there is a scarcity of information about chronic obstructed pulmonary disease (COPD), which is associated with a high rate of infection in COVID‐19 patients. Moreover, by combining the effects of the SARS‐CoV‐2 on COPD patients, we may be able to overcome formidable obstacles factors, and diagnosis influencers. Materials and Methods A retrospective study of 280 patients was conducted at DHQ Hospital Muzaffargarh in Punjab, Pakistan. Negative binomial regression describes the risk of fixed successive variables. The association is described by the Cox proportional hazard model and the model coefficient is determined through log‐likelihood observation. Patients with COPD had their survival and mortality plotted on Kaplan–Meier curves. Results The increased risk of death in COPD patients was due to the effects of variables such as cough, lower respiratory tract infection (LRTI), tuberculosis (TB), and body‐aches being 1.369, 0.693, 0.170, and 0.217 times higher at (95% confidence interval [CI]: 0.747–1.992), (95% CI: 0.231–1.156), (95% CI: 0.008–0.332), and (95% CI: −0.07 to 0.440) while it decreased 0.396 in normal condition. Conclusion We found that the symptoms of COPD (cough, LRTI, TB, and bodyaches) are statistically significant in patients who were most infected by SARS‐CoV‐2.