Maximum Likelihood Estimation Method Research Articles

On Modeling Bivariate Left Censored Data Using Reversed Hazard Rates

In this paper, we propose a model for analysing the bivariate left-censored data incorporating the dependence enjoyed between the components. This is achieved through the dynamic bivariate vector reversed hazard rate by Gürler (J Am Stat Assoc 91:1152–1165, 1996). The properties of the proposed model is studied. The maximum likelihood method of estimation and the Bayesian method of estimation of parameters is presented. The complexity of the likelihood function is handled through the Metropolis - Hastings algorithm. Interval estimation techniques of the parameters are also considered. Applications of this model is demonstrated by illustrating the usefulness of the model in analysing Australian twin dataset (Duffy in Am J Human Genet 47:530, 1990).

Stress-Strength Reliability Estimation of a Series System with Cold Standby Redundancy Based on Kumaraswamy Half-Logistic Distribution

This paper deals with study and estimation of stress-strength reliability for a system where strength and stress components are connected in series with cold standby redundancy at system level. It is supposed that the random stress and strength both follow Kumaraswamy half-logistic distribution. In this redundant system, we consider that there N subsystems and in each subsystem, there are M statistically independent strength components under the impact of M statistically independent stress components The problem of estimation is solved in two cases. First under the assumption that random stress and strength have common first shape parameter and different second shape parameter and second with the assumption that common shape parameter is known. The stress-strength reliability is estimated using maximum likelihood and Bayesian estimation methods. Also asymptotic and Bayesian intervals for the stress-strength reliability under both the cases are constructed. Monte Carlo simulations will be performed to compare the performance of various methods. Finally a real life data set is analyzed to demonstrate the findings.

A novel extension of generalized Rayleigh model with engineering applications

In this study, we introduce a new flexible distribution constructed by a modification to the Rayleigh distribution and we referred it as unit generalized Rayleigh distribution (UGRD). Varied statistical properties were established, such as reliability, hazard rate, survival rate, moments, quantiles, ordered statistics, etc. The maximum likelihood estimation method is applied to estimate the parameters of the proposed model and different entropy measures including: Rényi entropy, Shannon entropy, Havrda and Charvat entropy, Tsallis entropy, Arimoto entropy, and Mathai–Haubold entropy are provided. The effectiveness of the proposed entropy estimators have been conducted through Monte Carlo (MC) simulation experiments regarding average estimate, average bias, mean square error, and mean relative errors compared to the simple random sample. Finally, we illustrated two real engineering data sets to assess the potential of the proposed UGRD among some existing models.

Analysis and Comparison of Weibull Parameters for Wind Energy Potential Using Different Estimation Methods: A Case Study of Isparta Province in Turkey

In this study, the success of the numerical methods and a metaheuristic algorithm in parameter estimation of Weibull distribution, which is frequently used in wind energy applications, are compared. Numerical methods are Justus empirical method, moment method, graphical method, energy pattern factor method (EPM), energy trend method, maximum likelihood estimation method (MLE). The metaheuristic algorithm is manta ray foraging optimization method (MRFO). The wind data used in the study were recorded hourly in the Isparta region in the southwest of Turkey. A graphical user interface design has been made to easily perform the calculations in this study. The success of the methods was tested with four different statistical error analysis methods. According to the results of the analysis, the MRFO method was by far the most successful method. EPM and MLE methods were the most unsuccessful methods.

Predictors of Children’s Literacy: A Meta-Analysis Study Alphabet of Knowledge

Alphabetic skills were one of the early literacy skills. Several studies on alphabetic skills have been conducted in Indonesia. Meta-analysis was used to describe the children's alphabet skills aged 3 to 6 years as an aggregate. The maximum likelihood estimation method and random effect design were performed to aggregate children's alphabetic skills that can be generalized in Indonesia. The articles were obtained from research published between 2014 and 2021. Those were accessed and collected through a collection of bachelor's thesis on Google Scholar and university digital libraries. The meta-analysis was carried out with JASP. The results showed that the ability to recognize letters among children aged 3 to 6 years in Indonesia was 50.16 (scale 0-100). Despite the fact that mastering letters has an impact on children’s growth in early literacy, the study’s findings show that youngsters in Indonesia still have a low level of letter recognition. These results encourage to improve the quality of kindergartens literacy instruction in Indonesia

