Maximum Likelihood Estimation Method Research Articles

Birnbaum Saunders distribution for imprecise data: statistical properties, estimation methods, and real life applications

A neutrosophic statistic is a random variable and it has a neutrosophic probability distribution. So, in this paper, we introduce the new neutrosophic Birnbaum–Saunders distribution. Some statistical properties are derived, using Mathematica 13.1.1 and R-Studio Software. Two different estimation methods for parameters estimation are introduced for new distribution: maximum likelihood estimation method and Bayesian estimation method. A Monte-Carlo simulation study is used to investigate the behavior of parameters estimates of new distribution, compare the performance of different estimates, and compare between our distribution and the classical version of Birnbaum–Saunders. Finally, study the validity of our new distribution in real life.

Issues related to typological fragility curves derivation starting from observed seismic damage

In this study typological fragility curves are proposed with a macro-seismic approach. To this scope, a stock of 56.338 residential masonry buildings struck by L’Aquila 2009 seismic sequence is analyzed, whose AeDES forms are archived within Da.D.O. platform, that is a web-gis database collecting the observed seismic damage data related to buildings surveyed after several Italian earthquakes.Moreover, issues significantly influencing the fragility curves derivation are in depth discussed. In particular, a criterion for the buildings stock completion adding undamaged and not surveyed buildings is proposed, based on the distributions known of the residential building typologies. Comparisons highlight that the database completion affects the resulting fragility curves, and in particular for low damage levels. Furthermore, it is shown how the fundamental parameters estimation, by using the Maximum Likelihood Estimation (MLE) method, is conspicuously influenced by the PGA intervals number (nint), that is an issue often ignored when fragility curves are derived. The numerical investigations show that, although a non-monotonic trend is observed, the fundamental parameters tend to converge to the asymptotic values as the nint of PGA increases, and that they are markedly dispersed when nint is low.

Lifetime Analysis of Dies Manufactured by Conventional Processes and Reconditioned by Deposition Welding Operation.

The refurbishment of dies by the deposition welding of wear areas is an efficient and economical process. The aim of this study was to conduct a comparative analysis of the lifetimes of different types of dies for the manufacturing of wagon wheels. The analyzed dies were manufactured by conventional processes (Type I) and reconditioned through a deposition welding procedure using a dedicated electrode (Type II). The Anderson-Darling test was conducted to analyze the goodness of fit of the lifetime data specific to the die types. The maximum likelihood estimation method (MLE) with a 95% confidence interval (CI) was applied in order to estimate the lifetime distribution parameters. It was found that the lifetimes of type II dies were longer than those of type I dies. The mean time to failure (MTTF) recorded for reconditioned dies was 426 min, while the mean time to failure of dies manufactured by conventional processes was approximatively 253 min. In addition, an accentuated hazard rate for type I dies compared to type II dies was observed. The results of this analysis emphasized the fact that dies can be restored to their initial operating capacity by successfully using deposition welding procedures that confer a high resistance to operational loads. At the same time, the use of these procedures allows for the sustainable development of resources and waste management.

Faktor-Faktor Yang Memengaruhi Risiko Produksi Bawang Putih Di Indonesia

Garlic productivity in Indonesia is still low and fluctuates every year. The productivity fluctuations indicate production risks. This research aims to analyze the factors that influence the productivity and risks of garlic production in Indonesia. The data used in this study is secondary data from BPS 2014 in the three largest production centers, namely Central Java, West Nusa Tenggara, and East Nusa Tenggara, with a total sample of 305 farmer respondents from 333 farmer respondents. The method used in this study is a multiple linear regression model with the Just and Pope model approach. Multiple linear regression analysis for the productivity function is estimated through the Ordinary Least Squares (OLS) method, whereas for the production risk function, estimation is conducted using the Maximum Likelihood Estimation (MLE) method. The results showed that the risk level of garlic production in Indonesia was high. Factors significantly increased productivity, including seeds, labor, the dry season, and climate change. Meanwhile, factors that significantly reduced productivity are organic fertilizers and SP36 fertilizers. The risk-inducing production factor is climate change, while the risk-reducing factors are pest attacks and liquid pesticides. To boost productivity, farmers can cultivate garlic during the dry season, increase the use of high-quality seedlings and labor, and reduce the application of organic and SP36 fertilizers. To mitigate production risks, farmers can enhance the use of liquid pesticides following recommended usage standards.

