Maximum Likelihood Estimation Approach Research Articles

The Efficiency of Hazard Rate Preservation Method for Generating Discrete Rayleigh–Lindley Distribution

In this study, we introduce two novel discrete counterparts for the Rayleigh–Lindley mixture, constructed through the application of survival and hazard rate preservation techniques. These two-parameter discrete models demonstrate exceptional adaptability across various data types, including skewed, symmetric, and monotonic datasets. Statistical analyses were conducted using maximum likelihood estimation and Bayesian approaches to assess these models. The Bayesian analysis, in particular, was implemented with the squared error and LINEX loss functions, incorporating a modified Lwin Prior distribution for parameter estimation. Through simulation studies and numerical methods, we evaluated the estimators’ performance and compared the effectiveness of the two discrete adaptations of the Rayleigh–Lindley distribution. The simulations reveal that Bayesian methods are especially effective in this setting due to their flexibility and adaptability. They provide more precise and dependable estimates for the discrete Rayleigh–Lindley model, especially when using the hazard rate preservation method. This method is a compelling alternative to the traditional survival discretization approach, showcasing its significant potential in enhancing model accuracy and applicability. Furthermore, two real data sets are analyzed to assess the performance of each analog.

Role of financial openness in Ghana’s financial sector development episode

PurposeThis paper aims to reexamine the relationship between financial openness and financial development in Ghana.Design/methodology/approachThe study applied maximum likelihood estimation and autoregressive distributed lag approach and tested Granger causality using quarterly data from 1990:1 to 2020:4.FindingsThis study revealed a long-run equilibrium relationship between financial openness and development, indicating that financial openness is a critical factor in Ghana’s financial development. Therefore, the study recommends with caution that policies aimed at promoting financial openness could be an effective way to encourage sustainable financial development in Ghana, as financial openness alone may not bring the desired outcome.Research limitations/implicationsThe study contributes to the existing body of knowledge by providing empirical evidence of the link between financial openness and financial sector development in Ghana. Future research could delve deeper into the mechanisms through which financial openness affects financial development, exploring potential channels and transmission mechanisms.Practical implicationsThe findings suggest that policymakers, particularly the Ministry of Finance and the Bank of Ghana, should prioritize policies aimed at promoting financial openness. This includes continued efforts toward financial liberalization and creating an environment conducive to domestic and international financial transactions. Moreover, policies aimed at increasing trade openness, boosting real GDP and maintaining moderate real interest rates are essential for fostering financial sector development.Social implicationsEnhancing financial sector development can have significant implications for society, including increased access to financial services, improved economic opportunities and enhanced overall economic stability. By promoting financial openness and development, policymakers would contribute to poverty reduction, job creation and overall socio-economic development. The study bridges the gap between theory and practice by providing empirical evidence supporting the theoretical proposition that financial openness stimulates financial sector development.Originality/valueThis study fills a crucial gap in the literature on the effects of financial openness on Ghana’s financial sector development. It focuses on Ghana, which liberalized its financial sector in 1988 as part of the overall economic reforms in 1983, and this justifies the starting point of this paper in 1990, as there are no adequate data before 1990. The study uses principal component analysis to construct an index that measures financial development. The study considers the recent financial crises in Ghana in 2017 and underscores the importance of understanding the link between financial openness and financial development, which becomes useful for policymakers and researchers studying financial system development in sub-Saharan Africa which includes Ghana.

Pairwise Likelihood Estimation of the 2PL Model with Locally Dependent Item Responses

The local independence assumption is crucial for the consistent estimation of item parameters in item response theory models. This article explores a pairwise likelihood estimation approach for the two-parameter logistic (2PL) model that treats the local dependence structure as a nuisance in the optimization function. Hence, item parameters can be consistently estimated without explicit modeling assumptions of the dependence structure. Two simulation studies demonstrate that the proposed pairwise likelihood estimation approach allows nearly unbiased and consistent item parameter estimation. Our proposed method performs similarly to the marginal maximum likelihood and pairwise likelihood estimation approaches, which also estimate the parameters for the local dependence structure.

