Maximum Likelihood Estimation Method Research Articles

Calibration of the Ueno’s Shadow Rate Model of Interest Rates

Shadow rate models of interest rates are based on the assumption that the interest rates are determined by an unobservable shadow rate. This idea dates back to Fischer Black, who understood the interest rate as an option that cannot become negative. Its possible zero values are consequences of negative values of the shadow rate. In recent years, however, the negative interest rates have become a reality. To capture this behavior, shadow rate models need to be adjusted. In this paper, we study Ueno’s model, which uses the Vasicek process for the shadow rate and adjusts its negative values when constructing the short rate. We derive the probability properties of the short rate in this model and apply the maximum likelihood estimation method to obtain the parameters from the real data. The other interest rates are—after a specification of the market price of risk—solutions to a parabolic partial differential equation. We solve the equation numerically and use the long-term rates to fit the market price of risk.

Development of Rainfall Intensity Duration Frequency Curves for Debre Tabor Town, Ethiopia Using Non-stationary Method

Stationary rainfall intensity duration frequency curves have historically influenced urban infrastructure designs. In contrast to the stationary model, which takes constant parameters into account throughout the observation periods, the non-stationary method takes into account changes in the extreme parameters that determine the distribution of precipitation over time. The parameters were estimated using maximum likelihood estimator method. The best model were computed using the R-studio software by comparing information criteria then model parameters, return levels, rainfall intensity are computed. The National Meteorological Agency, situated in Addis Ababa, Ethiopia, provided the essential historical rainfall data of the Debre Tabor rainfall station for this study, Tests and trends were looked for in the rainfall data. Due to its ability to produce the lowest Akaike, corrected Akaike information criteria, and diagnosis test of goodness of fitness Model Type-MV was chosen for Debre Tabor stations. The parameters of the best models were used to forecast the return levels for each of the following return periods: 2, 5, 10, 25, 50, and 100 years. Because the non-stationary technique has varied intensity levels over time, the annual maximum rainfall from the best appropriate model was calculated using its exceedance probability. Using the 95% of exceedance of the return level, the highest rainfall in each fit was determined. In comparison to the stationary model, the non-stationary model produced higher rainfall intensity values. Therefore, when developing IDF curves, the non-stationary approach should be taken into consideration.

Hemoglobin level and common mental disorder among school adolescent girls in Central Ethiopia: Structural Equation Model.

The prevalence of common mental disorder (CMD) and anemia is observed to be on the rise over time, adversely affecting the health and overall quality of life among adolescents. Extensive literature corroborates the significant impact of anemia on cognitive development, intelligence and developmental milestones. Nevertheless, the linkage between hemoglobin level and CMD emerging during adolescence remains relatively unexplored. Thus, the objective of this study was to investigate the association between hemoglobin level and CMD as well as the mediating factor among school adolescent girls residing in Central Ethiopia. A cross-sectional study design was conducted among adolescent girls attending schools in Silti Woreda, Central Ethiopia, comprising a total sample size of 516 individuals during the period from October 2-20, 2023. Hemoglobin level was adjusted for altitude, while CMD was evaluated utilising the summation score of a 20-item Self-Reporting Questionnaire. Data were analysed through fitting Structural Equation Model and the maximum likelihood estimation method. Goodness of fit was assessed using the χ2The -test statistic, Comparative Fit Index, Root Mean Square Error of Approximation, Standardised Root Mean Square Residual, Non-Normed Fit Index, Pclose and coefficient of determination (R2). The prevalence of CMD was 22.3% (95% CI: 18.6%-25.8%). Hemoglobin level (UTE = -0.73, CI: -0.93, -0.53) and experience of morbidity symptoms (UTE = 1.05; CI: 0.74, 1.38) were significantly associated with CMD. Furthermore, hemoglobin level is significantly influenced by morbidity frequency symptoms (UDE = -0.63, CI = -0.77, -0.49) and animal source food (ASF) (UDE = 0.09, CI = 0.01, 0.17). Hemoglobin level has been identified as a significant mediator of the experience of morbidity symptoms and ASF on CMD. However, household food insecurity and wealth index had no significant association with CMD. A significant proportion of adolescent girls face CMD, often linked to a lower hemoglobin level. Having a significant association with CMD, the hemoglobin level is found to mediate a significant effect of morbidity symptom experience and ASF on CMD. Hence, addressing early infection prevention, promoting ASF and treating anemia are promptly needed.

