Search Results (81)

We present Bayesian Binary Search (BBS), a novel framework that bridges statistical learning theory/probabilistic machine learning and binary search. BBS utilizes probabilistic methods to learn the underlying probability density of the search space. This learned distribution then informs a modified bisection strategy, where the split point is determined by probability density rather than the conventional midpoint. This learning process for search space density estimation can be achieved through various supervised probabilistic machine learning techniques (e.g., Gaussian Process Regression, Bayesian Neural Networks, and Quantile Regression) or unsupervised statistical learning algorithms (e.g., Gaussian Mixture Models, Kernel Density Estimation (KDE), and Maximum Likelihood Estimation (MLE)). Our results demonstrate substantial efficiency improvements using BBS on both synthetic data with diverse distributions and in a real-world scenario involving Bitcoin Lightning Network channel balance probing (3–6% efficiency gain), where BBS is currently in production. Full article

This paper introduces a novel and flexible class of continuous probability distributions, termed the Alpha Power Survival Ratio-X (APSR-X) family. Unlike many existing transformation-based families, the APSR-X class integrates an alpha power transformation with a survival ratio structure, offering a new mechanism for enhancing shape flexibility while maintaining mathematical tractability. This construction enables fine control over both the tail behavior and the symmetry properties, distinguishing it from traditional alpha power or survival-based extensions. We focus on a key member of this family, the two-parameter Alpha Power Survival Ratio Exponential (APSR-Exp) distribution, deriving essential mathematical properties including moments, quantile functions and hazard rate structures. We estimate the model parameters using eight frequentist methods: the maximum likelihood (MLE), maximum product of spacings (MPSE), least squares (LSE), weighted least squares (WLSE), Anderson–Darling (ADE), right-tailed Anderson–Darling (RADE), Cramér–von Mises (CVME) and percentile (PCE) estimation. Through comprehensive Monte Carlo simulations, we evaluate the estimator performance using bias, mean squared error and mean relative error metrics. The proposed APSR-X framework uniquely enables preservation or controlled modification of the symmetry in probability density and hazard rate functions via its shape parameter. This capability is particularly valuable in reliability and survival analyses, where symmetric patterns represent balanced risk profiles while asymmetric shapes capture skewed failure behaviors. We demonstrate the practical utility of the APSR-Exp model through three real-world applications: economic (tax revenue durations), engineering (mechanical repair times) and medical (infection durations) datasets. In all cases, the proposed model achieves a superior fit over that of the conventional alternatives, supported by goodness-of-fit statistics and visual diagnostics. These findings establish the APSR-X family as a unique, symmetry-aware modeling framework for complex lifetime data. Full article

This study introduces a new and flexible class of probability distributions known as the novel alpha-power X (NAP-X) family. A key development within this framework is the novel alpha-power half-logistic (NAP-HL) distribution, which extends the classical half-logistic model through an alpha-power transformation, allowing for greater adaptability to various data shapes. The paper explores several theoretical aspects of the proposed model, including its moments, quantile function and hazard rate. To assess the effectiveness of parameter estimation, a detailed simulation study is conducted using seven estimation techniques: Maximum likelihood estimation (MLE), Cramér–von Mises estimation (CVME), maximum product of spacings estimation (MPSE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson–Darling estimation (ADE) and a right-tailed version of Anderson–Darling estimation (RTADE). The results offer comparative insights into the performance of each method across different sample sizes. The practical value of the NAP-HL distribution is demonstrated using two real datasets from the metrology and engineering domains. In both cases, the proposed model provides a better fit than the traditional half-logistic and related distributions, as shown by lower values of standard model selection criteria. Graphical tools such as fitted density curves, Q–Q and P–P plots, survival functions and box plots further support the suitability of the model for real-world data analysis. Full article

