Maximum Likelihood Estimation Method Research Articles

Pricing of Aquaculture Industry Microinsurance Premiums with Standard Deviation Principle Approach (Case Study: Tasikmalaya)

Aquaculture is a rapidly growing industry and has enormous potential to increase the income and welfare of fish farmers. The majority of aquaculture businesses in Indonesia are small-scale cultivators, low productivity and limited business accessibility. As a result, there is an aquaculture industry that does not understand the use of aquaculture-specific financial risk management tools. Therefore, an insurance instrument is needed to manage losses that occur so as to achieve financial and income benefits, namely Micro Insurance. This study aims to calculate premium prices with a standard deviation principle approach. The data used is loss data if aquaculture cultivators do not pay in accordance with the initial capital in Tasikmalaya obtained through primary data based on the results of field surveys through questionnaires. The method of analyzing the number of event data uses the Poisson distribution, while the loss data uses the Exponential distribution. Next, calculate the parameter estimation using the Maximum Likelihood Estimation method. The results of parameter estimation are used to find a collective risk model. From the calculation results in this study, a premium price of IDR was obtained.

Mitigation of The Risk of Failed Harvest Pond Farming Fisheries Using The Calculating of The Premium Through The Approach to The Principle of Expectation Value

Pond cultivation is a promising business to be engaged in at this time, the demand for fish in the market is high, it opens opportunities for entrepreneurship in the field of fish cultivation. It is undeniable that several factors will cause crop failure in fish farming, both from weather factors and in the livestock process. If such an unexpected thing happened, the cultivators would be slightly affected. Therefore, there is a need for special insurance to protect farmers from financial losses due to possible risks, namely Fishery Microinsurance. This study aims to determine a reasonable amount of insurance premiums for small-scale shrimp pond aquaculture cultivators using the expectancy value principle calculation method. The data on the number of events uses the Poisson distribution, while the loss data uses the Exponential distribution in Pandeglang Regency. Next use the Maximum Likelihood Estimation method to calculate the parameter estimate. After that, the results of the parameter estimation are used to search for a collective risk model. Thus, the result of the premium calculation in this study was Rp 25.893.046

Equal Pay and Employment in Serbia During the COVID-19 Pandemic

Introduction and objectives: Before the COVID-19 pandemic, Serbia belonged to the group of post-transition countries that were determined to reduce gender inequalities in the labour market through an improved institutional framework and measures to promote women's employment. However, the gender wage gap remains significant. This paper uses data from the Survey on Income and Living Conditions to examine the gender wage gap in Serbia. Methods: The estimates of the stochastic frontier model were obtained using the maximum likelihood estimation method. Results: The results indicate a statistically significant gender wage gap, showing that women on average have a log hourly wage 0.109 and 0.098 lower than men in 2019 and 2020, respectively. The labour market shows similar efficiency of employees. Conclusion: It is predicted that women are paid less than men, even after controlling for the observed factors. Comparing this with the results of previous studies, it can be concluded that the COVID-19 pandemic has contributed to a slight worsening of gender inequalities in the Serbian labour market. Implications and research limitation: Women's financial vulnerability can be exacerbated by leaving the workforce, taking up part-time employment or working in a job with lower benefits. The latter position of women in the labour market or their recognition as potential beneficiaries by pension and social security systems are two ways in which this has practical implications for the public policy. Similar research using data from the post-COVID-19 period would be of great value in assessing changes in women's position in the labour market.

Different Methods for Estimating Default Parameters of Alpha Power-Transformed Power Distributions Using Record-Breaking Data

The current study addresses the estimation of the default parameters of alpha power-transformed power (APTPO) distributions. For the location and scale parameters of the APTPO distributions, we provide coefficients for both the best linear unbiased estimators (BLUE) and the best linear invariant estimators (BLIE) methods. Furthermore, we establish a forecast for future records. The parameters of the APTPO distribution are estimated using the maximum likelihood estimation method (MLE). The goodness-of-fit test (using Akaike information criterion (AIC)) is computed using both the inter-record time sequence and the entire sample. Also, we utilize a simulation approach to demonstrate the practicality and benefits of our perspective. Finally, we demonstrate the accuracy of these parameters and the performance of estimators through a real-life example.

