Maximum Likelihood Estimation Method Research Articles

Copula-based markov chain logistic regression modeling on binomial time series data

A first-order autoregressive time series model with binomial distributed random variables has been developed using the copula-based Markov chain model approach. By still utilizing conditional probability, covariate variables can also be included in the model and can be assumed as the independent variable. The time series dependent variable with a binomial distribution and continuous independent variables can be modelled using a copula-based Markov chain model with the probability of success expressed in the logit model. This study proposes a copula-based Markov chain logistic regression model with marginal binomial and joint distribution functions built through the copula function. Besides that, this study aims to estimate the parameters involved in the model. The parameters are the parameters of the logistic regression model as the relationship between the dependent and independent variables and the copula parameter as a time dependency. Using the bivariate copula functions are Clayton, Gumbel and Frank, the parameter estimation method is Maximum Likelihood Estimation (MLE). Simulations were carried out to see the efficiency of the parameter estimation and asymptotic results. Based on the simulation results, it was concluded that MLE provides an accurate estimate of the copula-based Markov chain logistic regression. In addition, the copula-based Markov chain logistic regression model can not only see the relationship between the independent and dependent variables but also provide an estimate of the time dependency of the dependent variable. The following are some of the proposed approach's highlights:•This method proposes a binomial time series data model with covariate variables by combining the logistic regression model and the first-order Markov chain model.•Parameter estimation in this model uses the Maximum Likelihood Estimation method.•The model provides the possibility to see the relationship between variables and the time dependency.

Application of Principal Component Analysis and Maximum Likelihood Estimation Method to Identify the Determinant Factors Intention to Use of Paylater in E-Commerce

This research aims to analyze which factors are most determining in influencing interest in using pay-later. This type of research is multivariate analytical research using a quantitative approach. All pay-later service customers who engage in e-commerce make up the study's population. Purposive sampling and non-probability sampling were employed in the sample-taking process based on this study. There are one hundred samples. Researchers have made observations to gather data. The author intends to employ principal component analysis and maximum likelihood estimation techniques for data analysis. Following the completion of the study, the following findings were made. The principal component analysis method's RMSE value is 0.02. The maximum likelihood estimates method's root mean square error is 0.015. Therefore, it can be said that the principal component analysis approach is appropriate for usage because it can explain factor formation due to its strong factor loading value and low RMSE value. The influence of advantages is the most important element determining interest in pay-later utilizing the principal component analysis method since it has the highest loading factor value in decision-making.

Fitting Statistical Distributions to Rainfall Data with Different Estimation Techniques: An Empirical Study from Pabna and Dinajpur Districts

Bangladesh is a country of diverse climatic conditions because of its rainfall and other geographical conditions which have a complex impact on economic and social aspects. The statistical distributions are used in many real life data for modeling and predicting. Knowing the real distribution of rainfall rather than depending on basic summary statistics would improve many uses of rainfall data. The aim of this paper is twofold: first, the performance of different statistical distributions such as Normal, Log-Normal, Gamma Weibull, and Gumbel are compared for modeling the monthly rainfall data from Pabna and Dinajpur districts from January 1971 to December 2015; second, the performance of the Maximum Likelihood Estimation (MLE), Quantile Matching Estimation (QME), and the Maximum Spacing Estimation are also compared for fitting these statistical distributions. The empirical study showed that Gamma distribution performs better for fitting the monthly rainfall data for both Pabna and Dinajpur districts of the three methods like Maximum Likelihood Estimation (MLE) method, the Quantile Matching Estimation (QME), and the Maximum Spacing Estimation (MSE) method. The Normal distribution performs worse of these study areas. By the comparison of these three methods we found that Maximum Likelihood Estimation (MLE) gives better results. This study provides the actual distribution of rainfall data of these study areas. International Journal of Statistical Sciences, Vol. 23(2), November, 2023, pp 87-106

Modeling Extreme Floods Susceptibility Using The Generalized Extreme Value Distribution: Case Study Of Gonse And Wayen, Burkina Faso.