Bayesian estimation under different loss functions for the case of inverse Rayleigh distribution

In this study, the best parameter estimator for the scale parameter of the inverse Rayleigh distribution was determined based on a comparison of the maximum likelihood estimator (MLE) method, the Bayesian generalized squared error loss function (SELF), the Bayesian linear exponential loss function (LINEX LF), and the Bayesian entropy loss function (ELF). The prior distribution chosen was the non-informative prior, namely the Jeffrey prior, and the informative prior using the exponential distribution. The estimator evaluation method used was based on the smallest value of the Akaike information criterion (AIC), corrected Akaike information criterion (AICc), and Bayesian information criterion (BIC). Based on simulation studies and real data, it was found that the best parameter estimator on the data for the scale parameter of the inverse Rayleigh distribution is the Bayes ELF prior exponential .

Financial Fraud Detection Study - Based on Logit Model

The problem of financial fraud has always been a key issue of concern for researchers at home and abroad, and financial fraud of listed companies occurs from time to time at home and abroad, which produces a huge loss of interest for investors as well as the downturn and instability of the capital market, for this reason, it is necessary to carry out a study on the detection of financial fraud. This paper analyzes the financial fraud detection of Chinese listed companies by establishing a Logit model, firstly, obtain the financial statement sample data of Chinese listed companies from CSMAR, and divide the sample into training set and test set with the ratio of 9:1 to preprocess the sample data and fill in the missing values; secondly, this paper selects the financial statement data, and based on the previous research, selects the characteristics that are related to the risk of financial fraud and constitute the risk of financial fraud. high features, and constitute the feature indicators for financial fraud detection; again, since detecting financial fraud is a binary classification problem, the sample is divided into fraudulent companies and normal companies, so this paper studies the financial fraud problem through the discrete choice model in the econometric model, constructs a Logit model, conducts a goodness-of-fit test on the sample data of CSMAR, and estimates the parameters using the method of maximum likelihood estimation ; finally, the test set data is used to test the model's ability to predict financial fraud.

Testing the molecular cloud paradigm for ultra-high-energy gamma ray emission from the direction of SNR G106.3+2.7

Context. Supernova remnants (SNRs) are believed to be capable of accelerating cosmic rays (CRs) to PeV energies. SNR G106.3+2.7 is a prime PeVatron candidate. It is formed by a head region, where the pulsar J2229+6114 and its boomerang-shaped pulsar wind nebula are located, and a tail region containing SN ejecta. The lack of observed gamma ray emission from the two regions of this SNR has made it difficult to assess which region would be responsible for the PeV CRs. Aims. We aim to characterize the very-high-energy (VHE, 0.1–100 TeV) gamma ray emission from SNR G106.3+2.7 by determining the morphology and spectral energy distribution of the region. This is accomplished using 2565 days of data and improved reconstruction algorithms from the High Altitude Water Cherenkov (HAWC) Observatory. We also explore possible gamma ray production mechanisms for different energy ranges. Methods. Using a multi-source fitting procedure based on a maximum-likelihood estimation method, we evaluate the complex nature of this region. We determine the morphology, spectrum, and energy range for the source found in the region. Molecular cloud information is also used to create a template and evaluate the HAWC gamma ray spectral properties at ultra-high-energies (UHE, > 56 TeV). This will help probe the hadronic nature of the highest-energy emission from the region. Results. We resolve one extended source coincident with all other gamma ray observations of the region. The emission reaches above 100 TeV and its preferred log-parabola shape in the spectrum shows a flux peak in the TeV range. The molecular cloud template fit on the higher energy data reveals that the SNR’s energy budget is fully capable of producing a purely hadronic source for UHE gamma rays. Conclusions. The HAWC observatory resolves one extended source between the head and the tail of SNR G106.3+2.7 in the VHE gamma ray regime. The template fit suggests the highest energy gamma rays could come from a hadronic origin. However, the leptonic scenario, or a combination of the two, cannot be excluded at this time.