A novel extended inverse‐exponential distribution and its application to COVID‐19 data

AbstractThe aim of this article is to define a new flexible statistical model to examine the COVID‐19 data sets that cannot be modeled by the inverse exponential distribution. A novel extended distribution with one scale and three shape parameters is proposed using the generalized alpha power family of distributions to derive the generalized alpha power exponentiated inverse exponential distribution. Some important statistical properties of the new distribution such as the survival function, hazard function, quantile function, moment, Rényi entropy, and order statistics are all derived. The method of maximum likelihood estimation is used to estimate the parameters of the new distribution. The performance of the estimators are assessed through Monte Carlo simulation, which shows that the maximum likelihood method works well in estimating the parameters. The GAPEIEx distribution was applied to COVID‐19 data sets in order to access the flexibility and adaptability of the distribution, and it happens to perform better than its submodels and other well‐known distributions.

Properties of PSR J1023+0038 Based on Kepler, TESS, and FAST

The pulsar system PSR J1023+0038 is a very interesting binary with radio millisecond pulsar and low-mass X-ray binary transitions, which depend on the stellar accretion process. We have used Kepler light curves with 1 minute cadence and TESS light curves with 2 minute cadence to study the flare properties of PSR J1023+0038. We detected 516 flare events in the K2 data and 84 flare events in the TESS survey data. We determined the flare rise and delay times, the flare durations and amplitudes, and flare energies. We obtained a value of the power-law index of 0.359 ± 0.023 between the flare energies and decay times, which is similar to the theoretically predicted value of 1/3. This in turn indicates that PSR J1023+0038 might be exhibiting physical mechanisms described by magnetic reconnection theory. Using the maximum likelihood estimation method, we also calculated the power-law index of the cumulative flare frequency distribution, finding 1.87 ± 0.27 for the Kepler data and 1.74 ± 0.29 for the TESS data. Meanwhile, we reduced six FAST observations of PSR J1023+0038 from 2019–2021 using a standard pulsar search procedure. We report that we detected a prompt signal with a period compatible with that found in previous observations of PSR J1023+0038. However, there are several reasons (statistical, excess DM, pulse shape, etc.) as to why the association is not likely.

Noise analysis of irregularly sampled VLBI position time series using maximum likelihood estimation

Identification of the optimal noise model for space geodetic time series is crucial for various studies in geodynamics and geodesy. However, the position time series of Very Long Baseline Interferometry (VLBI) are typically irregularly sampled. There is no clear evidence from previous studies to support that the Maximum Likelihood Estimate (MLE) method can allow for stable and reliable noise estimates for irregularly sampled data. To address this issue, we first conducted simulation studies. Results indicate that when the number of data points in the VLBI position time series reaches 300, reliable noise estimations result can be obtained using the MLE. We also found that the higher proportion of white noise a station has, the less influences the data gaps would be on noise estimations. Second, we apply the MLE to investigate the noise properties in the 32 VLBI position time series. About 12 (37.5%) stations exhibit pure white noise, and 15 (46.9%) stations display a combination of white noise and flicker noise. For these stations, the median amplitudes of white noise in the East, North, and Up components are 3.9, 4.6, and 11.9 mm, respectively. Moreover, white and flicker noise amplitudes show a latitude-dependent pattern, with stations located in the southern hemisphere and low latitudes (0-30°N) in the northern hemisphere exhibiting higher noise amplitudes. The remaining approximately 5 stations (15.6%) have the optimal noise model of power law noise with the mean spectral index of −0.32, −0.36, and −0.53 for the East, North, and Up components, respectively. Simply assuming pure white noise can significantly affect velocity uncertainty estimates when compared to using a noise model that includes colored noise. The velocity uncertainty will be underestimated by a factor of 2.9 on average. The effects of a small proportion of colored noise in VLBI data on velocity uncertainty estimation can be ignored only when the time series length exceeds 32.6 years. Additionally, the choice of different noise model can lead to a maximum difference of 0.84 mm for the annual signal of the Up component.

