Search

Abstract The primary purpose of this article is to examine the issue of estimating the finite population distribution function from auxiliary information, such as population mean and rank of the auxiliary variables, that are already known. In order to better estimate the distribution function (DF) of a finite population, two improved estimators are developed. The bias and mean squared error of the suggested and existing estimators are derived up to the first order of approximation. To improve the efficiency of an estimators, we compare the suggested estimators with existing counterpart. Based on the numerical outcomes, it is to be noted that the suggested classes of estimators perform well using six actual data sets. The strength and generalization of the suggested estimators are also verified using a simulation analysis. Based on the result of actual data sets and a simulation study, we observe that the suggested estimator outperforms as compared to all existing estimators which is compared in this study.

Absolute rate constants for hydrogen abstractions from carbon by the t-butoxyl radical are reported for several hydrocarbons and tertiary amines in solution. The analysis of the available data reveals that most hydrogen abstractions from carbon are entropy controlled.

In this article, a one-parameter probability mass function called Poisson XRani is proposed by combining the Poisson and the XRani distributions. A wide range of distributional properties such as the shape of the probability mass function, probability generating function, factorial moments, moment generating function, characteristic function, raw moments, dispersion index, mean, variance, coefficient of skewness, and coefficient of kurtosis are investigated. It is proven that the proposed probability mass function can easily handle overdispersed and right-skewed count observations with heavy tails. Both maximum likelihood and Bayesian estimation techniques are used to estimate the unknown parameter of the proposed distribution and a simulation study was conducted to examine and analyze the performance of the maximum likelihood estimation procedure based on sample size, absolute bias, relative absolute bias, and root mean square error. The usefulness of the proposed distribution is assessed using two distinctive real datasets. These applications reveal that the new distribution provides an adequate fit compared to the other eight discrete distributions.

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.

In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis.

In this study, Secant Kumaraswamy family of distributions is proposed and studied. This is motivated by the fact that no one distribution can model all types of data from different fields. Therefore, there is the need to develop distributions with desirable properties and flexible enough for modelling data exhibiting different characteristics. Some properties of the new family of distributions, including the quantile function, moments, moment generating function, and mean residual life function, are derived. Five special cases of the family of distributions are presented, and their flexibility is shown by the varying degrees of skewness and kurtosis and nonmonotonic hazard rates. The maximum likelihood estimation method is used to obtain estimators of the family of distributions. Two location-scale regression models are developed for the Secant Kumaraswamy Weibull distribution, which is a special case of the family of distributions. Six different real datasets are used to demonstrate the usefulness of the family of distributions and the regression models. The results show that the family of distributions can be used to model real datasets.

A substance achieves supercritical state when taken above its critical temperature and pressure. A supercritical fluid (SCF) has intermediate bulk properties between those of a gas and a liquid. Well known reactions in conventional solvents were used to seek divergent behaviour in an SCF solvent, based on the examination of the free radical chlorination of several alkanes in supercritical carbon dioxide (SC-CO(sub2)). There was no evidence of enhanced cage effect in SC-CO(sub2), and its magnitude was as anticipated.

Solvent effect highly influences the chemoselectivity of the free radical chlorination of cyclopropane. Internal pressure of the solvent is related to the ratio between ring-opened and hydrogen-abstraction products. Gas and condensed-phase chlorination of cyclopropane differ due to the solvent pressure effect of the phase. Results obtained from extrapolation techniques are in good agreement with the experimental data.

Analysis of the effect of phenyl and vinyl radicals on the ring opening of various cyclopropylcarbinyl radicals and structurally similar cyclopropylketyl anions reveals that placement of a phenyl group on the cyclopropane ring compensates for the resonance stabilization loss. The radical anion-based resonance and losses are not fully compensated for by substitution and ring strain relief, implying that radical anions are useless in single-electron transfer probes.

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.

A study shows a connection between the internal pressure of solvent and selectivity in free radical brominations. An analysis of 18 solvents and solvent mixtures shows that the rate constant ratio for SH2 ring opening of cyclopropylbenzene (kc) versus hydrogen abstraction from toluene (kH) by bromine atom differed by almost a factor of two as a function of solvent. The observed rate constant ratio for the examined solvents is almost the same as the internal pressure. The volume of stimulation related to kc is more negative than for kH by ca. 20 cubic centimeters per mol, and this probably causes the difference in selectivity with solvent pressure.

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.