On Poisson-Samade Distribution: Its Applications in Modelling Count Data

A new mixed Poisson model is proposed as a better alternative for modelling count data in the presence of overdispersion and/or heavy-tail. The mathematical properties of the model were derived. The maximum likelihood estimation method is employed to estimate the model’s parameters and its applications to the three real data sets discussed. The model is used to model sets of frequencies that have been used in different literature on the subject. The results of the new model were compared with Poisson, Negative Binomial and Generalized Poisson-Sujatha distributions (POD, NBD and GPSD, respectively). The parameter estimates expected frequencies and the goodness-of-fit statistics under each model are computed using R software. The results show that the proposed PSD fits better than POD, NBD and GPSD for all the data sets considered. Hence, PSD is a better alternative provided to model count data exhibiting overdispersion property.

Multinomial Logistic Regression To Model The Combination Of Phdi Status And Hdi Status Of Districts/Cities In Kalimantan Island

Multinomial Logistics Regression (MLR) is a regression model developed from the Binary Logistics Regression (BLR) model. The response variable of the RLM model has three or more categories and has a multinomial distribution, with the data scale being nominal. The response variable in this study is a combination of the Public Health Development Index (PHDI) status and the Human Development Index (HDI) status of districts/cities in Kalimantan Island, 2018, divided into four categories with category one as a comparison. The predictor variables used were the number of the public health center, the percentage of poor people, economic growth, the pure junior high school participation rate, and the percentage of the population with a minimum of junior high school education. The MLR parameter model was estimated using the Maximum Likelihood Estimation (MLE) method and Newton-Raphson iteration. The hypothesis testing of the MLR model was used by the Likelihood Ratio Test (LRT) method and the Wald test. The best model selection in this study uses the backward method, and the interpretation of the best MLR model uses the odds ratio value. The results showed that the best MLR model is a model that has three predictor variables. The factors that significantly influenced the combination of PHDI status and the HDI status of districts/cities in Kalimantan Island in 2018 were the percentage of poor people, economic growth, and the percentage of people with the minimum level of education in junior high school.

Fracture Load of Veneered and Monolithic Single-Unit Fixed Dental Prostheses Made from the High-Performance Thermoplastic Polyphenylene Sulfone

To investigate the fracture load of different veneers for monolithic single-unit fixed dental prostheses (FDPs) made of a novel potential framework material, polyphenylene sulfone (PPSU). The fracture loads of four PPSU frameworks with different veneers (manual polymer veneer with Ceramage Body A3B; prefabricated polymer veneer with Novo.lign; digital polymer veneer with Telio CAD; digital ceramic veneer with IPS Empress CAD) and a monolithic control group (PPSU, Gehr) were examined initially and after 1,200,000 masticatory (50 N, 1.3 Hz) and 6,000 thermal cycles (5°C/55°C). Fracture analysis was performed using light microscope imaging. Fracture types were classified, and relative frequencies were determined. Univariate analysis of variance, post hoc Scheffé, partial eta squared, Kruskal-Wallis test, and Weibull moduli using the maximum likelihood estimation method were calculated. The defined level of significance was adjusted by Bonferroni correction (P < .005). Aging did not affect the fracture load values. Single-unit FDPs with a digital ceramic veneer showed lower values than monolithic and manual polymer-veneer specimens. Single-unit FDPs with a prefabricated and digital polymer veneer were in the same value range as specimens with a manual polymer and digital ceramic veneer. No differences were observed between manual polymer veneer and monolithic single-unit FDPs. All veneered specimens showed a fracture of the veneer. For monolithic single-unit FDPs, a plastic deformation was observed. Veneered and monolithic PPSU showed sufficient fracture load values to indicate successful clinical use in single-unit FDPs. The choice of veneering method and material may play a minor role.