Over recentes decades, Burkina Faso has experienced extremes events such as droughts and floods. In this study, flood frequency has been ascertained based on Generalized Extreme Value (GEV). To this end, discharge data from Gonse and Wayen stations are collected from the National Center for Water resources. The period of analysis goes from 1980 to 2022. The Kolmogorov-Smirnov test is applied to check the distribution of the time series. Then, the Maximum Likelihood Estimation (MLE) method is implemented to estimate the location, the scale and the shape parameters of the GEV distribution. The goodness-of-fit between the empirical data and the theorical distribution is then evaluated based on Akaike criterion (AIC) and Bayenan criterion (BIC). The results revealed that across Gonse station, the probability that the annual maximun discharge will be less than 30m3/s is 0.7 and the 50-year return period discharge is 37.33 m3/s. In Wayen station, the probability that the annual maximun discharge will be less than 200m3/s is 0.5 and the 50-year return period discharge is 226.38m3/s. The AIC is 308.10 and 484.61 respectively for Gonse and Wayen station. The BIC is 313.65 and 490.16 respectively for Gonse and Wayen station. The findings may provide a scientific base for managing the risks of floods to advance climate change adaptation over the Nakambe watershed.

The Predicted Failure on A Two-Dimensional Warranty Using the Bayesian Approach

Traditionally, the warranty cost is assumed to be the cost of repairs based on the average cost that arises from a damage claim. Several studies have considered the Least Square and Maximum Likelihood Estimation methods in estimating the parameters of the failure distribution. However, this study uses the Bayesian method using the posterior distribution obtained from the prior distribution and the likelihood function. The Bayesian approach is more optimal to use in estimating parameters because it has the smallest value of Aikaike’s Information Criterion (AIC) compared to other methods. Failure expectations that are close to natural can be used to analyze survival to determine how long a product will last before the failure. The numerical example in this study, is the type of motorcycle with an engine capacity of 125 CC with the Weibull distribution, while the 150 CC and 160 CC with Exponential distribution. The novelty in this study is that the free repair approach in two-dimensional can be anticipated with failure considering the dimensions of age and mileage.

Generalized Partially Functional Linear Model with Unknown Link Function

In existing models with an unknown link function, the issue of predictors containing both multiple functional data and multiple scalar data has not been studied. To fill this gap, we propose a generalized partially functional linear model, which not only models the relationship between multiple scalar and functional predictors and responses, but also automatically estimates the link function. Specifically, we use the functional principal component analysis method to reduce the dimensionality of functional predictors, estimate the regression coefficients using the maximum likelihood estimation method, estimate the link function using the method of local linear regression, iteratively obtain the final estimator, and establish the asymptotic normality of the estimator. The asymptotic normality is illustrated through simulation experiments. Finally, the proposed model is applied to study the influence of environmental, economic, and medical levels on life expectancy in China. In the study, functional predictors are the daily air quality index, temperature, and humidity of 58 cities in 2020, and scalar predictors are GDP and the number of beds in hospitals. The experimental results indicate that the unknown link function model has a smaller prediction error and better performance than both the model with the known link function and the model without a link function.

Relative evaluation of probabilistic methods for spatio-temporal wind forecasting

