Maximum Likelihood Estimation Method Research Articles

Neutrosophic Laplace Distribution with Properties and Applications in Decision Making

This paper introduces the concept of the neutrosophic Laplace distribution ( ), a probability distribution derived from the Laplace distribution. The offers a versatile framework for describing various real-world problems. We highlight the neutrosophic extension of the Laplace distribution and explore its applications in different areas. Extensive investigations into the mathematical properties of the distribution are presented, including the derivation of its probability density function, mean, variance, raw moment, skewness, and kurtosis. To estimate the parameters of the , we employ the method of maximum likelihood (ML) estimation within a neutrosophic environment. Furthermore, we conduct a simulation study to assess the effectiveness of the maximum likelihood approach in estimating the parameters of this new distribution. The findings demonstrate the potential of the in modeling and analyzing real-world phenomena. Eventually, some illustrative examples related to system reliability are provided to clarify further the implementation of the neutrosophic probabilistic model in real-world problems.

Interaction and Segmentation Analysis in Green Science: A Maximum Likelihood Approach

In the context of the current environmental crisis, the importance of effective communication strategies for promoting sustainable development is undeniable. This article is devoted to the study of audience segmentation methods in green science initiatives using the Maximum Likelihood Estimation (MLE) method. The main focus is on the development of approaches that allow for more accurate and effective division of target groups, such as scientists, politicians and activists in order to maximize the influence on each of them. The study presents the results of the analysis of interactions within and between communities, which allows for the optimization of communication strategies for different audiences. The application of MLE in community segmentation emphasizes its importance for increasing the effectiveness of environmental initiatives aimed at achieving sustainable development.

Modeling COVID-19 cases using NB-INGARCH and ARIMA models: A case study in Iligan City, Philippines

Modeling COVID-19 cases using count data approach has been scarce in the Philippine setting. This study compares the NB-INGARCH with the traditional ARIMA in modeling daily COVID-19 cases in Iligan City (August 14, 2020 – October 31, 2021). We employ the maximum likelihood estimation method and compare the models using the Akaike's information criterion (AIC). Empirical results reveal that the NB-INGARCH(7,0) outperforms ARIMA(2,1,3) in terms of forecast evaluation measures. However, the results show that rainfall and air pressure have no significant effects on the cases. We conclude that the NB-INGARCH model is a viable alternative approach to modeling count time series.

Estimation for stochastic differential equation mixed models using approximation methods

<abstract><p>We used a class of stochastic differential equations (SDE) to model the evolution of cattle weight that, by an appropriate transformation of the weight, resulted in a variant of the Ornstein-Uhlenbeck model. In previous works, we have dealt with estimation, prediction, and optimization issues for this class of models. However, to incorporate individual characteristics of the animals, the average transformed size at maturity parameter $ \alpha $ and/or the growth parameter $ \beta $ may vary randomly from animal to animal, which results in SDE mixed models. Obtaining a closed-form expression for the likelihood function to apply the maximum likelihood estimation method is a difficult, sometimes impossible, task. We compared the known Laplace approximation method with the delta method to approximate the integrals involved in the likelihood function. These approaches were adapted to allow the estimation of the parameters even when the requirement of most existing methods, namely having the same age vector of observations for all trajectories, fails, as it did in our real data example. Simulation studies were also performed to assess the performance of these approximation methods. The results show that the approximation methods under study are a very good alternative for the estimation of SDE mixed models.</p></abstract>

Neutrosophic Beta-Lindley distribution: Mathematical properties and modeling bladder cancer data

The beta-Lindley distribution is used in the field of survival analysis to imitate techniques employed with human lifetime data. The neutrosophic beta-Lindley distribution (NBL) is designed to characterize a range of survival statistics with indeterminacies. The established distribution is used, for instance, to describe unknown data that is roughly favorably skewed. The evolved NBL's three main statistical characteristics—the neutrosophic moments, hazard, and survival functions are covered in this article. Additionally, The well-known maximum likelihood estimation method is used to estimate the neutrosophic parameters. To check if the predicted neutrosophic parameters were met, a simulation study was done. Notably, talks of prospective NBL uses in the real world have made use of actual data. Actual data were utilized to show how well the suggested model performed in compared to the current distributions.