We introduce the tangent Topp-Leone family of distributions in this study and derive some of its statistical properties. Further, we develop five special distributions and a location-scale regression model based on the new proposed tangent Topp-Leone Weibull distribution. Three real datasets are used to demonstrate the usefulness and flexibility of the developed models in comparison with other existing competing models. The study reveals that the proposed tangent Topp-Leone-Weibull perform better than competing models for the given datasets. The proposed log tangent Topp-Leone-Weibull regression model also performs better than competing models for a given dataset.

The choice of an appropriate regression model for econometric modeling minimizes information loss and also leads to sound inferences. In this study, we develop four quantile regression models based on trigonometric extensions of the unit generalized half-normal distributions for the modeling of a bounded response variable defined on the unit interval. The desirable shapes of these distributions, such as left-skewed, right-skewed, reversed-J, approximately symmetric, and bathtub shapes, make them competitive models for bounded responses with such traits. The maximum likelihood method is used to estimate the parameters of the regression models, and Monte Carlo simulation results confirm the efficiency of the method. We demonstrate the utility of our models by investigating the relationship between OECD countries’ educational attainment levels, labor market insecurity, and homicide rates. The diagnostics reveal that all our models provide a good fit to the data because the residuals are well behaved. A comparative analysis of the trigonometric quantile regression models with the unit generalized half-normal quantile regression model shows that the trigonometric models are the best. However, the sine unit generalized half-normal (SUGHN) quantile regression model is the best overall. It is observed that labor market insecurity and the homicide rate have significant negative effects on the educational attainment values of the OECD countries.

The usefulness of (probability) distributions in the field of biomedical science cannot be underestimated. Hence, several distributions have been used in this field to perform statistical analyses and make inferences. In this study, we develop the arctan power (AP) distribution and illustrate its application using biomedical data. The distribution is flexible in the sense that its probability density function exhibits characteristics such as left-skewedness, right-skewedness, and J and reversed-J shapes. The characteristic of the corresponding hazard rate function also suggests that the distribution is capable of modeling data with monotonic and non-monotonic failure rates. A bivariate extension of the AP distribution is also created to model the interdependence of two random variables or pairs of data. The application reveals that the AP distribution provides a better fit to the biomedical data than other existing distributions. The parameters of the distribution can also be fairly accurately estimated using a Bayesian approach, which is also elaborated. To end the study, the quantile and modal regression models based on the AP distribution provided better fits to the biomedical data than other existing regression models.

This research aimed to determine the effect of the problem-based learning model on students’ learning outcomes on the colloid topic. This research applied an experimental method with a quasi-experimental design using a pretest-posttest control group design. The sample in this study was conducted in one of the SMA in The Bone Bolango district. To determine the effect of the problem-based learning model on students’ learning outcomes in the colloid topic, the researcher used a test in the form of an essay with five questions that have been tested for validity and reliability. In the meantime, the hypothesis testing in this study was carried out by employing a t-test. The results of hypothesis testing obtained that the tcount value of 7,7 was higher than 1,67649. Where H0 was rejected and Ha was accepted. Thus, it could be concluded that the problem-based learning model affected students’ learning outcomes in the colloid topic.

The cubic set (CS) is a basic simplification of several fuzzy notions, including fuzzy set (FS), interval-valued FS (IVFS), and intuitionistic FS (IFS). By the degrees of IVFS and FS, CS exposes fuzzy judgement, and this is a much more potent mathematical approach for dealing with information that is unclear, ambiguous, or indistinguishable. The article provides many innovative operational laws for cubic numbers (CNs) drawn on the Schweizer–Sklar (SS) t-norm (SSTN), and the SS t-conorm (SSTCN), as well as several desired properties of these operational laws. We also plan to emphasise on the cubic Schweizer–Sklar power Heronian mean (CSSPHM) operator, as well as the cubic Schweizer–Sklar power geometric Heronian mean (CSSPGHM) operator, in order to maintain the supremacy of the power aggregation (PA) operators that seize the complications of the unsuitable information and Heronian mean (HM) operators that contemplate the interrelationship between the input data being aggregated. A novel multiple attribute decision-making (MADM) model is anticipated for these freshly launched aggregation operators (AOs). Finally, a numerical example of enterprise resource planning is used to validate the approach’s relevance and usefulness. There is also a comparison with existing decision-making models.

In this study, we propose a four-parameter probability distribution called the harmonic mixture Fréchet. Some useful expansions and statistical properties such as moments, incomplete moments, quantile functions, entropy, mean deviation, median deviation, mean residual life, moment-generating function, and stress-strength reliability are presented. Estimators for the parameters of the harmonic mixture Fréchet distribution are derived using the estimation techniques such as the maximum-likelihood estimation, the ordinary least-squares estimation, the weighted least-squares estimation, the Cramér–von Mises estimation, and the Anderson–Darling estimation. A simulation study was conducted to assess the biases and mean square errors of the estimators. The new distribution was applied to three-lifetime datasets and compared with the classical Fréchet distribution and eight (8) other extensions of the Fréchet distribution.