A New Modified-X family of distributions with applications in modeling biomedical data

In the present article, we derive a new Modified-X (NM-X) family of probability distributions by using a popular approach known as the T-X method. For the NM-X family, some of the main distributional (or statistical) properties such as quantile function, identifiability property, order statistics, residual life and reverse residual life, moments, and moments generating function are determined. A well-known method of estimation such as the Maximum Likelihood estimation method is used for estimating the model parameters of the introduced family of distributions. A Monte Carlo simulation method is incorporated to judge the performance of the estimators with different selected values of parameters. To check the tails behaviors of the proposed model, the risk measurements such as value-at-risk (VaR), tailed-value-at-risk (TVaR), tailed-variance (TV), and tailed-variance-premium (TVP) are investigated. For illustrative purposes, a special sub-model of the proposed class is derived and named a New Modified Weibull distribution (abbreviated as the NM-Weib). Furthermore, four applications from the field of medicine are analyzed to demonstrate the application, and effectiveness of the NM-Weib distribution. By adopting different diagnostic criteria, the NM-Weib distribution is compared with Weibull (Weib) distribution, Alpha Power Transformed-Weib (APTra-Weib) distribution, new Exponent-Weib (NExpo-Weib) distribution, Flexible Reduced Logarithmic-Weib (FRLog-Weib) distribution, Marshal Olkin-Weib (MO-Weib) distribution, and Kumaraswamy-Weib (K-Weib) distribution. Finally, based on the diagnostic criteria, it is observed that the NM-Weib distribution provides a suitable and best fit for each considered biomedical data set.

A Stochastic Frontier Approach to Study the Relationship between the Hygienic Quality of Bulk Tank Sheep Milk and Technical Efficiency of the Coagulation Process.

Sheep milk from local breeds is important for the production of high-quality cheeses throughout the Mediterranean region, such as Manchego cheese in Spain. To maintain sustainable and efficient production, it is necessary to reach a better understanding of how the composition and hygiene of the milk affect the coagulation process, with the aim of optimizing production yield. This study implemented a stochastic production frontier function to estimate the potential production of curd and efficiency using data from the four seasons of a study of 77 Manchega sheep farms. The Cobb-Douglas production frontier model was estimated using the maximum likelihood estimation method. The results showed that the content of protein, lactose, and fat exhibited increasing returns to scale, with protein content being the most significant factor for curd production. Approximately half of the inefficiency was due to factors related to the technological properties and the hygiene of the milk. The pH, curd firmness, and concentration of lactic acid bacteria improved the efficiency of coagulation, while the concentration of spores of lactate-fermenting Clostridium spp., Pseudomonas spp., staphylococci, and catalase-negative gram-positive cocci favored the inefficiency of the coagulation process. To date, this is the first study to evaluate the effect of different factors, such as microbial groups, milk composition, and technological properties, on the efficiency of the coagulation process in dairy sheep.

Probabilistic characterisation of rock mass deformation modulus from P-wave velocity based on information criteria

ABSTRACT Determination of rock mass deformation modulus (Erm ) is an important but very challenging task in rock mechanics and rock engineering. Direct measurements of Erm by in-situ tests are expensive, time-consuming, and sometimes even impossible. Since the nondestructive and easy geophysical method is commonly used to measure the P-wave velocity (Vp ) in the field, the study has developed an empirical correlation between Erm and Vp based on 834 collected datasets by considering both inherent and transformation uncertainties. The information criteria are employed to select the best model for deriving a general empirical correlation. The maximum likelihood estimation (MLE) method and computational intelligence techniques like particle swarm optimisation (PSO), artificial bee colony (ABC), and differential evolution (DE) algorithms are used to specify the incorporated parameters of each candidate model. Based on the derived general empirical equation, a Bayesian equivalent sample approach using Markov Chain Monte Carlo (MCMC) simulation is applied to conduct probabilistic characterisation of Erm by combining prior knowledge and project-specific observed Vp data. Comparative studies of the results from theory and in-situ measured Erm values suggest that the proposed method is effective and validate the applicability of the derived general empirical correlation.

