This study addresses the challenge of estimating parameters for two logistic populations that share a common scale parameter but have different location parameters in the presence of fuzzy data. To handle these complexities, both Maximum Likelihood Estimation (MLE) and Bayesian methods are employed. Asymptotic confidence intervals are constructed using ML estimates. For Bayesian estimation, a conjugate prior is utilized, and Bayes estimators are approximated using Lindley’s method due to the lack of closed-form solutions. Furthermore, Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC) techniques, including Hamiltonian Monte Carlo (HMC) and the Metropolis–Hastings (MH) algorithm, are utilized to sample from the posterior distributions and construct Highest Posterior Density (HPD) intervals. A detailed comparative analysis of MLE, Lindley’s approximation, ABC, HMC, and MH is conducted to assess their performance. The effectiveness of the proposed methodology is demonstrated using a real-world dataset under fuzzy conditions.

In the biology field of botany, leaf shape recognition is an important task. One way of characterising the leaf shape is through the centroid contour distances (CCD). Each CCD path might have different resolution, so normalisation is done by associating each contour to a circular density. Densities are rotated by subtracting the mean or mode preferred direction. Distance measures between densities are used to produce a hierarchical clustering method to cluster the leaves. We illustrate our approach with a motivating small dataset as well as a larger dataset.

AI applications in finance including those for the probability of default modeling largely involve using ML classification tools. Oversampling the very minor (very underrepresented) class of defaulted borrowers seems to be a must-be-done step always. However, by crunching more than a thousand of confidence intervals for the classification accuracy metrics, we demonstrate when such oversampling is worth engaging in. Moreover, we argue to what portion of total initial sample size such oversampling should be carried out. Our findings are valuable primarily for the credit risk modeling and Internal Ratings Based (IRB) banks, but are not limited to those and have general applications for the binary classifications in ML domain.

Analytic Hierarchy Process (AHP) is a unique tool which can help in improvising the usage of machine learning in attaining organizational effectiveness. True, machine learning has emerged as one of the most important tools in enhancing organizational effectiveness through improved strategic decision-making vis-à-vis key performance indicators. It has redefined the way companies can create, and measure value added, and experiences generated for the end users of their products, services, and other offerings. Machine learning algorithms are being leveraged for making more predictive and prescriptive key performance indicators which ultimately contribute towards optimizations of business processes and overall improvement in the competitiveness of the organizations. It also helps the organizations in attaining excellence in execution of strategic decisions through almost accurate predictive insights on various management functions related to HR, marketing, finance, and operations which in turn boost stakeholder satisfaction. In this study, the authors have developed an analytic hierarchy process framework based on review of 166 peer-reviewed research papers to determine how the organizations can priorities management functions and their attributes coupled with machine learning applications for higher levels of efficiencies. Insights from this article may help the practicing managers in prioritizing use of machine learning in management functions for optimizing results and improving overall organizational effectiveness.

Understanding relationships between stress, resilience, mental wellbeing, and task-performance is critical for success in today’s sustainable workplaces. Thus, we aimed to analyse and develop a management framework to deal with this criticality. Inspired by Salutogenesis theory – prioritizing positive variables over the absence of negative ones, our emphasis was on resilience and mental wellbeing for stress management and improving task performance. Data from 445 employees was collected by a survey instrument employing standardised scales. Reliability and validity of constructs were established through the measurement model, while the structural model tested the strength of the relationships. Low stress and high resilience were identified as having a strong effect on mental wellbeing, which in-turn improved task-performance. This study highlights that resilience and mental wellbeing, in addition to stress management, significantly improves task performance for sustainable workplaces.

Volatility is a matter of concern for time series modeling. It provides valuable insights into the fluctuation and stability of concerning variables over time. Volatility patterns in historical data can provide valuable information for predicting future behaviour. Nonlinear time series models such as the autoregressive conditional heteroscedastic (ARCH) and the generalized version of the ARCH model, i.e. generalized ARCH (GARCH) models are popularly used for capturing the volatility of a time series. The realization of any time series may have significant statistical dependencies on its distant counterpart. This phenomenon is known as the long memory process. Long memory structure can also be present in volatility. Fractionally integrated volatility models such as the fractionally integrated GARCH (FIGARCH) model can be used to capture the long memory in volatility. In this paper, we derived the out-of-sample forecast formulae along with the forecast error variances for the AR (1) -FIGARCH (1, d, 1) model by recursive use of conditional expectations and conditional variances. For empirical illustration, the modal spot prices of onion for Delhi, Lasalgaon and Bengaluru markets, India and S&P 500 index (close) data are used.

In this manuscript, we discuss the substantial importance of Bayesian reasoning in Social Science research. Particularly, we focus on foundational elements to fit models under the Bayesian paradigm. We aim to offer a frame of reference for a broad audience, not necessarily with specialized knowledge in Bayesian statistics, yet having interest in incorporating this kind of methods in studying social phenomena. We illustrate Bayesian methods through case studies regarding political surveys, population dynamics, and standardized educational testing. Specifically, we provide technical details on specific topics such as conjugate and non-conjugate modeling, hierarchical modeling, Bayesian computation, goodness of fit, and model testing.

We obtain new mathematical properties of the exponentiated odd log-logistic family of distributions, and of its special case named the exponentiated odd log-logistic Weibull, and its log transformed. A new location and scale regression model is constructed, and some simulations are carried out to verify the behavior of the maximum likelihood estimators, and of the modified deviance-based residuals. The methodology is applied to the Japanese-Brazilian emigration data.

This paper proposes a new logistic smooth transition autoregressive (LSTAR) cointegration test by combining the Fourier function to catch the structural changes that occur over time and the LSTAR model to consider the nonlinearity. Logistic and exponential functions are the main transition functions defining the nonlinearity in STAR models since the exponential smooth transition autoregressive (ESTAR) and LSTAR models can explain the different structures of economic variables. The Fourier approach is a simple and effective way to model the structural changes in time series as an alternative to dummy variables. The most significant advantage of the method is that it does not require prior knowledge about the date, number of breaks, or forms. Monte Carlo simulation results show that the proposed test has good size and power properties for different sample sizes and parameters. The results also revealed that the power performance of the proposed test and the Fourier ESTAR test offered by Güriş and Sedefoğlu (2022) are close to each other. The steps of the Fourier-based tests are illustrated by providing an empirical example of testing the validity of the purchasing power parity (PPP) hypothesis in Türkiye.

At its core, copula theory focuses on constructing a copula function, which characterizes the structure of dependence between random variables. In particular, the creation of extreme value copulas is crucial because they allow accurate modeling of extreme dependence that traditional copulas can ignore. In this article, we propose theoretical developments on this subject by proposing two new extreme value copulas. They aim to extend the functionalities of the so-called Tawn copula. This is of interest because the Tawn copula is known to be a powerful tool in modeling joint distributions, particularly in capturing asymmetric and upper tail dependences, making it valuable for analyzing extreme events and tail risk. The proposed copulas are designed to go beyond these attractive features. On the mathematical side, they are derived from new Pickands dependence functions; one modifies the Pickands dependence function of the Tawn copula by using a polynomial-exponential function, and the other does the same but by introducing a power function. The proofs are based on diverse differentiation, arrangement, and inequality techniques. Overall, the created copulas are attractive because (i) they possess modulable levels of asymmetry, (ii) they depend on several tuning parameters, making them very flexible in terms of upper tail dependence in particular, and (iii) they benefit from interesting correlation ranges of values. Several figures and value tables support the theoretical findings.