Maximum Likelihood Estimation Approach Research Articles

Epidemiological modeling of COVID-19 data with Advanced statistical inference based on Type-II progressive censoring

This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets.

Analysis of leukemia and forest fires data using new Poisson Quasi-Shanker distribution

In this study, a new two-parameter discrete distribution is introduced by mixing Poisson and Quasi-Shanker distributions. The new model is named Poisson Quasi-Shanker-(PQS) distribution. Some important mathematical properties of the proposed distribution are derived including factorial moments, moment-generating function, variance, and dispersion index. The parameters of PQS distribution are estimated using the maximum likelihood estimation approach. A Monte Carlo simulation is carried out to illustrate the behavior of derived estimators. The applicability of the new model is assessed using two datasets from different areas. It is concluded the proposed distribution is more flexible as compared to the considered competitive distributions.

Technical Efficiency of Indonesian Potato Farming during Rainy and Dry Seasons: Evidence from Merangin District, Indonesia

Potatoes are among the vegetables highly susceptible to climate change, and its consequences can significantly affect technical efficiency.However, the production of potato relatively fluctuated due to some factors influencing it. The study aims to analyze the factors affecting potato production, measure the level of technical efficiency in potato farming, and identify the socio-economic factors that influence technical inefficiency in potato farming, both in the rainy and dry seasons. The study was conducted in Merangin Regency, Jambi Province. A purposive sampling method was used to select the research area and collect data from 102 potato farmers. The data were analyzed using the Stochastic Frontier Cobb-Douglas production function model with a maximum likelihood estimation (MLE) approach. The research results show that land and seed variables significantly influence potato production, both in the rainy and dry seasons. Meanwhile, fertilizer P and labor only significantly influence the dry season. The average level of technical efficiency in the dry season (0.89) is higher than in the rainy season (0.73). The results of the average difference test (t-test) show that in the dry season, the level of technical efficiency has a higher value than in the rainy season, with a significance of 1%. The significant socio-economic variables influencing technical efficiency are membership in farmer groups.

A novel equipment remaining useful life prediction approach considering dynamic maintenance threshold

AbstractIn conventional remaining useful life (RUL) prediction approaches grounded on maintenance, the maintenance threshold is typically established as a stationary value. However, the actual maintenance threshold may exceed its preset value due to the uncertainty of degradation and other factors. Therefore, it is necessary to consider the dynamic maintenance threshold to improve the precision of remaining useful life prediction. By considering the Wiener process, the maintenance threshold error is introduced to reflect the dynamic nature of the maintenance threshold. The influence of maintenance on degradation amount, degradation rate, and degradation path are comprehensively considered to establish a multi‐stage maintenance‐affected degradation process model. The RUL formula of the equipment is derived using the first hitting time (FHT). The maximum likelihood estimation (MLE) approach and Bayesian theory are employed to estimate the model's parameters. The proposed approach is validated using simulation data and gyroscope degradation data. The outcomes reveal that the proposed approach can significantly enhance the precision of life prediction for the equipment.

Local calibration of flexible performance models using maximum likelihood estimation approach

The pavement mechanistic-empirical design (PMED) is a widely used pavement analysis and design approach. The transfer functions are generally calibrated to implement the PMED for local conditions. The least square (LS) approach has been commonly used to calibrate these transfer functions. Although LS is a simplistic approach, the assumptions may not be valid, especially for non-normally distributed data. This paper uses the maximum likelihood estimation (MLE) approach to calibrate bottom-up cracking, total rutting, and international roughness index (IRI) transfer function for flexible pavements. The results show that overall, MLE outperforms the LS approach for synthetic and measured data. The difference is more evident in the case of bottom-up cracking data, which does not follow a normal distribution. Gamma distribution for bottom-up cracking and total rutting, whereas negative binomial for IRI is the most suitable distribution for the MLE approach. Overall, MLE using resampling methods provides a robust and better estimate than the LS approach.

Factor-augmented transformation models for interval-censored failure time data.

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

On ZLindley distribution: statistical properties and applications

The modeling and analysis of lifetime data is critical in many areas, including actuarial science, management, engineering, medicin, physics, biology, hydrology, and computer science. Classical probability distributions have been used to manage data sets of varied sizes. However, considerable issues occur when real-world data does not fit into any of the classical or conventional probability models. Consequently, there arises a crucial requirement to enhance the flexibility of existing probability models by including the blending of two distributions or introducing additional parameters. This work introduces a ZLindley distribution with a single parameter. Both symmetric and left-skewed data can utilize the proposed model. We generate statistical features such as the mode, moments, quantile function, and moment-generating function to accurately represent the usefulness of the suggested distribution. We compute the parameter using the maximum likelihood estimation approach. A thorough simulation exercise evaluates the goodness-of-fit performance. We demonstrate the applicability and flexibility of the new recommended distribution by using a real dataset.

Reliability inference based on inverted exponentiated Rayleigh lifetime distribution under unified hybrid censored scheme

In this study, we investigated the Inverted Exponentiated Rayleigh Distribution (IERD), a significant and efficient continuous lifetime distribution commonly applied in lifespan research. Our focus was on estimating unknown parameters for a two-parameter inverted exponentiated Rayleigh distribution using unified hybrid censored data. We considered both maximum likelihood and Bayesian estimation approaches. Specifically, we employed the Gibbs within Metropolis–Hastings samplers method to develop approximate Bayes estimators utilizing informative and non-informative priors, along with symmetric and asymmetric loss functions. In addition, we utilized Markov chain Monte Carlo (MCMC) samples to derive maximum posterior density credible intervals. Simulation experiments were conducted to assess the efficacy of the proposed methodologies, and actual data analysis was performed to validate the proposed estimators.

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.

Analysis, Estimation, and Practical Implementations of the Discrete Power Quasi‐Xgamma Distribution

In this study, we introduce a new three‐parameter discrete power quasi‐Xgamma (DPQXg) distribution. A detailed analysis of the mathematical and statistical properties of the DPQXg distribution demonstrates various important features. It has been observed that the DPQXg distribution can be used for analyzing both asymmetric and symmetric datasets exhibiting platykurtic and leptokurtic shapes. The hazard rate function of the distribution has both increasing and decreasing failure rates. Furthermore, the dispersion index of the DPQXg distribution indicates that the new statistical model can analyze both over‐ and underdispersed datasets. The parameter estimation of the statistical model is conducted using the maximum likelihood estimation approach. A simulation is carried out to assess the performance of the DPQXg estimator. Finally, real‐world datasets from different fields are used to demonstrate the practical utility of the DPQXg distribution.

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.