Improved hourly estimate of aerosol optical thickness over Asian land by fusing geostationary satellites Fengyun-4B and Himawari-9

Asian over-land aerosols are complexities due to a mixture of anthropogenic air pollutants and natural dust. The accuracy of the aerosol optical thickness (AOT) retrieved from the satellite is crucial to their application in the aerosol data assimilation system. Fusion of AOTs with high spatiotemporal resolution from next-generation geostationary satellites such as Fengyun-4B (FY-4B) and Himawari-9, provides a new high-quality dataset capturing the aerosol spatiotemporal variability for data assimilation. This study develops a complete fusion algorithm to estimate the optimal AOT over-land in Asia from September 2022 to August 2023 at 10 km × 10 km resolution with high efficiency. The data fusion involves four steps: (1) investigating the spatiotemporal variability of FY-4B AOT within the past 1 h and 12 km radius calculation domain; (2) utilizing the aerosol spatiotemporal variability characteristics to estimate FY-4B pure and hourly merged AOTs; (3) performing bias corrections for FY-4B and Himwari-9 hourly merged AOT for different observation times and seasons considering pixel-level errors for each satellite; (4) fusing the bias-corrected FY-4B and Himawari-9 hourly merged AOT based on maximum-likelihood estimation (MLE) method. Compared to the original FY-4B AOT, validation with AERONET observation confirms that the root mean square error (RMSE) of hourly merged FY-4B AOT decreases by around 40.6 % and the correlation coefficient (CORR) increases by about 27.8 %. Compared to FY-4B and Himawari-9 merged AOT, the fused AOT significantly decreases (increases) RMSE (CORR) by around 24.7 % (7.3 %) and 20.2 % (5.6 %). In addition, fused AOT is double the number of single-sensor merged AOT. Fusion aerosol map accurately describes the spatial and temporal variations in Asian regions controlled by air pollution and dust storms. Further studies are required for other landscapes with different satellite combinations to promote the application in the data assimilation system.

A finite failure software reliability model using extended log-logistic distribution

Software reliability engineering has been developed to examine software systems over the years. Non-homogeneous Poisson process (NHPP) models are widely employed for analyzing software reliability data, as they have the ability to describe the expected number of failures over time using the mean value function. In addition, these models have an intensity function representing the failure rate over time. This article proposes a new non-homogeneous Poisson process model based on extended log-logistic (NHPP ELL) distribution with three parameters. The model properties were derived and represented graphically. Furthermore, the maximum likelihood estimation method was utilized to estimate the model parameters, which were computed numerically using the Newton–Raphson method. Three real software reliability datasets were utilized to evaluate the performance of the new NHPP ELL model based on three distinct criteria: the mean square error, the coefficient of determination (R2), the Theil statistic, the predictive-ratio risk, and the predictive power. Moreover, a comparative study was conducted between the proposed model and several well-known NHPP models regarding goodness-of-fit and predictive performance. All the evaluation measures indicate that the proposed model outperforms the other models across all the considered datasets. In addition, the graphical plots depicting the actual data and the prediction results for all the fitted models show that the proposed model performs well in all three considered software reliability datasets compared to other models.

A New Hybrid Algorithm Based on the Firefly Algorithm and Cuckoo Search to Estimate Survival Analysis of Truncated Inverse Gompertz Distribution

This paper introduces the Right Truncated Inverse Gompertz Distribution (RTIGD) with two parameters δ and ϑ with some of its properties as; (Survival-Function, Hazard-Function, cumulative distribution function, probability density function, ‎r-th moment, mean, variance, Moment Generating Function, Median, and Mode. In addition, we propose a new hybrid algorithm, namely the firefly Algorithm with Cuckoo Search Algorithm (FA_CSA) to estimate the parameters based on the survival functions of RTIGD. Simulation is utilized to compare the proposed algorithm with traditional methods, for example, the Maximum Likelihood Estimator and moment method and the standard algorithms Firefly Algorithm and Cuckoo Search. In most cases, the results demonstrate that the proposed algorithm (FA_CSA) provides an accurate estimation for the survival function since it has less mean squared error than the other estimation methods.