Topology sensing of FANET under missing data

The topological structure of a flying ad hoc network (FANET) is crucial to understand, explain, and predict the behavior of unmanned aerial vehicle (UAV) swarms. Most studies focusing on topology sensing use perfect observations and complete datasets. However, the received signal dataset, being non-cooperative, commonly encounters instances of missing data, causing the performance of the existing algorithms to degrade. We investigate the issue of topology sensing of FANET based on external observations and propose a topology sensing method for FANET with missing data while introducing link-prediction methods to correct the topology inference results. First, we employ multi-dimensional Hawkes processes to model the communication event sequence in the network. Subsequently, to solve the problem in which the binary decision threshold is difficult to determine and cannot be adapted to the application scenario, we propose an extended multi-dimensional Hawkes model suitable for FANET and use the maximum likelihood estimation method for topology inference. Finally, to solve the problem of the low accuracy of inference results owing to missing data, we perform community detection on the observation network and combine the community detection and inference results to construct a mixed connection probability matrix, based on which we perform topology correction. The results of the analysis show that the topology sensing method proposed in this study is robust against missing data, indicating that it is an effective solution for solving this problem.

The Representative Points of Generalized Alpha Skew-t Distribution and Applications

Assuming the underlying statistical distribution of data is critical in information theory, as it impacts the accuracy and efficiency of communication and the definition of entropy. The real-world data are widely assumed to follow the normal distribution. To better comprehend the skewness of the data, many models more flexible than the normal distribution have been proposed, such as the generalized alpha skew-t (GAST) distribution. This paper studies some properties of the GAST distribution, including the calculation of the moments, and the relationship between the number of peaks and the GAST parameters with some proofs. For complex probability distributions, representative points (RPs) are useful due to the convenience of manipulation, computation and analysis. The relative entropy of two probability distributions could have been a good criterion for the purpose of generating RPs of a specific distribution but is not popularly used due to computational complexity. Hence, this paper only provides three ways to obtain RPs of the GAST distribution, Monte Carlo (MC), quasi-Monte Carlo (QMC), and mean square error (MSE). The three types of RPs are utilized in estimating moments and densities of the GAST distribution with known and unknown parameters. The MSE representative points perform the best among all case studies. For unknown parameter cases, a revised maximum likelihood estimation (MLE) method of parameter estimation is compared with the plain MLE method. It indicates that the revised MLE method is suitable for the GAST distribution having a unimodal or unobvious bimodal pattern. This paper includes two real-data applications in which the GAST model appears adaptable to various types of data.

Predicting shear strength of corroded RC columns: A probabilistic model with enhanced Gaussian Process Regression

This study proposes a new probabilistic model for predicting the shear strength of corroded reinforced concrete (RC) columns. The probabilistic model addresses limitations of traditional methods by combining mechanical understanding with enhanced Gaussian Process Regression (GPR). A novel mean function for enhanced GPR is developed first based on the shear resistance mechanism of corroded RC columns. Then the hyper-parameters of both the mean function and kernel function for the enhanced GPR are optimized using the maximum likelihood estimation method. This leads to the establishment of the probabilistic model that is based on the enhanced GPR. Finally, the accuracy and effectiveness of the enhanced GPR probabilistic model are validated by comparing it with both traditional mechanical models and machine learning models. The results indicate that the proposed probabilistic model can not only describes the probabilistic characteristics for shear strength of corroded RC columns based on probability density functions, but also provides an efficient calibration method for traditional prediction models based on confidence intervals.