Probability models are instrumental in a wide range of applications by being able to accurately model real-world data. Over time, numerous probability models have been developed and applied in practical scenarios. This study introduces the AAP-X family of distributions—a novel, flexible framework for continuous data analysis named after authors Aadil Ajaz and Parvaiz. The proposed family effectively accommodates both symmetric and asymmetric characteristics through its shape-controlling parameter, an essential feature for capturing diverse data patterns. A specific subclass of this family, termed the “AAP Exponential” (AAPEx) model is designed to address the inflexibility of classical exponential distributions by accommodating versatile hazard rate patterns, including increasing, decreasing and bathtub-shaped patterns. Several fundamental mathematical characteristics of the introduced family are derived. The model parameters are estimated using six frequentist estimation approaches, including maximum likelihood, Cramer–von Mises, maximum product of spacing, ordinary least squares, weighted least squares and Anderson–Darling estimation. Monte Carlo simulations demonstrate the finite-sample performance of these estimators, revealing that maximum likelihood estimation and maximum product of spacing estimation exhibit superior accuracy, with bias and mean squared error decreasing systematically as the sample sizes increases. The practical utility and symmetric–asymmetric adaptability of the AAPEx model are validated through five real-world applications, with special emphasis on cancer survival times, COVID-19 mortality rates and reliability data. The findings indicate that the AAPEx model outperforms established competitors based on goodness-of-fit metrics such as the Akaike Information Criteria (AIC), Schwartz Information Criteria (SIC), Akaike Information Criteria Corrected (AICC), Hannan–Quinn Information Criteria (HQIC), Anderson–Darling (A*) test statistic, Cramer–von Mises (W*) test statistic and the Kolmogorov–Smirnov (KS) test statistic and its associated p-value. These results highlight the relevance of symmetry in real-life data modeling and establish the AAPEx family as a powerful tool for analyzing complex data structures in public health, engineering and epidemiology. Full article

This paper investigates various estimation methods for the parameters of the unit Lindley distribution (U-LD) under both ranked set sampling (RSS) and simple random sampling (SRS) designs. The distribution parameters are estimated using the maximum likelihood estimation, ordinary least squares, weighted least squares, maximum product of spacings, minimum spacing absolute distance, minimum spacing absolute log-distance, minimum spacing square distance, minimum spacing square log-distance, linear-exponential, Anderson–Darling (AD), right-tail AD, left-tail AD, left-tail second-order, Cramér–von Mises, and Kolmogorov–Smirnov. A comprehensive simulation study is conducted to assess the performance of these estimators, ensuring an equal number of measuring units across both designs. Additionally, two real datasets of items failure time and COVID-19 are analyzed to illustrate the practical applicability of the proposed estimation methods. The findings reveal that RSS-based estimators consistently outperform their SRS counterparts in terms of mean squared error, bias, and efficiency across all estimation techniques considered. These results highlight the advantages of using RSS in parameter estimation for the U-LD distribution, making it a preferable choice for improved statistical inference. Full article

This study presents a model for estimating forest productivity based on a sample of 2048 permanent field plots covering a wide range of growing sites in Mexico. Our state-space approach assumes that the growth behavior of any stand over time can be estimated on the basis of its current state, defined by the dominant height (H), number of trees per hectare (N), and stand basal area (BA). We used transition functions to estimate the change in states as a function of the current state. We also present transition functions for the change in stand volume (V) and total above-ground biomass (AGB). The first transition function relates dominant height to dominant diameter by using the guide-curve method to estimate site form. The transition function for N consists of two models, one for estimating natural mortality and the other for estimating recruitment. These models were developed in two steps: in the first step, the logistic regression and maximum likelihood approach were used to estimate the probability of the occurrence of mortality or recruitment, and in the second step, the rate of change associated with each event was modeled when mortality or recruitment was assumed to have occurred as a result of the first step. The remaining three transition functions (BA, V, and AGB) were fitted simultaneously to account for possible correlations between errors. The model estimating total above-ground biomass (AGB), which can be considered a state variable that summarizes the performance of the whole model, explained more than 97% of the observed variability, with a root mean square error value of 10.57 Mg/ha. Full article

This review article is concerned to provide a global context to several works on the fitting of continuous time nonhomogeneous Markov chains with finite state space and also to point out some selected aspects of two techniques previously introduced—estimation and calibration—relevant for applications and used to fit a continuous time Markov chain model to data by the adequate selection of parameters. The denomination estimation suits the procedure better when statistical techniques—e.g., maximum likelihood estimators—are employed, while calibration covers the case where, for instance, some optimisation technique finds a best approximation parameter to ensure good model fitting. For completeness, we provide a short summary of well-known important notions and results formulated for nonhomogeneous Markov chains that, in general, can be transferred to the homogeneous case. Then, as an illustration for the homogeneous case, we present a selected Billingsley’s result on parameter estimation for irreducible chains with finite state space. In the nonhomogeneous case, we quote two recent results, one of the calibration type and the other with more of a statistical flavour. We provide an ample set of bibliographic references so that the reader wanting to pursue her/his studies will be able to do so more easily and productively. Full article