A New Cubic Transmuted Inverse Weibull Distribution: Theory and Applications

This paper introduces a new cubic transmutation of the inverse Weibull distribution, known as a cubic transmuted inverse Weibull distribution. The model is thought to be useful for the analysis of complex life data, modeling failure times, accessing product reliability, and many other fields like economics, hydrology, biology, and engineering. Some statistical features of the proposed distribution are explored. These include moments, generating functions, quantile functions, reliability functions, and hazard rate functions. The distribution of order statistics for the proposed cubic transmuted inverse Weibull distribution is also studied. The maximum likelihood estimation approach is used to estimate the model parameters. The effectiveness of the estimation is investigated through extensive simulation study. The suitability of the proposed distribution has been studied by using five real-life datasets. It is found that the proposed distribution is the most suitable fit for the used data sets.

Application of Odd Lomax log-logistic distribution to cancer data

The effectiveness of the parental distribution is modified in this article by adding flexibility, allowing it to capture all characteristics of the provided real-world data sets. This is accomplished by using the T-X class of distributions to generalize the parental distribution. Odd Lomax log-logistic distribution or OLLLD in short, is the name of the generalized parental distribution. The fundamental statistical properties of OLLLD are explicitly expressed. The maximum likelihood estimation approach is used to estimate the unidentified OLLLD parameters. In order to investigate the fit of the approach employed in estimating the parameters of OLLLD, the data are generated and an investigation done. Again, the ability of OLLLD is evaluated by fitting it to the real survival time data set of breast cancer.

Regression analysis of group-tested current status data

Summary Group testing is an effective way to reduce the time and cost associated with conducting large-scale screening for infectious diseases. Benefits are realized through testing pools formed by combining specimens, such as blood or urine, from different individuals. In some studies, individuals are assessed only once and a time-to-event endpoint is recorded, for example, the time until infection. Combining group testing with this type of endpoint results in group-tested current status data (Petito & Jewell, 2016). To analyse these complex data, we propose methods that estimate a proportional hazard regression model based on test outcomes from measuring the pools. A sieve maximum likelihood estimation approach is developed that approximates the cumulative baseline hazard function with a piecewise constant function. To identify the sieve estimator, a computationally efficient expectation-maximization algorithm is derived by using data augmentation. Asymptotic properties of both the parametric and nonparametric components of the sieve estimator are then established by applying modern empirical process theory. Numerical results from simulation studies show that our proposed method performs nominally and has advantages over the corresponding estimation method based on individual testing results. We illustrate our work by analysing a chlamydia dataset collected by the State Hygienic Laboratory at the University of Iowa.

Study of a bounded interval perks distribution with quantile regression analysis

AbstractIn this article, a novel bounded interval model called the unit‐Perks model is developed by suitably transforming the positive random variable of the Perks distribution. Numerous statistical features of the bounded interval Perks model are being explored based on the expansion of the density function. Eight distinct estimation approaches are being used to estimate the parameters of the unit‐Perks model. A throughout simulation analysis is also included to evaluate the precision of the resulting estimators from eight estimating approaches. Two real bounded interval data sets are being utilized to investigate the practical applicability of the unit‐Perks model. A comparison is also made to determine which method of estimation works better for the given model. According to a comparison of eight different estimation approaches, the maximum likelihood estimation approach outperformed than the other seven estimating approaches. The unit‐perks model is then used to introduce the quantile regression model named as quantile unit‐Perks distribution. Application to real data set for the quantile unit‐Perks distribution is also performed. The quantile residuals are used for the residual analysis of the fitted regression model. On the basis of mathematical, computational, and pictorial evidences, it is concluded that the presented model exhibited greater modeling capabilities.