Real‐Time Nuclear Magnetic Resonance Detection Using Maximum Likelihood Estimation with Single‐Shallow‐Nitrogen‐Vacancy Centers in Quantum Heterodyne Measurements

Single‐nitrogen‐vacancy (NV) centers in diamond are highly promising quantum nuclear magnetic resonance (NMR) sensors. However, their exposure to many sources of noise, such as surface impurities, shot noise from avalanche photodiode overlaps, and spin‐state projection errors inherent in quantum systems, limits their usefulness. Often, long measurement durations are required to accumulate sufficient data for NMR signal detection via fast Fourier transform spectrometry. For practical reasons, methods to shorten the necessary accumulation time for NMR signal detection are greatly desired. In this article, an on‐line formulation of maximum likelihood estimation (MLE) signal processing for quantum heterodyne NMR measurements is presented as a step toward this goal. This MLE method reduces the required data accumulation time by orders of magnitude and provides good estimates of target frequency locales in real time. These results are significant to practitioners of NMR detection with single‐NV centers in diamond who require a quick litmus test for potential signals when probing a wide area.

Bayesian mixture model for accurate assessment of monthly maximum wind speed: A case study in Gwadar

Assessment of monthly maximum wind speed (MMWS) is essential in various environmental disciplines, including architectural risk assessment, climatology, renewable energy sources, building design, and agricultural activities. The distribution of wind speed is an important module of its development. Presently, several mixing distributions have been suggested for fitting the theoretical maximum wind speed distributions. However, the drawback of various distribution elements is the outcome of numerous fitting presentations, and it is challenging to choose the best form of single distribution to employ when building a hybrid model. In order to solve those difficulties, utilizing the mixtures of Sine-skewed-von Mises distributions (MSS-VM) with various prior parameter distributions is extended in the present study. In this research, the assessment of MMWS employing the maximum-likelihood estimation (MLE) method is taken into consideration for the wind speed data from the Pakistan province of Baluchistan Gwadar station. The results of the Anderson Darling (AD), Chi-square, BIC, and AIC tests, as well as the Kolmogorov Smirnov (KS) test, indicated that MSS-VM was the best distribution for the Gwadar station. The suggested models automatically find the optimum number of elements, in addition to having more appropriate performance. The outcomes demonstrate that MSS-VM performance is more suitable than other heterogeneous and single-distribution models. The design estimations derived using the Bayesian mixture distribution provide a sense of the highest wind speed that will occur across a particular area. It is therefore crucial for designers and policymakers in the planning, designing, and building of various structures.

Fast and Robust Noise Background Modeling and Quasiperiodic Oscillation Detection for Astronomical Time Series

Spectrum with confidence levels is a commonly used method for quasiperiodic oscillation (QPO) detection, but it is prone to yield false positives for two reasons: poor choice and/or biased modeling of the null hypothesis (or noise background). Motivated by this, we propose a new time-domain maximum-likelihood estimation method, which can quickly and accurately estimate the noise background free from background trends, spectra peaks, and even QPOs. Our method provides a wide range of candidate stochastic models (e.g., conventional first-order autoregressive, power law, generalized Gauss–Markov, Matérn, and damped random walk), some of which have not been considered previously. Some pitfalls (e.g., detrending) in previous QPO detections are also correctly processed to minimize the false detections. Along with the multitaper method and wavelet, we revisit QPO detection in the X-ray emission from the active galaxies RE J10341+396 and 1H 0707-495, and point out why the significance levels of the QPO at ∼2.6 × 10−4 Hz would be different in previous detections and reduced if the whole observation duration is considered. Our algorithm can be easily extended to other branches of astrophysics and beyond.

Optimal Subsampling for Functional Quasi-Mode Regression with Big Data

We propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Using data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against nonnormal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this article are available online.