This study introduces a novel trigonometric-based family of distributions for modeling continuous data through a newly proposed framework known as the ASP family, where ‘ASP’ represents the initials of the authors Aadil, Shamshad, and Parvaiz. A specific subclass of this family, termed the “ASP Rayleigh distribution” (ASPRD), is introduced that features two parameters. We conducted a comprehensive statistical analysis of the ASPRD, exploring its key properties and demonstrating its superior adaptability. The model parameters are estimated using four classical estimation methods: maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), and maximum product of spaces estimation (MPSE). Extensive simulation studies confirm these estimation techniques’ robustness, showing that biases, mean squared errors, and root mean squared errors consistently decrease as sample sizes increase. To further validate its applicability, we employ ASPRD on three real-world engineering datasets, showcasing its effectiveness in modeling complex data structures. This work not only strengthens the theoretical framework of probability distributions but also provides valuable tools for practical applications, paving the way for future advancements in statistical modeling. Full article

This article introduces a new continuous lifetime distribution within the Gamma family, called the induced Xgamma distribution, and explores its various statistical properties. The proposed distribution’s estimation and prediction are investigated using Bayesian and non-Bayesian approaches under progressively Type-II censored data. The maximum likelihood and maximum product spacing methods are applied for the non-Bayesian approach, and some of their performances are evaluated. In the Bayesian framework, the numerical approximation technique utilizing the Metropolis–Hastings algorithm within the Markov chain Monte Carlo is employed under different loss functions, including the squared error loss, general entropy, and LINEX loss. Interval estimation methods, such as asymptotic confidence intervals, log-normal asymptotic confidence intervals, and highest posterior density intervals, are also developed. A comprehensive numerical study using Monte Carlo simulations is conducted to evaluate the performance of the proposed point and interval estimation methods through progressive Type-II censored data. Furthermore, the applicability and effectiveness of the proposed distribution are demonstrated through three real-world datasets from the fields of medicine and engineering. Full article

Crystallography, a cornerstone of materials science, provides critical insights into material structures through techniques such as X-ray diffraction (XRD). Among the metrics derived from XRD, intensity serves as a key parameter, reflecting the electron density distribution and offering information about atomic arrangements and sample quality. Due to its inherent variability and susceptibility to extreme values, intensity is best modeled using heavy-tailed, location-scale probability distributions. This paper investigates the model parameter estimation problem for three such distributions—log-Cauchy, half-Cauchy, and Cauchy Birnbaum–Saunders—using several methods, including maximum likelihood and the maximum product of spacings estimation methods. Monte Carlo simulations are conducted to assess the performance of these methods across various scenarios. Additionally, two real XRD intensity datasets are analyzed to compare the applicability and effectiveness of the proposed models. The results demonstrate the potential of heavy-tailed distributions for modeling XRD intensity data, providing a robust framework for future research and practical applications in material characterization. Full article

Unlike the precise methods implemented in constrained programming environments, the proposed approach to preventive planning of Product-as-a-Service offers implements a competitive solution based on Genetic Population Stepping Crawl Threads (GPSCT).GPSCT techniques are used to determine the so-called stepping crawl threads (SCT) that recreate, in subsequent steps, variants of the allocation of sets of leased devices with parameters that meet the expectations of the customers ordering them by means of genetic algorithms. SCTs initiated at a selected point of the Cartesian product space of the functional repertoire of the equipment offered penetrate it in search of offer variants that meet the constraints imposed by the size of the budget and the risk level (i.e., expressed as the likelihood of damaging the device or losing part of its functionality) of individual customers. Two approaches of implementation techniques were used to determine the initial SCT population for the genetic algorithm—branch and bound (BBA) and linear programming (LPA). Many experiments assessed their impact on the computation time and the quality of the obtained solution. The performed computational experiments indicate that the effectiveness of both approaches depends on the specificity of the problem considered each time. Interestingly, for different instances of the problem, an alternative solution can always be selected that is competitive with the exact methods, allowing for a 10-fold increase in scalability. Full article