Option Pricing and Portfolio Optimization under a Multi-Asset Jump-Diffusion Model with Systemic Risk

We explore a multi-asset jump-diffusion pricing model, combining a systemic risk asset with several conditionally independent ordinary assets. Our approach allows for analyzing and modeling a portfolio that integrates high-activity security, such as an exchange trading fund (ETF) tracking a major market index (e.g., S&P500), along with several low-activity securities infrequently traded on financial markets. The model retains tractability even as the number of securities increases. The proposed framework allows for constructing models with common and asset-specific jumps with normally or exponentially distributed sizes. One of the main features of the model is the possibility of estimating parameters for each asset price process individually. We present the conditional maximum likelihood estimation (MLE) method for fitting asset price processes to empirical data. For the case with common jumps only, we derive a closed-form solution to the conditional MLE method for ordinary assets that works even if the data are incomplete and asynchronous. Alternatively, to find risk-neutral parameters, the least-square method calibrates the model to option values. The number of parameters grows linearly in the number of assets compared to the quadratic growth through the correlation matrix, which is typical for many other multi-asset models. We delve into the properties of the proposed model, its parameter estimation using the MLE method and least-squares technique, the evaluation of VaR and CVaR metrics, the identification of optimal portfolios, and the pricing of European-style basket options. We propose a Laplace-transform-based approach to computing Value at Risk (VaR) and conditional VaR (also known as the expected shortfall) of portfolio returns. Additionally, European-style basket options written on the extreme and average stock prices or returns can be evaluated semi-analytically. For numerical demonstration, we examine a combination of the SPDR S&P 500 ETF (as a systemic risk asset) with eight ordinary assets representing diverse industries. Using historical assets and options prices, we estimate the real-world and risk-neutral parameters of the model with common jumps, construct several optimal portfolios, and evaluate various basket options with the eight assets. The results affirm the robustness and efficiency of the estimation and evaluation methodologies. Computational results are compared with Monte Carlo estimates.

Estimating amino acid substitution models from genome datasets: a simulation study on the performance of estimated models.

Estimating parameters of amino acid substitution models is a crucial task in bioinformatics. The maximum likelihood (ML) approach has been proposed to estimate amino acid substitution models from large datasets. The quality of newly estimated models is normally assessed by comparing with the existing models in building ML trees. Two important questions remained are the correlation of the estimated models with the true models and the required size of the training datasets to estimate reliable models. In this article, we performed a simulation study to answer these two questions based on simulated data. We simulated genome datasets with different numbers of genes/alignments based on predefined models (called true models) and predefined trees (called true trees). The simulated datasets were used to estimate amino acid substitution model using the ML estimation methods. Our experiments showed that models estimated by the ML methods from simulated datasets with more than 100 genes have high correlations with the true models. The estimated models performed well in building ML trees in comparison with the true models. The results suggest that amino acid substitution models estimated by the ML methods from large genome datasets are a reliable tool for analyzing amino acid sequences.

Research on the Improvement of University Restaurant Service Capability: Based on IE and Flexsim Simulation

<p>According to the example of University restaurant, in order to improve the service ability, the industrial engineering method is used to optimize the meal purchasing process and restaurant layout. Considering the process random events, queuing, popular routes and other factors, the simulation model is established by using Flexsim software. The data are collected by field measurement and random sampling, and the data distribution is verified by maximum likelihood estimation method and goodness of fit test method, and the simulation parameters are calculated. The simulation results show that the optimized model can serve 124 people more than the current model in one hour, and the working rate of the four checkout counters has been improved, which proves that the optimized scheme can effectively alleviate the crowd congestion, improve the service ability, and provide data support for the implementation of the optimization scheme.</p>

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.