In this study, two new distributions are developed by compounding Sine-Weibull and zero-truncated geometric distributions. The quantile and ordinary moments of the distributions are obtained. Plots of the hazard rate functions of the distributions show that the distributions exhibit nonmonotonic failure rates. Also, plots of the densities of the distributions show that they exhibit decreasing, skewed, and approximately symmetric shapes, among others. Mixture and nonmixture cure rate models based on these distributions are also developed. The estimators of the parameters of the cure rate models are shown to be consistent via simulation studies. Covariates are introduced into the cure rate models via the logit link function. Finally, the performance of the distributions and the cure rate and regression models is demonstrated using real datasets. The results show that the developed distributions can serve as alternatives to existing models for survival data analyses.

Research describing applications of the method of tert-Butoxyl for exploring radicals found in biological systems is presented. Particular attention is given to measurements of hydrogen abstraction constants at absolute rates and to intrinsic reactivities.

The study presents the mechanical properties of polymer-based composites reinforced with chemically modified banana fibers, by alkalization in different concentrations of sodium hydroxide (NaOH). The fiber weight fraction has a great effect on the mechanical properties of the composites. Stiff composites were obtained at 6 wt% fiber fractions with Young’s modulus of 254.00 ±12.70 MPa. Moreover, the yield strength was 35.70 ±1.79 MPa at 6 wt% fiber fractions. However, the ultimate tensile strength (UTS) and toughness of the composites were obtained at 5 wt% fiber fractions. Statistical analyses were used to ascertain the significant different on the mechanical properties of the fibers and composites. The implication of the results is then discussed for potential applications of PDMS-based composites reinforced with chemically modified banana fibers.

Probability distributions are very useful in modeling lifetime datasets. However, no specific distribution is suitable for all kinds of datasets. In this study, the bounded truncated Cauchy power exponential distribution is proposed for modeling datasets on the unit interval. The probability density function exhibits desirable shapes, such as left-skewed, right-skewed, reversed J, and bathtub shapes, whereas the hazard rate function displays J and bathtub shapes. For the purpose of modeling dependence between measures in a dataset, a bivariate extension of the proposed distribution is developed. The bivariate probability density function displays monotonic and non-monotonic shapes, making it suitable for modeling complex bivariate relations. Subsequently, the applications of the distribution are illustrated using COVID-19 data. The results revealed that the new distribution provides a better fit to the datasets compared to other existing distributions. Finally, a new quantile regression model is developed and its application demonstrated. The generated quantile regression model offers a decent fit to the data, according to the residual analysis.

The possibility of using the chlorine atom cage effect as a highly sensitive probe for cage effects in supercritical fluid solvent was investigated. The chlorine atom cage effect was, therefore, studied in supercritical carbon dioxide. Related experiments were also conducted in conventional solvents. The photoinitiated free radical chlorination of cyclohexane was studied in various conventional solvents and in supercritical carbon dioxide. Findings failed to show the existence of an enhanced cage effect near the critical point in the supercritical carbon dioxide solvent.

In this study, the exponentiated generalized exponential Dagum distribution has been proposed and studied. This family of distribution consists of a number of sub-models such as the exponentiated generalized Dagum distribution, Dagum distribution, Fisk distribution, Burr III distribution and exponentiated generalized exponential Burr III distribution among others. Statistical properties of the new family were also derived. Maximum likelihood estimators of the parameters of the distribution were developed and simulation studies performed to assess the properties of the estimators. Applications of the model was demonstrated to show its usefulness. Keywords: Dagum, Quantile, Moment, Entropy, Reliability measure, Order statistics

In this paper, we introduce a new three-parameter distribution defined on the unit interval. The density function of the distribution exhibits different kinds of shapes such as decreasing, increasing, left skewed, right skewed, and approximately symmetric. The failure rate function shows increasing, bathtub, and modified upside-down bathtub shapes. Six different frequentist estimation procedures were proposed for estimating the parameters of the distribution and their performance assessed via Monte Carlo simulations. Applications of the distribution were illustrated by analyzing two datasets and its fit compared to that of other distributions defined on the unit interval. Finally, we developed a regression model for a response variable that follows the new distribution.

Deals with a study which focused on the use of chlorine atom cage effect as a highly sensitive probe for studying the effect of viscosity in supercritical fluid solvents. Methodology; Results and discussion and discussion of the study; Conclusions.

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.