Fast and noise-robust quantum state tomography based on ELM

This paper proposed a quantum state tomography approach based on the extreme learning machine (ELM), which is available in the reconstruction of quantum states via a lightweight neural network. The key step of the proposed tomography approach is to employ the ELM to approximate the complex mapping between the measurement values sequence and the real density matrix. After obtaining the output of the ELM-based estimator, a matrix transformation technique is used to make the network outputs satisfy quantum state constraints. Compared with deep learning-based tomography approaches, our proposed ELM-based approach enables both high-fidelity and high-efficiency quantum state tomography with only one training process under the condition of very few numbers of training samples, network layers and hidden layer nodes. In addition, the proposed tomography approach is robust to noisy measurement values, since the ELM-based estimator is quite lightweight. Simulations on the tomography of eigenstates, superposition states and mixed states are presented to verify our theoretical findings. Also, the superiority of the ELM-based tomography approach is demonstrated in comparison with that based on the radial basis function network, convolutional neural network and maximum likelihood estimation approach.

Pareto exponentiated log-logistic distribution (PELL) with an application to Covid-19 data

Recently, the Covid-19 pandemic has caused tremendous trauma over the world, leading to psychological and behavioral harm in addition to social and economic instabilities. Even though the pandemic’s statistical analysis is still in progress, it is essential to fit Covid-19 data using statistical models to prevent further harm. In order to model Covid-19 data, the study suggests a novel family of distributions called the exponentiated log-logistic family. The basic Pareto distribution is transformed as a special case, and certain properties of the proposed distribution are discussed. To estimate the model parameters, the maximum likelihood estimation approach is used. Moreover, a simulation study is conducted to ensure the consistency of parameter estimates. Three real-world datasets relevant to the Covid-19 pandemic are examined to demonstrate the applicability of the suggested approach. The proposed model is shown to be more flexible and provides an improved fit to describe the Covid-19 data when compared to various alternative forms of Pareto distribution.

Reliability Analysis and Its Applications for a Newly Improved Type-II Adaptive Progressive Alpha Power Exponential Censored Sample

Recently, a newly improved Type-II adaptive progressive censoring plan was devised, which can successfully ensure that the test length will not surpass a particular threshold period. In this study, we explore the statistical inference of the alpha power exponential distribution in the context of improved adaptive progressive Type-II censored data. The parameters, reliability, and hazard functions were estimated from both classical and Bayesian viewpoints using this censoring plan. To begin, we applied the maximum likelihood estimation approach to obtain parameter, reliability, and hazard function estimators. Following that, the approximate confidence intervals for the aforementioned metrics were derived, assuming the asymptotic normality traits of the maximum likelihood estimators. Additionally, by employing the Bayesian method via the Markov chain Monte Carlo technique, the point estimators and highest posterior density intervals of various parameters were created based on the symmetric squared error loss. A simulation study that incorporates numerous scenarios was used to assess the effectiveness of various estimation methodologies. The optimal progressive censorship plans are then discussed based on a set of criteria. Finally, three applications from the engineering and medical domains have been offered as examples.

On Power Chris-Jerry Distribution: Properties and Parameter Estimation Methods

In this study, we introduce the "Power Chris-Jerry" distribution, conducting a comprehensive analysis of its fundamental mathematical characteristics and an extensive exploration of various crucial aspects. These encompass investigations into its mode, quantile function, moments, coefficient of skewness, kurtosis, moment generating function, stochastic ordering, distribution of order statistics, reliability analysis, and mean past lifetime. Furthermore, we provide an in-depth assessment of four distinct parameter estimation methodologies: maximum likelihood estimation (MLE), Least Squares (LS), maximum product spacing method (MPS), and the Method of Cram`er-von-Mises (CVM). Our investigation uncovers a consistent pattern wherein the MLE, LS, and CVM approaches consistently yield underestimated parameter values. Intriguingly, we observe a consistent trend of decreasing Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and BIAS across all estimation techniques as sample sizes increase. Remarkably, our simulation results consistently favor the Maximum Product Spacing (MPS) method, highlighting its superiority in generating estimates with smaller MSE values across a broad spectrum of parameter values and sample sizes. These findings emphasize the robustness and dependability of the MPS estimator, offering valuable insights and practical guidance for both practitioners and researchers engaged in probability distribution modeling.