The Coach’s Role in Young Athletes’ Emotional Competence and Psychological Well-being

This paper presents a model that analyses the relationship between the coach’s emotional competences and the training climate as predictors of the youngsters’ emotional competences and psychological well-being. In the present study, 309 athletes and 17 coaches participated in the study. A general predictive model was estimated with path analysis and the maximum robust likelihood (MLR) estimation method. The results showed that the coach’s emotional competences are associated with autonomy-supportive climates (β = .15, p &lt; .005). This climate is related to youth’s emotional competences (β = .30, p &lt; .005) and lower emotional (β = -.27, p &lt; .005), behavioural (β = -.51, p &lt; .005), and social (β = -.33, p &lt; .005) symptomatology. These results have important practical implications in designing interventions that promote coaches’ emotional competences given its association with autonomy-supportive climates, which in turn are related to athletes’ emotional competences and psychological well-being. Keywords: coaching, athletes, autonomy-supportive climate, mental health, well-being.

PIN 추정을 위한 최적모형에 관한 연구

This study compares two models for estimating the probability of informed trading (PIN) and investigates which model is superior in the Korean index options market. The study uses the method of maximum likelihood estimation (MLE) and Bayesian methods to calculate the PIN. Using the bid and transaction data (TAQ) of KOSPI 200 index options from May 2019 to September 2020, we obtain the following results. First, there were no cases where there was no solution in either method. Second, when estimating delta using the Bayesian method, no boundary solutions occurred, but with the MLE method, multiple boundary solutions occurred. Specifically, 10% of the total solutions in 5-minute tick data and 47% in 20-minute tick data were boundary solutions. Third, in the case of 20-minute tick data, the PIN estimated by the MLE method for ITM options significantly decreased compared to that of the 5-minute data. This is estimated to be caused by the previous boundary solutions inducing a downward bias in the PIN. Fourth, in the MLE method, the standard error of the estimate is almost zero, while the Bayesian method shows an error rate of around 2% based on PIN from 20-minute data. In conclusion, the Bayesian method is superior when there is no boundary problem, given a sufficient size of closing data, but when not, the magnitude of the error rate is considered to be an important factor in the choice of method.

부모의 놀이신념과 부모효능감이 부모-자녀 놀이상호작용에 미치는 영향

The purpose of this study was to verify the effect of parents’ play beliefs and parental efficacy on parent-child play interactions. The participants in this study were 325 parents who used daycare centers, kindergartens, and toy libraries located in Daegu, Gyeongsangbuk-do, and Gyeongsangnam-do. Data analysis was performed using statistical packages SPSS 26.0 and AMOS 26.0. The maximum likelihood estimation method was used to model the fit. The fitness was evaluated using CFI, TLI, SRMR, RMSEA, and 90% confidence intervals. The major findings were as follows: First, parents’ play beliefs and parental efficacy had a positive and direct effect on parent-child play interactions. Second, parents’ play beliefs had a positive and direct effect on parental efficacy. Third, parents’ play beliefs had an effect on parent-child play interactions, but partially mediated by parental efficacy. This study is theoretically meaningful, as it shows that parents’ play beliefs and parental efficacy can be major factors that can qualitatively improve parent-child play interactions.

Recurrent neural network based parameter estimation of Hawkes model on high-frequency financial data

This study examines the use of a recurrent neural network for estimating the parameters of a Hawkes model based on high-frequency financial data, and subsequently, for computing volatility. Neural networks have shown promising results in various fields, and interest in finance is also growing. Our approach demonstrates significantly faster computational performance compared to traditional maximum likelihood estimation methods while yielding comparable accuracy in both simulation and empirical studies. Furthermore, we demonstrate the application of this method for real-time volatility measurement, enabling the continuous estimation of financial volatility as new price data keeps coming from the market.

Effect modification of age and hypertension on cancer and prevalence of self-reported stroke - A cross-sectional study.