Comparison between estimates of beta regression model using MSE

The multiple linear regression analysis shows the effects of explanatory variables on the dependent variable. Its function is to represent data to understand the shape and nature of the relationship between explanatory variables and the response variable. One of the main problems faced by linear regression is the nature of the data, as sometimes it does not follow a normal distribution. This has led to the emergence of different types of linear regression models such as the beta regression model, where the data of the dependent variable is less than one and confined within the period (0,1), and the data is relative and decimal. Non-traditional methods will be used to estimate beta regression parameters because some traditional methods do not provide suitable and accurate results when dealing with one of the main problems encountered in regression, which is multicollinearity. To address this issue, we used some methods include The Maximum Likelihood Estimation (MLE), ridge regression, modified Liu, and Ozkale and Kaciranlar method. Shrinking parameters are proposed for each method, and a comparison between the methods is conducted using the Mean Squared Error comparison criterion through a simulation experiment with two approaches, the simulation results showed that the ridge regression method is the best for the first and second methods of simulation. Paper type Research Paper

A New Extension of Topp-Leone Distribution (NETD) Using Generalized Logarithmic Function

Study’s Excerpt New Extension of Topp-Leone Distribution (NETD), derived using a generalized logarithm function, expanding the Topp-Leone family of distributions, is introduced. Mathematical properties of the NETD, including its quantile function, moments, Renyi entropy, and order statistics were investigated. The model demonstrates superior goodness-of-fit over existing models across four real-world datasets. Full Abstract In this study, we introduce a novel statistical model termed the New Extension of Topp-Leone Distribution (NETD), constructed using a generalized logarithm function. The derivation of the cumulative density function (CDF) and the probability density function (PDF) for this new distribution is thoroughly detailed. A validity test was conducted to confirm the legitimacy of the proposed NETD, and the results affirm that it is indeed a valid probability distribution. We investigate several key mathematical and statistical properties of the NETD, including the quantile function, moments, Renyi entropy, probability-weighted moments, and order statistics. These properties provide a comprehensive understanding of the distribution's behaviour and characteristics. To estimate the parameters of the NETD, we applied the Maximum Likelihood Estimation (MLE) method, which is known for its efficiency and asymptotic properties. The flexibility, versatility, and performance of the NETD were evaluated using four diverse real-world datasets. Through the application of model selection criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Corrected Akaike Information Criterion (CAIC), and Hannan-Quinn Information Criterion (HQIC), we demonstrated that the NETD exhibits superior goodness-of-fit compared to existing variants of the Topp-Leone distribution. Our findings suggest that the NETD is a robust and adaptable distribution, capable of effectively modelling a wide range of empirical data. This new extension not only broadens the applicability of the Topp-Leone family of distributions but also enhances the toolkit available for statistical analysis and modelling in various fields.

Analysis of Reliability for the Electrical Industries Company in Diyala using Modified Extension Weibull Distribution (An Application and Simulation study)

In this paper defining modified extension Weibull distribution, reliability function and hazerd function, we explain the maximum likelihood method under type one censoring sample. The censored samples play an important role in reliability analysis .In this paper we estimate and derived modified extension Weibull distribution whith three parameters under the censored samples type one by maximum likelihood estimation method depend on Newton-Raphson method. Then we applied simulation procedure using Monte-Carlo technique to estimate reliability function under different samples sizes and various initial values for the parameters for all estimated parameters of modified extension Weibull model by used MATLAB program. Finally we find the probability density function f(t), reliability function R(t),and hazard function h(t) for real data which get it from (Diyala province Company) is one of the formations of the Ministry of Industry and Minerals. Paper type: Research paper

Analysis of Reliability for the Electrical Industries Company in Diyala using Modified Extension Weibull Distribution (An Application and Simulation study)