Remaining useful life prediction of equipment considering dynamic thresholds under the influence of maintenance

A novel approach for predicting remaining useful life (RUL) is proposed for situations where maintenance threshold and failure threshold exhibit dynamic behavior due to uncertainties in degradation and the influence of detection strategies during maintenance processes. The approach introduces maintenance threshold error to establish a multi-stage maintenance-impact degradation model with dynamic maintenance threshold based on the Wiener process. This model considers the impact of maintenance on degradation rate, amount, and path. Moreover, by using the first hitting time (FHT) and introducing failure threshold error to reflect the dynamic behavior of the failure threshold, the formula for predicting equipment RUL is derived. The model parameters are estimated using both the maximum likelihood estimation (MLE) approach and Bayesian formula. The proposed approach was validated with simulation data and gyroscope degradation data, and the results demonstrate its ability to effectively enhance the precision of equipment RUL prediction.

Interpreting effective hydrologic depth estimates derived from soil moisture remote sensing: A Bayesian non-linear modeling approach

The water balance equation (WBE) describes how net water inflows into a system relate to storage changes over a time span (dt). This equation is fundamental in hydrologic studies, helping to determine water supply and elucidate the terrestrial water cycle. For land surface, the WBE links water fluxes like precipitation (P), evapotranspiration, drainage and surface runoff to soil moisture (SM) changes within a discrete soil layer (dSM). While traditional focus has been on the precision of the WBE-estimated fluxes, there has been increased recent interest in fitting the WBE using remotely-sensed P and SM data to infer water balance parameters, particularly the ΔZ that associates net fluxes and dSM within dt. However, obtaining physically interpretable WBE parameters like ΔZ is a potentially ill-posed problem due to simplifying assumptions imbedded in a WBE implementation, missing hydrologic constraints, and accuracy and revisit limitations in available remotely-sensed data. In addition, WBE parameters obtained from classical maximum likelihood estimation approaches can vary significantly. Here, using a Bayesian non-linear modeling approach, we demonstrate how these factors can impede the identification of useful ΔZ estimates. Specifically, we find that ΔZ estimates are likely to be spuriously biased due to limitations in the temporal resolution and accuracy of satellite-based dSM estimates – as well as the neglect of other hydrological components in the WBE. Maps showcasing the lower and upper bounds of the 94 % HDI from our Bayesian model further elucidate these biases. Results suggests that estimates of ΔZ are effective in nature and great care should be exercised when attempting to interpret them physically. Instead, they should be defined as effective parameters reflecting the characteristics of their fitted remotely-sensed data sets. Drawing from current progress, accurate ΔZ estimates, informed by more advanced remote sensing techniques and precise WBE, will enhance our understanding of terrestrial water cycle.

Application of Generalized Poisson Regression for the development of modeling motorcycle accidents based on rider characteristics

Motorcycles are a mode of transportation that has experienced many traffic accidents in developing countries. This incident can occur intentionally or not and cause great loss of life and property. Therefore, this work aims to develop a model of the number of motorcycle accidents based on driver characteristics using Generalized Poisson Regression in East Java Province, Indonesia. The modeling can identify the relationship between the number of motorcycle accidents with variables that contribute to accident based on driver characteristics. This characteristic is a combination of socioeconomic factors and movements. Research analysis includes descriptive statistics and accident modeling using Generalized Poisson Regression Models. Model parameter values are estimated using the Maximum Likelihood Estimation (MLE) approach. The optimal solution for parameter estimation uses the Newton-Raphson algorithm. The results found two models and then selected the best model. Based on the parameter significance test, the population density, the percentage of low education, the gender ratio, and the percentage of accident perpetrators without a driver’s license significantly impact the number of motorcycle accidents in East Java Province.

Statistical Analysis of the Beta Transmuted Standardized Half Logistic Distribution: Properties, Estimation, and Real-Data Application

In this paper, a new distribution called the Beta Transmuted Half Logistic Distribution is derived and studied using the Beta Transmuted-G distribution. The distribution generalizes the half logistic distribution for more flexibility. Then expressions for the moments, moment generating function, order statistic, survival function, and the hazard function were studied. Estimation of parameters of the model was done using the maximum likelihood estimation approach. Simulation studies were conducted to assess the performance of the estimates of the parameter. Furthermore, the distribution is applied to a real-life dataset, demonstrating its superior performance in terms of producing a better fit compared to its submodels. This research contributes to the field of probability distributions and provides a valuable tool for modeling and analyzing various types of data.