The objective of this study was to examine the effect modification of age on the relationship between cancer and prevalence of self-reported stroke. We used cross-sectional data from the 2015-2016 iteration of the Canadian Community Health Survey. A multivariable logistic regression model was used to assess the association between cancer and self-reported stroke. Covariates were assessed for effect modification using the maximum likelihood estimation method. We analyzed 86,809 subjects; the prevalence of self-reported stroke was 1.11%. The odds ratio for the association between cancer and self-reported stroke was 1.26 (95% CI 0.98-1.61) after adjusting for age, sex, dyslipidemia, hypertension, diabetes, heart disease, education, and household income. Age and hypertension were found to be effect modifiers, and the association between cancer and self-reported stroke was stronger in younger adults and in those without hypertension. These results suggest that cancer-associated strokes may have unique underlying mechanisms compared to conventional strokes.

The Generalised Extreme Value Distribution Approach to Comparing the Riskiness of BitCoin/US Dollar and South African Rand/US Dollar Returns

In this paper, the generalised extreme value distribution (GEVD) model is employed to estimate financial risk in the form of return levels and the value at risk (VaR) for the two exchange rates, BitCoin/US dollar (BTC/USD) and the South African rand/US dollar (ZAR/USD). The Basel Committee on Banking Supervision (BCBS) responsible for developing supervisory guidelines for banks and financial trading desks recommended that VaR be computed and reported. The maximum likelihood estimation (MLE) method is used to estimate the parameters of the GEVD. The estimated risk values are used to compare the riskiness of the two exchange rates and help both traders and investors to define their position in forex trading. This is to helping understanding the risk they are taking when they convert their savings/investments to BitCoin instead of the South African currency, the rand. The high extreme value index associated with the BTC/USD compared to the ZAR/USD implies that BitCoin is riskier than the rand. The BTC/USD has higher values of expected extreme/tail losses of 13.44%, 18.02%, and 23.41% at short (6 months), medium (12 months), and long (24 months) terms, compared to the ZAR/USD expected extreme/tail losses of 2.40%, 2.84%, and 3.28%, respectively. The computed VaR estimates for losses of USD 0.17, USD 0.22, and USD 0.38 per dollar invested in BTC/USD at 90%, 95%, and 99%, compared to ZAR/USD’s USD 0.03, USD 0.03, and USD 0.04 at the respective confidence levels, confirm the high risk associated with BitCoin. The conclusion drawn from this study is that BTC/USD is riskier than ZAR/USD, despite the rand being a developing country’s currency, hence perceived as being risky. The perception is that the rand is riskier than BitCoin and perceptions do influence exchange rates. Kupiec’s backtest results confirmed the model’s adequacy. These findings are helpful to investors, traders, and risk managers when deciding on trading positions for the two currencies.

Localization System for Vehicle Navigation Based on GNSS/IMU Using Time-Series Optimization with Road Gradient Constrain

In this paper, we propose a GNSS/IMU localization system for mobile robots when wheel speed sensors cannot be attached. Highly accurate location information is required for autonomous navigation of mobile robots. A typical method of acquiring location information is to use a Kalman filter for position estimation. The Kalman filter is a maximum-likelihood estimation method that assumes normally distributed noise. However, non-normally distributed GNSS multipath noise that frequently occurs in urban environments causes the Kalman filter to break down, and degrades the estimation performance. Other GNSS/IMU localization methods capable of lane-level estimation in urban environments use wheel speed sensors, which are unsuitable for the present situation. In this study, we aim to improve the performance of lane-level localization by adding a vehicle speed estimation function to adapt the method to those requiring wheel speed sensors. The proposed method optimizes time-series data to accurately compensate for accelerometer bias errors and reduce GNSS multipath noise. The evaluation confirmed the effectiveness of the proposed method, with improved velocity and position estimation performance compared with the Kalman filter method.