Short-term wind power forecasting has become a de facto tool to better facilitate the integration of such renewable energy resources into modern power grids. Instead of point predictors, which produce single-value predictions for the expected power, probabilistic forecasts predict probability distributions over the expected power output or associated confidence intervals. In this study, three different parametric and non-parametric methods for uncertainty modelling in wind power forecasting were studied, namely quantile regression (QR), variational inference and a maximum likelihood estimation (MLE) method. Johnson’s SU distribution was studied as a novel candidate for modelling wind power, which is a transformed normal distribution that exhibits both skew and heavy tails. This was one of the first studies to provide a thorough investigation of Johnson’s SU distribution for uncertainty modelling in a complex deep learning framework for wind forecasting. It was found that Johsnon’s SU likelihood and QR-based models significantly outperformed models using Gaussian likelihoods, based on a range of quantitative metrics to evaluate probability distributions and qualitative investigation of produced forecasts. Variational inference models using Johnson’s SU likelihoods performed remarkably well, with near-perfect calibration and higher precision than models using any of the other methods for uncertainty modelling, as evaluated through the pinball loss, Average Coverage Error (ACE) and Prediction Interval Coverage Percentage (PICP) metric. With the superior performance of Johnson’s SU likelihood models, the study mainly contributes to the literature by introducing another candidate distribution for probabilistic wind forecasting, which is analytical, unbounded and easy to integrate into modern deep learning frameworks.

A Study on Time-Varying Synergy of Energy Consumption, Economic Growth, and CO2 Emissions in China

Since its reform and opening, the Chinese economy has witnessed unprecedented development. This long-term high-speed development has significantly impacted the environment. In the process of energy development and consumption, the environment has been severely polluted, and greenhouse emissions have increased. This has resulted in environmental imbalances such as global climate change, rising sea levels, and extreme weather. Using annual energy consumption (EC), economic growth (GDP), and carbon dioxide (CO2) emissions in China from 1981 to 2021, this study employed the maximum likelihood estimation method to estimate the parameters of the nonlinear MS-VAR model. Cointegration tests, regimes analysis methods, and impulse response function analysis methods were adopted to explore the differences or similarities in the dynamics of the three under various regimes. The research results are as following. (i) The cointegration test findings demonstrate a long-term equilibrium relationship among EC, economic growth, and CO2 emissions. (ii) Regime analyses exhibit that there are three regimes: “low-level regime,” “medium-level regime,” and “high-level regime.” The three regimes have a mutual transfer transmission mechanism that exhibits nonlinear properties. (iii) Impulse response function analyses show that external EC and GDP shocks favorably impact the other two variables in all three regimes. EC in all three regimes is negatively impacted by external CO2 shocks. Moreover, in the “low-level regime,” the relationship between CO2 and GDP has an inverted U-curve, whereas in the other two regimes, the relationship has a negative association. This study can help China formulate reasonable and effective CO2 emissions reduction and energy policies and successfully achieve the emissions reduction goal of the 14th Five Year Plan as well as dual carbon goals.

Failure rate, vitality, and residual lifetime measures: Characterizations based on stress-strength bivariate model with application to an automated life test data

In this article, we introduce some reliability concepts for the bivariate Pareto Type II distribution including joint hazard rate function, CDF for parallel and series systems, joint mean residual lifetime, and joint vitality function. The maximum likelihood and Bayesian estimation methods are utilized to estimate the model parameters. Simulation is carried out to assess the performance of the maximum likelihood and Bayesian estimators, and it is found that the two approaches work quite well in estimation process. Finally, a real lifetime data is analyzed to show the flexibility and the importance of the introduced bivariate mode.

Generalized Fiducial Inference for the Generalized Rayleigh Distribution

This article focuses on the interval estimation of the generalized Rayleigh distribution with scale and shape parameters. The generalized fiducial method is used to construct the fiducial point estimators as well as the fiducial confidence intervals, and then their performance is compared with other methods such as the maximum likelihood estimation, Bayesian estimation and parametric bootstrap method. Monte Carlo simulation studies are carried out to examine the efficiency of the methods in terms of the mean square error, coverage probability and average length. Finally, two real data sets are presented to demonstrate the applicability of the proposed method.