A new factor analysis model for factors obeying a Gamma distribution

The traditional factor analysis model assumes that the factors obey a normal distribution, which is not appropriate in fields whose data are nonnegative. For this kind of problem, we construct a more practical factor model, assuming that the factors obey a Gamma distribution. We develop a new factor analysis model and discuss its true loading matrix. Then we study its parameter estimation with the maximum likelihood estimation (MLE) method based on an Expectation-Maximization (EM) algorithm, where step E is realized by the Metropolis-Hastings (M-H) algorithm in the Markov Chain Monte Carlo (MCMC) method. We use the new model to empirically study real data, and evaluate its information extraction ability, using the defined true loading matrix to calculate the true loading of the factor. We compare the new model and traditional factor analysis models on simulated and real data, respectively, whose results show that the new model has better information extraction ability for nonnegative data when the number of factors is the same.

Groundwater–surface water exchange from temperature time series: A comparative study of heat tracer methods

The importance of the interaction between groundwater and surface water is increasingly being recognized for both understanding and managing water systems. Many efforts have been made to characterize and quantify groundwater–surface water exchange. In particular, temperature–based methods have quickly established themselves given their monetary and practical advantages. In the last 15 years, several methods for interpreting passive temperature time series measured in the streambed have been developed. Still, the benchmarking of these methods has only been carried out in specific and distinct hydrological conditions.This article aims to fill this research gap by benchmarking the performance of six commonly used methods for deriving seepage fluxes using a two-year-long temperature time series covering various meteorological and thermal conditions. This work compares three analytical methods that calculate seepage flux using the amplitude and/or phase of the temperature signals, and three numerical methods that use different schemes to inversely solve the one–dimensional heat transport equation in the streambed. The temperature measurements were made in the context of an international dispute between Chile and Bolivia over the status and use of the waters of the Silala River, Northern Chile. Flux estimations are tested against Darcy’s flux derived from measured hydraulic gradient and hydraulic conductivity.Flux estimations from the benchmarked methods ranged from −0.5 to 3.5 m/d (with positive fluxes directed downwards), whereas fluxes estimated using Darcy’s law ranged from 0.5 to 6 m/d. Results show that the amplitude method is the best–performing method. This method is best suited for estimating the direction of the fluxes, while the method using both the thermal amplitude and phase is best suited for monthly flux trends, and the combination of a Local Polynomial (LP) method and a Maximum Likelihood Estimator (MLE) method (LPMLEn) is appropriate for estimating flux in transient conditions.The use of heat as a tracer proved to be an effective tool for monitoring groundwater–surface water exchange in a river reach for two years, and yielded exchange flux estimates with lower point-scale variability than Darcy’s law.

Structural flexibility identification from impact test data through a subband estimation method

SummaryFlexibility is an important parameter reflecting bridge load‐carrying capacity. Dynamic testing is a fast and effective method to obtain the structural modal flexibility of small‐ and medium‐span bridges. The Deterministic‐stochastic subspace identification (DSI) algorithm is a well‐established structure identification method in the time domain. However, the estimation of damping, especially the modal scaling factor, is not always reliable due to inevitable measurement noise, which directly affects the identification accuracy of flexibility. This paper proposes a maximum likelihood estimation method in subbands (SMLE), which can be regarded as an add‐on method of the DSI algorithm because the initial parameters are obtained from the DSI algorithm. The processing of frequency band division is implemented first, and the frequency response function curve in each subband of the whole frequency range is fit separately. Then, subband cyclic iteration is proposed to improve the identification accuracy in a closely spaced mode system. The proposed SMLE method maintains the advantages of the DSI algorithm while improving the accuracy of parameter estimation and flexibility identification. Two lumped mass models are used to verify that the proposed method can effectively improve estimates to obtain a precise flexibility matrix and predict the displacement of the structure under static loading. Experimental example of a continuous girder bridge is considered to verify the availability and effectiveness of the proposed method in practice.