Paddy fields are essential for food security and sustaining global dietary needs, yet urban expansion often encroaches on agricultural lands. Analyzing paddy fields and land use/land cover changes over time using satellite images provides critical insights for sustainable food production and balanced urban growth. However, mapping the paddy fields in tropical monsoon areas presents challenges due to persistent weather interference, monsoon-submerged fields, and a lack of training data. To address these challenges, this study proposed a flooding-assisted maximum likelihood classification (F-MLC) method. This approach utilizes accurate training datasets from intersecting flooded paddy field maps from the rainy and dry seasons, combined with the Automated Water Extraction Index (AWEI) to distinguish natural water bodies. The F-MLC method offers a robust solution for accurately mapping paddy fields and land use changes in challenging tropical monsoon climates. The classified images for 1989, 2000, 2013, and 2021 were produced and categorized into the following five major classes: urban areas, vegetation, paddy fields, water bodies, and other lands. The paddy field class derived for each year was validated using samples from various sources, contributing to the overall accuracies ranging from 83.6% to 90.4%, with a Kappa coefficient of between 0.80 and 0.88. The study highlights a significant decrease in paddy fields, while urban areas rapidly increased, replacing 23% of paddy fields between 1989 and 2021 in the watershed. This study demonstrates the potential of the F-MLC method for analyzing paddy fields and other land use changes over time in the tropical watershed. These findings underscore the urgent need for robust policy measures to protect paddy fields by clearly defining urban expansion boundaries, prioritizing paddy field preservation, and integrating these green spaces into urban development plans. Such measures are vital for ensuring a sustainable local food supply, promoting balanced urban growth, and maintaining ecological balance within the watershed. Full article

This article defines a new distribution using a novel alpha power-transformed method extension. The model obtained has three parameters and is quite effective in modeling skewed, complex, symmetric, and asymmetric datasets. The new approach has one additional parameter for the model. Certain distributional and mathematical properties are investigated, notably reliability, quartile, moments, skewness, kurtosis, and order statistics, and several approaches of estimation, notably the maximum likelihood, least square, weighted least square, maximum product spacing, Cramer-Von Mises, and Anderson Darling estimators of the model parameters were obtained. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed techniques of estimation of the model parameters. The actuarial measures are computed for our recommended model. At the end of the paper, two insurance applications are illustrated to check the potential and utility of the suggested distribution. Evaluation using four selection criteria indicates that our recommended model is the most appropriate probability model for modeling insurance datasets. Full article

In lifetime tests, the waiting time for items to fail may be long under usual use conditions, particularly when the products have high reliability. To reduce the cost of testing without sacrificing the quality of the data obtained, the products are exposed to higher stress levels than normal, which quickly causes early failures. Therefore, accelerated life testing is essential since it saves costs and time. This paper considers constant stress-partially accelerated life tests under progressive Type II censored samples. This is realized under the claim that the lifetime of products under usual use conditions follows Vtub-shaped lifetime distribution, which is also known as log-log distribution. The log–log distribution is highly significant and has several real-world applications since it has distinct shapes of its probability density function and hazard rate function. A graphical description of the log–log distribution is exhibited, including plots of the probability density function and hazard rate. The log–log density has different shapes, such as decreasing, unimodal, and approximately symmetric. Several mathematical properties, such as quantiles, probability weighted moments, incomplete moments, moments of residual life, and reversed residual life functions, and entropy of the log–log distribution, are discussed. In addition, the maximum likelihood and maximum product spacing methods are used to obtain the interval and point estimators of the acceleration factor, as well as the model parameters. A simulation study is employed to assess the implementation of the estimation approaches under censoring schemes and different sample sizes. Finally, to demonstrate the viability of the various approaches, two real data sets are investigated. Full article

Araucaria angustifolia is a species known for its valuable wood and nuts, but it is threatened with extinction. The plantation of forests for genetic resource conservation is a complementary strategy designed to reduce the species’ genetic variability loss. This study aimed to evaluate the technical and economic viability of A. angustifolia for genetic conservation through use. The analyzed provenance and progeny trial was established in 1982 in Itapeva, Brazil. It was structured using a compact family blocks design with 110 open-pollinated progenies from five natural populations, three replicates, ten plants per subplot, and 3.0 m × 2.0 m spacing. After 33 years, the trial was evaluated for total height, diameter at breast height, wood volume, and survival. The variance components and genetic parameter estimates were performed using Restricted Maximum Likelihood/Best Linear Unbiased Prediction methods (REML/BLUP) methods with the Selegen software (version 2014). The production and management scenarios were obtained using the SisAraucaria software (version 2003). Sensitivity analysis and economic parameter estimates were obtained through various economic evaluation methods using the Planin software (version 1995). In general, the genetic parameters indicated that the population has enough variability for both conservation and breeding purposes, suggesting technical viability for the establishment of a seed orchard. The economic parameters indicated that the commercialization of wood and araucaria nuts proved to be more profitable than wood production by itself. In conclusion, araucaria genetic conservation through use is a technically and economically viable ex situ conservation strategy. Full article