Pemodelan Besar Klaim Asuransi untuk Jaminan Third Party Liability Menggunakan Distribusi Campuran Rayleigh-Rayleigh

This paper will discuss the modeling claim severity of ThirdParty Liability insurance using a mixed Rayleigh-Rayleigh distribution. The mixed Rayleigh-Rayleigh distribution is a distribution built on the basis of an infinitely mixed distribution. The mixed Rayleigh-Rayleigh distribution is a continuous distribution with one parameter, namely α. Parameters in the mixed Rayleigh-Rayleigh distribution can be estimated using the maximum likelihood estimator method through the Newton-Raphson iteration numerical method. The distribution fit test was carried out using the Kolmogorov-Smirnov fit test. The data used is data on Third Party Liability insurance claims with comprehensive coverage at PT. X for the 2019 policy for category 2 in all regions. Based on the results of applying the mixed Rayleigh-Rayleigh distribution on the data claim severity of Third Party Liability insurance with comprehensive coverage at PT. X in 2019 category 2 using the Kolmogorov-Smirnov test it can be concluded that the claims severity in regions 1 and 3 come from populations with a mixed Rayleigh-Rayleigh distribution, while the claim severity claims in region 2 come from populations that don't have a mixed Rayleigh-Rayleigh distribution.
 

Deep correlation and precise prediction between static features of froth images and clean coal ash content in coal flotation: An investigation based on deep learning and maximum likelihood estimation

This research combines deep learning with sophisticated likelihood analysis to achieve precise detection of clean coal ash content in the domain of froth flotation through image acquisition and processing. The utilization of maximum likelihood estimation method establishes a robust correlation between static features of froth images and clean coal ash content, while the application of the BFGS algorithm efficiently searches for optimal parameter estimates. Furthermore, a deep neural network model is constructed using Keras to accommodate multi-feature and hybrid data inputs. The model's performance is rigorously evaluated using metrics such as mean squared error, mean absolute error, and root mean squared error. Experimental results demonstrate remarkable accuracy, with the mean squared error, mean absolute error, and root mean squared error on the test set being 0.003475 %, 0.044740 %, and 0.044585 %, respectively.

Fracture toughness, work of fracture, flexural strength and elastic modulus of 3D-printed denture base resins in two measurement environments after artificial aging

ObjectivesTo investigate the fracture toughness (KIC), work of fracture (WOF), flexural strength (FS) and elastic modulus (E) of four additively manufactured denture base resins in two different measurement environments after artificial aging. MethodsRectangular specimens in two different dimensions (n = 480) were 3D-printed with four denture base resins: Denture 3D+ (DEN; NextDent), Fotodent Denture (FOT; Dreve ProDiMed), Freeprint Denture (FRE; Detax), V-Print dentbase (VPR; VOCO)). KIC, WOF, FS and E were measured after (1) water-storage (37 °C; KIC = 7 d; FS = 50 h); (2) water-storage + hydrothermal-aging (20 min, 0.2 MPa, 134 °C); (3) water storage + thermocycling (10,000 cycles, 5/55 °C) in two measurement environments (i) air-23 °C and (ii) water-37 °C. For FS, fracture types were classified, and relative frequencies determined. Univariate ANOVA, Kruskal–Wallis, Mann–Whitney U, and Spearman’s correlation were calculated (p < 0.05, SPSS V.27.0). Weibull modulus (m) was calculated using the maximum likelihood estimation method. ResultsDEN showed the highest KIC (5/6 groups), WOF and highest corresponding m (1/6 groups), while FRE presented the highest FS (2/6 groups) and E values. Hydrothermal-aging and thermocycling reduced KIC and WOF, FS and E, and the number of FS fracture pieces. For 6/8 groups, hydrothermal aging resulted in lower FS than thermocycling. Measurement in air-23 °C led to higher FS for 7/12 groups and a more brittle fracture behavior. A positive correlation between KIC and FS was observed. SignificanceWith measurements in air-23 °C resulting in higher FS than reported in water-37 °C, the measurement environment should be adapted to the clinical situation to allow valid predictions on the mechanical behavior of denture base resins when in situ.