In this paper defining modified extension Weibull distribution, reliability function and hazerd function, we explain the maximum likelihood method under type one censoring sample. The censored samples play an important role in reliability analysis .In this paper we estimate and derived modified extension Weibull distribution whith three parameters under the censored samples type one by maximum likelihood estimation method depend on Newton-Raphson method. Then we applied simulation procedure using Monte-Carlo technique to estimate reliability function under different samples sizes and various initial values for the parameters for all estimated parameters of modified extension Weibull model by used MATLAB program. Finally we find the probability density function f(t), reliability function R(t),and hazard function h(t) for real data which get it from (Diyala province Company) is one of the formations of the Ministry of Industry and Minerals. Paper type: Research paper

A New Lifetime Distribution and its Application to Cancer Data

Introduction: Recently, researchers have introduced new generated families of univariate lifetime distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution or compounding two distributions to get more flexibility in fitting data in different areas such as medical sciences, environmental sciences, and engineering. The addition of parameter(s) has been proven useful in exploring tail properties and for improving the goodness-of-fit of the family of the proposed distributions. Methods:A new Three-Parameter Weibull-Generalized Gamma distribution which provides more flexibility in modeling lifetime data is developed using a two-component mixture of Weibull distribution (with parameters θ and λ) and Generalised Gamma distribution (with parameters α=4,θ and λ). Some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, moment generating function, Renyi entropy and order statistics are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study is performed to examine the performance of the maximum likelihood estimators of the parameters. Results: Real life applications of the proposed distribution to two cancer datasets are presented and its fit was compared with the fit attained by some existing lifetime distributions to show how the Three-Parameter Weibull-Generalized Gamma distribution works in practice Conclusion: The results suggest that the proposed model performed better than its competitors and it’s a useful alternative to the existing models.

The Two Component Generalized Finite Erlang Mixture and its Properties and Special Cases

This research proposes the construction of a two-component generalized finite Erlang mixture with four parameters. Three distinct cases of this mixture are presented, differing in their mixing weights and corresponding component probability (Erlang) distributions. Special cases of these mixtures, including the one-, two-, and three-parameter finite Erlang mixtures, have also been derived. The statistical properties examined for these mixtures include the distribution function, survival function, hazard function, moment generating function, raw and central moments, mean, variance, coeffcient of skewness, coeffcient of kurtosis, and order statistics. Parameter estimation for the finite Erlang mixtures was conducted using both the method of moments and maximum likelihood estimation. Furthermore, the 4-parameter mixed Erlang distributions were applied to a real dataset on the relief times of patients receiving an analgesic, to evaluate their goodness of fit. The results demonstrate the potential of these mixtures to provide robust modeling for empirical data, suggesting their applicability in various statistical and practical contexts.

Association of crop commercialization and rural households' multidimensional poverty using targeted maximum likelihood estimation

Recent evidence shows the highest prevalence of multidimensional poverty in the world. To alleviate poverty, Ethiopia is investing in stimulating agricultural commercialization for poverty reduction, driving sustainable economic growth, and creating jobs. Therefore, this study investigated the causal relationship between crop commercialization and multidimensional poverty across Ethiopian rural households using the Ethiopia Socioeconomic Survey 2018/19 data, which included 1129 crop commercialized and 1585 completely subsistence rural households. Moreover, this study also examined the causal effect of crop commercialization on the multidimensional poverty mediated by mobile phone ownership status. The study used the double robust method of the augmented inverse probability of treatment weighted (AIPTW) and targeted maximum likelihood estimation (TMLE) methods. The result showed that crop commercialization has an association with multidimensional poverty. Specifically, the TMLE with a default super learner model estimates were the most precise and suggest that the prevalence of risk of being multidimensionally poor among rural households who were crop commercialized is 12.2 % lower than for those who were completely subsistence households. Thus, it is important to have more robust policies like crop commercialization to target rural multidimensional poverty reduction. Moreover, the controlled direct effect estimation analyses showed that crop-commercialized rural households reduced the adjusted risk of multidimensional poverty by; 12 % for those who owned mobile phones and 7.8 % for those who did not. To ensure sustainable livelihoods for rural multidimensional poor households, it is necessary to have a multidisciplinary policy intervention to promote crop commercialization through the spread of mobile phones in rural areas.