The new Topp-Leone exponentied exponential model for modeling financial data

<abstract><p>We proposed in this article a new three-parameter distribution, which is referred as the Topp-Leone exponentiated exponential model is proposed. It is used in modeling claim and risk data applied in actuarial and insurance studies. The probability density function of the suggested distribution can be unimodel and positively skewed. Different distributional and mathematical properties of the TL-EE model were provided. Furthermore, we established a maximum likelihood estimation method for estimating the unknown parameters involved in the model, and some actuarial measures were calculated. Also, the potential of these actuarial statistics were provided via numerical simulation experiments. Finally, two real datasets of insurance losses were analyzed to prove the performance and superiority of the suggested model among all its competitors distributions.</p></abstract>

Higher-Order INAR Model Based on a Flexible Innovation and Application to COVID-19 and Gold Particles Data

INAR models have the great advantage of being able to capture the conditional distribution of a count time series based on their past observations, thus allowing it to be tailored to meet the unique characteristics of count data. This paper reviews the two-parameter Poisson extended exponential (PEE) distribution and its corresponding INAR(1) process. Then the INAR of order p (INAR(p)) model that incorporates PEE innovations is proposed, its statistical properties are presented, and its parameters are estimated using conditional least squares and conditional maximum likelihood estimation methods. Two practical data sets are analyzed and compared with competing INAR models in an effort to gauge the performance of the proposed model. It is found that the proposed model performs better than the competitors.

Generalized asymmetric mixture normal distribution: properties and applications

A new class of skew generalized normal distribution as a generalization of the skew-normal distribution of Arellano-Valle (Commun. Statist. Theor. Meth., 2004) and Kumar and Anusree (Commun. Statist. Theor. Meth., 2015) are considered. Several statistical properties of the proposed class of distributions are investigated and the location-scale extension of the model is obtained. Further, the estimation of its parameters by the method of maximum likelihood estimation is discussed and the distribution has been fitted to specific real-life data sets to illustrate the model’s usefulness. In addition, a brief simulation study is conducted for examining the performance of likelihood estimators of the parameters of the proposed model.

Pricing of Fisheries Microinsurance Premiums using the Poisson-Exponential Aggregate Distribution Approach

Engaged in pond aquaculture is currently an attractive choice amid the high demand for fish in the market. Entrepreneurial opportunities in the pond fish farming sector are increasingly open, although the risk of crop failure remains, both due to weather factors and livestock processes. Crop failure can have a significant financial impact on pond fishery farmers. Therefore, there is a need for special insurance to protect against financial losses due to risks that can occur, namely Micro Fisheries Insurance. Microinsurance is a type of insurance product specifically designed for people with low income levels, offers features and administration that is simple, easily accessible, has an economical price, and a fast compensation settlement process. The focus of this study is to calculate premium prices by applying an aggregate risk model approach. The data used are the number of events and the magnitude of losses due to crop failure in shrimp pond cultivation in Pandeglang Regency in the period January 1, 2019-January 1, 2021. Data on the number of events follow the Poisson distribution, while data on the magnitude of losses follow the Exponential distribution. Next, it uses the Maximum Likelihood Estimation (MLE) method to calculate parameter estimation. The average and variance of aggregate risk is used to determine the size of the premium. The premium selection results in this study amounted to Rp42,005,600. The amount of the premium reflects the collective premium resulting from the calculation based on the standard deviation principle.

Determining Pure Premium of Motor Vehicle Insurance with Generalized Linear Models (GLM)

Motor vehicle insurance guarantees protection, coverage, and compensation for the risks of accidents, damages, and loss of motor vehicles. It is crucial for companies to determine appropriate insurance premium rates as a preventive measure to avoid difficulties in meeting claims filed by policyholders. This research aims to determine the pure premium of motor vehicle insurance using the Generalized Linear Models (GLM) method, which utilizes the concept of a general linear relationship between independent variables and the dependent/response variable, as well as identifying motor vehicle characteristics that influence the determination of pure premiums. The data used in this study is from Swedish motor vehicle insurance. The research aims to determine the pure premium in the data by modeling claim frequency using the Poisson distribution and claim severity using the Gamma distribution, depending on the significantly influential characteristics. The Maximum Likelihood Estimation method is employed for parameter estimation. After conducting the research, the estimated parameters , , and the pure premium of motor vehicle insurance are found to be 35,572,223.27 kr, with the characteristics influencing the pure premium being the distance traveled by the vehicle, the insured's geographic zone, and the no-claim bonus.

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>