Joint optimization of selective maintenance and repairpersons assignment problem for mission-oriented systems operating under [formula omitted]-dependent competing risks

Mission-oriented systems (MOS) are designed to operate a series of missions seceded by scheduled breaks of limited duration. For MOS, the most appropriate maintenance strategy is the selective maintenance (SM). Under limited maintenance resources, the SM problem (SMP) aims to identify the optimal set of components to maintain in order to meet the required minimum performance for the next missions. However, the majority of the existing SM models merely relies on stochastic independent (s-independent) components. To overcome this restrictive and unrealistic assumption, this work develops a novel SM approach for jointly optimizing SM and repairpersons assignment (RA) problem (RAP) in a MOS operating under s-dependent competing risks. The s-dependent competing risks between components are captured through copula functions whose unknown parameters are estimated by a two-stage maximum likelihood estimation (MLE) method. Furthermore, the MOS operate several missions and scheduled breaks, and multiple repair channels are available. The resulting joint SM and RAP (JSM-RAP) optimization model is formulated as a mixed-integer non-linear program (MINLP) where the objective is to minimize the total maintenance and labor costs for a SM plan that ensures a required minimum reliability threshold for each mission. A genetic algorithm (GA) is used as a solution method. Several numerical experiments are conducted on a ball screw system. The results obtained demonstrate the validity and the add value of the proposed approach, in addition to the robustness and efficiency of the solution method.

A hybrid distribution characteristics of equivalent structural stress method for fatigue evaluation of welded structures

In the fields of engineering design and fatigue life prediction, handling limited sample data has consistently posed a challenge. A hybrid distribution characteristics of equivalent structural stress (HDC-ESS) method is presented for the design of fatigue life prediction models with small sample sizes. The method integrates the equivalent structural stress (ESS) method with the maximum likelihood estimation (MLE) method based on the idea of sample augmentation, and adds closed-loop reliability verification to ensure its robustness and correctness. By employing three distinct approaches, an analysis and comparison were conducted on the failure data of small specimen obtained from high-frequency fatigue tests of welded joints. The outcomes reveal that the HDC-ESS method, in comparison to the conventional direct method and the MLE-integrated equivalent structural stress approach, exhibited an enhancement of goodness of fit by 0.1866 and 0.1988, respectively. Furthermore, it exhibited remarkable performance in enhancing stability and optimizing sample quantity.

Estimation of a Shape Parameter of a Gompertz-lindley Distribution Using Bayesian and Maximum Likelihood Methods

The Gompertz-Lindley distribution is an extension of the Lindley distribution with three parameters. It was found to be more flexible for modeling real life events. The distribution contains two shape parameters and a scale parameter. Despite the necessity of parameter estimation theory in modeling, it has not been shown that a method of estimation method is better for any of these three parameters of the Gompertz-Lindley distribution. This paper identifies the best estimation method for the shape parameter of the Gompertz-Lindley distribution by deriving Bayesian estimators for the shape parameter of the distribution using two non-informative prior distributions (Uniform and Jeffery) and an informative prior (gamma) under squared error loss function (SELF), quadratic loss function (QLF) and precautionary loss function (PLF). These estimators were evaluated and the results compared with the maximum likelihood estimation method using Monte Carlo simulations with the mean square error (MSE) as a criterion for choosing the best estimator.

Unit upper truncated Weibull distribution with extension to 0 and 1 inflated model – Theory and applications

A two-parameter unit distribution and its regression model plus its extension to 0 and 1 inflation is introduced and studied. The distribution is called the unit upper truncated Weibull (UUTW) distribution, while the inflated variant is called the 0−1 inflated unit upper truncated Weibull (ZOIUUTW) distribution. The UUTW distribution has an increasing and a J-shaped hazard rate function. The parameters of the proposed models are estimated by the method of maximum likelihood estimation. For the UUTW distribution, two practical examples involving household expenditure and maximum flood level data are used to show its flexibility and the proposed distribution demonstrates better fit tendencies than some of the competing unit distributions. Application of the proposed regression model demonstrates adequate capability in describing the real data set with better modeling proficiency than the existing competing models. Then, for the ZOIUUTW distribution, the CD34+ data involving cancer patients are analyzed to show the flexibility of the model in characterizing inflation at both endpoints of the unit interval.