The Construction of English Teaching Resource Library in Universities Based on Mathematical and Statistical Multiple Regression Model

Abstract This research creates an online communication platform using a mathematical statistics multiple regression model to modify the online lesson plan. The irregular variables in the resource base data are precisely measured, and the regularity of the variables is discovered using mathematical statistics. To improve the teaching resource base, the partial derivatives of the sum of squares are found, the regression values are obtained, and the dispersion of the regression values are all obtained using the maximum likelihood estimation approach. Learning English using the developed instructional resource base increased average score by 1.7 points. It demonstrates how the created teaching resource base for English in colleges and universities is effectively used and how multiple linear regression causes the independent and dependent variables to correlate nicely.

A unifying switching regime regression framework with applications in health economics

Motivated by three health economics-related case studies, we propose a unifying and flexible regression modeling framework that involves regime switching. The proposal can handle the peculiar distributional shapes of the considered outcomes via a vast range of marginal distributions, allows for a wide variety of copula dependence structures and permits to specify all model parameters (including the dependence parameters) as flexible functions of covariate effects. The algorithm is based on a computationally efficient and stable penalized maximum likelihood estimation approach. The proposed modeling framework is employed in three applications in health economics, that use data from the Medical Expenditure Panel Survey, where novel patterns are uncovered. The framework has been incorporated in the R package GJRM, hence allowing users to fit the desired model(s) and produce easy-to-interpret numerical and visual summaries.

The effect of research intensity on total factor productivity in OECD countries during 1890–2018: evidence from a new Poisson pseudo maximum likelihood estimation approach

The effect of research intensity on total factor productivity in OECD countries during 1890–2018: evidence from a new Poisson pseudo maximum likelihood estimation approach

Modelling Wind Speed Data in Langkawi Island with Functional Relationship

Wind speed influenced weather predictions, aerospace operations, and maritime operations, construction projects. This research aims to examine the relationship between Pulau Langkawi wind speed data during the southwest monsoons in 2019 and 2020. To model wind speed data that follows a normal distribution. An error-in-variables model (EIVM) is utilised, which is a linear functional relationship model (LFRM). The QQ-plots will be utilised to investigate the adequacy of the model’s fit. The maximum likelihood estimation (MLE) approach is employed to estimate the parameters of the model, while the covariance is calculated using the Fisher Information matrix. As a result, it is found that the estimated values demonstrate consistency and reduced dispersion. Thus, the findings could lead to a better knowledge of wind energy prediction.

Statistical analysis of the Gompertz-Makeham model using adaptive progressively hybrid Type-II censoring and its applications in various sciences

Gompertz-Makeham (GomMak) lifetime model has been popularly utilized in explaining human mortality, actuarial tables, growth models, and others. This study focuses on the inference problem of the model parameters and some life parameters, such as the survival (or reliability) and failure rate functions of the GomMak distribution, in the presence of a sample produced from an adaptive progressively hybrid Type-II strategy. To acquire estimates of the unknown objectives, the maximum likelihood and Bayesian estimation approaches are considered. Asymptotic confidence intervals for the same unknown parameters are also estimated based on the observed Fisher information. According to the assumption of gamma intensity introductions, under squared error loss, Bayes’ estimates of various parameters cannot be explicitly expressed. To handle this issue, the Metropolis-Hastings technique is used, in turn, to evaluate the complex Bayes estimates and produce their highest-posterior density interval estimates. Comprehensive numerical examinations, in terms of four-accuracy metrics, namely: root mean squared-error, mean relative absolute-biases, interval lengths, and interval coverage-probabilities, are done to evaluate the supplied estimates. To suggest the best progressive scenario, various optimal criteria are estimated through the offered frequentist estimates. Finally, three applications from the natural sciences—engineering, chemistry, and physics—are utilized to show the utility of the presented methodologies and the possibility of adjusting research aims to real-world problems. Real-world data results stated that the GomMak model provides a useful explanation for various practical situations in the presence of such controlled data.