Marshall Olkin Exponentiated Dagum Distribution: Properties and Applications

Marshall Olkin Exponentiated Dagum distribution (MOED) with four shape parameters and one scale parameter is proposed. Alternative expressions are derived for the newly proposed distribution to sort out lengthy calculations. Various properties of MOED are derived, including the measure of central tendency, the measure of dispersion, hazard rate and survival rate are also derived for the MOED. Moreover, the network properties are also derived, including moments, moment generating function, quantile function, median, and mean deviation random number generator. Estimation of parameters is done through MLE (Maximum likelihood estimation) method, and to assess the value of the proposed distribution, the performance of the parameter’s estimates is studied through Monte Carlo Simulation. Three real-life data sets are used to evaluate the application and to scrutinize the performance of MOED as compared to the Marshall Olkin Dagum (MOD) distribution, Exponentiated Dagum (ED) distribution, Dagum (D) distribution, Burr III distribution, Kumaraswamy Burr III (KBurr III) distribution, Kumaraswamy Log Logistic (KLL) distribution and Log Logistic (LL) distribution. Four information criteria are used to examine the performance of the MOED with other special cases. The results showed that the newly proposed distribution performs better than the compared distributions.

A New Extension of the Kumaraswamy Exponential Model with Modeling of Food Chain Data

Statistical models are useful in explaining and forecasting real-world occurrences. Various extended distributions have been widely employed for modeling data in a variety of fields throughout the last few decades. In this article we introduce a new extension of the Kumaraswamy exponential (KE) model called the Kavya–Manoharan KE (KMKE) distribution. Some statistical and computational features of the KMKE distribution including the quantile (QUA) function, moments (MOms), incomplete MOms (INMOms), conditional MOms (COMOms) and MOm generating functions are computed. Classical maximum likelihood and Bayesian estimation approaches are employed to estimate the parameters of the KMKE model. The simulation experiment examines the accuracy of the model parameters by employing Bayesian and maximum likelihood estimation methods. We utilize two real datasets related to food chain data in this work to demonstrate the importance and flexibility of the proposed model. The new KMKE proposed distribution is very flexible, more so than numerous well-known distributions.

Some Methods to Estimate the Parameters of Generalized Exponential Rayleigh Model by Simulation

This paper shews how to estimate the parameter of generalized exponential Rayleigh (GER) distribution by three estimation methods. The first one is maximum likelihood estimator method the second one is moment employing estimation method (MEM), the third one is rank set sampling estimator method (RSSEM)The simulation technique is used for all these estimation methods to find the parameters for generalized exponential Rayleigh distribution. Finally using the mean squares error criterion to compare between these estimation methods to find which of these methods are best to the others

A New Generalized Gamma-Weibull Distribution and its Applications

In this paper, a New Generalized Gamma-Weibull (NGGW) distribution is developed by compounding Weibull and generalized gamma distribution. Some mathematical properties such as moments, Rényi entropy and order statistics are derived and discussed. The maximum likelihood estimation (MLE) method is used to estimate the model parameters. The proposed model is applied to two real-life datasets to illustrate its performance and flexibility as compared to some other competing distributions. The results obtained show that the new distribution fits each of the data better than the other competing distributions.

Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset

The Exponential Pareto (EP) model has been extended by applied and theoretical statisticians for wider applications and new knowledge using different techniques but the Weibull-X technique has not been considered. This article proposed a new extension of the EP model called the Weibull-Exponential Pareto (WEP) distribution to provide better modeling that fits real-life datasets and to explore the statistical theory of order statistics from the proposed distribution. Statistical properties investigated include the Shannon and Renyi entropies; the moments and moment generating function. Distribution of order statistics and the moment of order statistics were derived including the mean and variance of order statistics. WEP distribution has unimodal, decreasing, and increasing failure rates; and it can be negatively or positively skewed and approximately symmetric with the potential for fitting platykurtic, mesokurtic, and leptokurtic lifetime data. The parameters of the distribution were estimated using the method of maximum likelihood estimation (MLE), which was examined for consistency through a simulation study. The performance of the proposed distribution was investigated by application to flood peaks exceedances and some lifetime datasets from engineering. The results from data analysis using the R-software revealed that the WEP distribution has the potential to provide a superior model that fits the three data sets better than some notable existing distributions and previous extensions of the EP model in the literature. The statistical property of order statistics extended in the study established some important results that characterized some notable lifetime distributions in the literature.