Reliability and the engineering applications of the generalized half-normal model via an adaptive progressive hybrid censored mechanism

Recently, the generalized half-normal distribution with decreasing, increasing, and bathtub hazard function shapes was proposed, making it a more applicable, reliable, and flexible lifespan model. The task of estimating the unknown parameters and reliability features of the generalized half-normal distribution is looked at using adaptive progressively type-II hybrid censored data. The maximum likelihood and Bayesian estimation methods are both considered for this purpose. Two approximated confidence intervals, Bayes and highest posterior density intervals, are acquired for the various parameters. The Bayes estimates are obtained based on symmetric and asymmetric loss functions under the assumption of independent gamma priors. The Markov chain Monte Carlo approach is used to compute Bayes estimates as well as the various Bayes intervals. Monte Carlo experiments are used for assessing the efficiency of the various approaches. Finally, analysis is performed on two actual-life engineering datasets.

Beta-Geometric Regression for Modeling Count Data on First Antenatal Care Visit (ANC) with Application

Introduction: Little attention has been paid to modeling count data with the geometric distribution. There are many real-life phenomena with a constant probability of first success. However, in practice, the probability of the first success may vary, making simple geometric models unsuitable for modeling such data. One can assume one of many continuous distributions for modeling the probability of first success with the parameter space [0, 1]. In this respect Beta distribution defined on the standard unit interval [0,1] is the most useful distribution due to its ability to accommodate a wide range of shapes. Thus, in this paper, by mixing Beta and geometric distribution, we developed a Beta-geometric distribution for modeling the count data through application to real-life count data on time to the first antenatal care (ANC) visit.&#x0D; Methods: The estimation of the distribution parameters using the method of moments, maximum likelihood estimation (MLE) method, and Bayesian estimation approach are provided. Based on the Beta-geometric distribution, we developed a new Beta-geometric regression model for analyzing count data that follow the geometric distribution. The goodness of fit of the derived model has been tested using real data on time to the first ANC visit.&#x0D; Results: Beta-geometric distribution has a simple form for its probability mass function (pmf), and is flexible in capturing both underdispersion and overdispersion that may present in count data. It was found that the proposed Beta-geometric regression model fit the count data on the first ANC visit better than simple geometric distribution or Negative Binomial distribution.&#x0D; Conclusion: Unlike the Poisson or Negative Binomial distribution, Beta-geometric distribution does not need an additional parameter to accommodate underdispersion or overdispersion and thus could be a flexible choice for analyzing any count data. The goodness of fit test of the Beta-geometric model provides better fitting of the model to real data on time to first ANC visit than geometric or Negative binomial models.

Survival Analysis and Hazard of Log Logistic Distribution on Type I Censored Data Parametrically

Survival Analysis is a research method that examines the survival time of individuals or experimental units in relation to events such as death, disease, recovery, or other experiences. This study utilizes a parametric survival analysis model with a 2 parameter log logistic distribution and Maximum Likelihood Estimation (MLE) method to analyze the survival of students during their study period. The log logistic distribution is chosen due to its ability to capture early or late failure patterns. The objective of this research is to analyze type I censored survival data using the log logistic distribution applied to secondary data on student study duration. The dataset consists of 98 observations. The calculated values for the β and γ parameters of the 2 parameters log logistic distribution are 2.12831 and 0.0918891, respectively. The probability of students completing their studies by semester 8 (hazard function h(8)) is 0.370102, while the probability of students continuing their studies in semester 9 (survival function s(9)) is 0.320817.