Partly linear single-index cure models with a nonparametric incidence link function.

In cancer studies, it is commonplace that a fraction of patients participating in the study are cured, such that not all of them will experience a recurrence, or death due to cancer. Also, it is plausible that some covariates, such as the treatment assigned to the patients or demographic characteristics, could affect both the patients' survival rates and cure/incidence rates. A common approach to accommodate these features in survival analysis is to consider a mixture cure survival model with the incidence rate modeled by a logistic regression model and latency part modeled by the Cox proportional hazards model. These modeling assumptions, though typical, restrict the structure of covariate effects on both the incidence and latency components. As a plausible recourse to attain flexibility, we study a class of semiparametric mixture cure models in this article, which incorporates two single-index functions for modeling the two regression components. A hybrid nonparametric maximum likelihood estimation method is proposed, where the cumulative baseline hazard function for uncured subjects is estimated nonparametrically, and the two single-index functions are estimated via Bernstein polynomials. Parameter estimation is carried out via a curated expectation-maximization algorithm. We also conducted a large-scale simulation study to assess the finite-sample performance of the estimator. The proposed methodology is illustrated via application to two cancer datasets.

Cancer risk in patients treated with denosumab compared with alendronate: A population-based cohort study

BackgroundAntiresorptive treatment is currently used in millions of patients with osteoporosis and cancer worldwide. Early studies of denosumab suggested a small signal in ovarian cancer incidence and emerging data suggest that denosumab stimulates germ cell proliferation in the gonads. This study aims to determine the association between the use of denosumab and the risk of reproductive cancers compared with the use of alendronate. Research design and methodsUsing a cohort study design, we used the Danish nationwide registries to identify a population of subjects ≥50 years of age during 2010–2017 who started denosumab after being on alendronate treatment for at least six months. The cohort was matched 1:2 with patients who had been treated with alendronate alone for at least six months. The risk of reproductive cancers and the risk difference between groups were estimated using the Longitudinal Targeted Maximum Likelihood Estimation (L-TMLE) method. ResultsWe identified 6054 Danish individuals who underwent treatment with denosumab. These individuals were matched with 12,108 receiving alendronate. The absolute risk of reproductive cancer was 1.05 % (95 % CI 0.75–1.34) after three years for denosumab users and was not different 0.03 % (−0.34–0.39) than for alendronate users. In supplemental analyses, there was no increased risk of non-reproductive cancers associated with the use of denosumab (risk difference of 0.54 % (−0.41–1.19). Analysis comparing denosumab users with the general population gave similar results. ConclusionThere was no difference in the risk of cancer following treatment with denosumab compared to treatment with alendronate assessed after a short follow-up of 3 years.

Employing the generalized Pareto distribution to analyze extreme rainfall events on consecutive rainy days in Thailand's Chi watershed: implications for flood management

Abstract. Extreme rainfall events in the Chi watershed of northeastern Thailand have significant implications for the safe and economic design of engineered structures and effective reservoir management. This study investigates the characteristics of extreme rainfall events in the watershed and their implications for flood risk management. We apply extreme value theory to historical maximum cumulative rainfall data for consecutive rainy days from 1984 to 2022. The generalized Pareto distribution (GPD) was used to model the extreme rainfall data, with the parameters estimated using maximum likelihood estimation (MLE) and linear moment estimation (L-ME) methods based on specific conditions. The goodness-of-fit tests confirm the suitability of the GPD for the data, with p values exceeding 0.05. Our findings reveal that certain regions, notably Udon Thani, Chaiyaphum, Maha Sarakham, Tha Phra Agromet., Roi Et, and Sisaket provinces, show the highest return levels for consecutive 2 d (CONS-2) and 3 d (CONS-3) rainfall. These results underscore the heightened risk of flash flooding in these regions, even with short periods of continuous rainfall. Based on our findings, we developed 2D return level maps using the Q-geographic information system (Q-GIS) program, providing a visual tool to assist with flood risk management. The study offers valuable insights for designing effective flood management strategies and highlights the need for considering extreme rainfall events in water management and planning. Future research could extend our findings through spatial correlation analysis and the use of copula functions. Overall, this study emphasizes the importance of preparing for extreme rainfall events, particularly in the era of climate change, to mitigate potential flood-related damage.

The Computational Testing Procedure for the Comprehensive Lifetime Performance Index of Burr XII Products in Multiple Production Lines

Extending from a single production line to multiple production lines, a comprehensive life performance index is proposed for evaluating the quality of lifetime products. The connection between the comprehensive lifetime performance index and the individual lifetime performance index is explored. For products with a lifetime following Burr XII distribution for the ith production line, the maximum likelihood estimation method and the corresponding asymptotic distribution for all lifetime performance indices are derived. Checking whether the comprehensive lifetime performance index has achieved the target value is essentially the same as testing whether each individual lifetime performance index has reached its corresponding target value. A testing procedure is proposed for a given significance level using the maximum likelihood estimator as the test statistic, and the power analysis is presented through graphical representations. For the power analysis, the impacts of sample size, the number of inspection intervals, the removal probability, the level of significance, and the number of production lines on the test power are analyzed, and the results show that there is a monotonic relationship between the test power and the above five impact factors. To illustrate how to apply the proposed testing procedure, we give one practical example with two production lines to test whether the comprehensive production process is capable.

On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data

Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.

Tactical factors that influence shooting success in the Chinese Football Association Super League

This study aimed to investigate the tactical factors influencing shooting success in the Chinese Football Association Super League (CSL). The data set comprised 5914 shooting actions collected from all 240 matches in the CSL 2018 season, featuring 16 different teams. The variables assessed included pass number (PN), playing minute (M), match status (MS), final passing area (FPA), regaining possession position (RPP), offense category (OC), and shooting position (SP). To distinguish the attacking patterns of teams of varying strengths, all 16 teams were clustered into two groups based on two contextual factors: their starting season budgets and their rankings at the end of the season. Firstly, a descriptive analysis was conducted, followed by the application of a binomial-logit model ( p < 0.05). The Maximum Likelihood Estimation (MLE) method was employed to evaluate the factors impacting shooting success. The results revealed that: (1) Match status ( p = 0.0412), regaining possession position ( p = 0.0002), and shooting position ( p = 0.0001) play important roles in shooting success for all teams. (2) For strong teams, the offense category ( p = 0.0031) and the final passing area ( p = 0.0027) also have an important influence on shooting success. (3) The tactics of the weak teams should focus especially on the final passing area ( p = 0.0388) before shooting at the goal. These findings can provide guidance for coaches in developing more effective scoring strategies or defensive tactics and tailoring them appropriately to the strengths and weaknesses of their respective teams.

Perceived neighborhood walkable environment, neighborhood interaction and mental health among residents of different age groups: a case study in Shanghai, China

Purpose This study aims to investigate the relationships between the perceived neighborhood walkable environment (PNWE), neighborhood interaction (NI) and residents’ mental health, with a focus on examining differences among residents of different age groups.Design/methodology/approach Using an electronic survey questionnaire, data on PNWE, NI and mental health were collected from 1,159 residents across 205 communities in Shanghai, China. Our study utilized a structural equation modeling (SEM), employing the maximum likelihood estimation method. The structural equation model was fitted using the MPLUS software.Findings The mental health of young and middle-aged adults is generally poor, and they are at higher risk of depression than children and older adults. The effects of PNWE and NI on the mental health of residents varied among different age groups. As residents get older, their mental health is more affected by the PNWE. In addition, the influence of the PNWE on children and older adults’ mental health is direct and not mediated by NI. For young and middle-aged adults, the influence of the PNWE on their mental health needs to be mediated by NI.Originality/value This study marks the first examination of the relationship between PNWE, NI and mental health among different age groups of residents in China. The findings of this research can assist policymakers in gaining a deeper understanding of the underlying mechanisms by which PNWE affects mental health. Furthermore, it can contribute to the development of more targeted walkable environment designs aimed at enhancing mental health among various age groups.