Maximum Likelihood Estimates Of Parameters Research Articles

Improved point estimation for inverse gamma regression models

This paper develops a bias correction scheme for reparametrized inverse gamma regression models with varying precision [Bourguignon M, Gallardo DI. Reparametrized inverse gamma regression models with varying precision. Stat Neerl. 2020;74(4):611–627], which is tailored to situations where the response variable has an asymmetrical shape on the positive real line. In particular, we discuss maximum-likelihood estimation for the model parameters and derive closed-form expressions for the first-order bias of the estimators. The expressions derived are simple and only require the definition of a few matrices. This enables us to obtain corrected estimators that are approximately unbiased. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed corrected estimators. Finally, we apply the results obtained in three real-world datasets. This paper contains Supplementary Material.

Estimating the failure rate of the log-logistic distribution by smooth adaptive and bias-correction methods

The Log-logistic distribution has successfully earned attention in practical applications due to its good statistical properties. Because the traditional maximum likelihood estimators of the Log-logistic distribution parameters do not have an explicit form and are biased when the sample size is small. Therefore, the estimation and prediction of the failure rate is not well. In this study, we study the quality of the maximum likelihood, asymptotic maximum likelihood and bias-corrected maximum likelihood methods, and propose a smooth adaptive estimation method for estimating the Log-logistic distribution parameters. To reduce the bias of the asymptotic maximum likelihood and smooth adaptive estimators of the Log-logistic distribution parameters, the bias-corrected method is used to improve the asymptotic maximum likelihood and smooth adaptive estimation methods. Two new bias-corrected estimation methods are also proposed to obtain reliable estimates of the Log-logistic distribution parameters. An intensive Monte Carlo simulation study is conducted to evaluate the performance of these estimation methods. Simulation results show that the smooth adaptive and two new bias-corrected estimation methods are more competitive than other competitors. Finally, two real example is used for illustrating the applications of the smooth adaptive, CAML and CSA estimation methods.

Modeling Time-Varying Tail Dependence, with Application to Systemic Risk Forecasting

Abstract Empirical evidence for multivariate stock suggests that there are changes from asymptotic independence to asymptotic dependence and vice versa. Under asymptotic independence, the probability of joint extremes vanishes, whereas under asymptotic dependence, this probability remains positive. In this paper, we propose a dynamic model for bivariate extremes that allows for smooth transitions between regimes of asymptotic independence and asymptotic dependence. In doing so, we ignore the bulk of the distribution and only model the joint tail of interest. We propose a maximum-likelihood estimator for the model parameters and demonstrate its accuracy in simulations. An empirical application to losses on the CAC 40 and DAX 30 illustrates that our model provides a detailed description of changes in the extremal dependence structure. Furthermore, we show that our model issues adequate forecasts of systemic risk, as measured by CoVaR. Finally, we find some evidence that our CoVaR forecasts outperform those of a benchmark dynamic t-copula model.returns

Comparing Parametric, Nonparametric, and Semiparametric Estimators: The Weibull Trials.

We use simple examples to show how the bias and standard error of an estimator depend in part on the type of estimator chosen from among parametric, nonparametric, and semiparametric candidates. We estimated the cumulative distribution function in the presence of missing data with and without an auxiliary variable. Simulation results mirrored theoretical expectations about the bias and precision of candidate estimators. Specifically, parametric maximum likelihood estimators performed best but must be "omnisciently" correctly specified. An augmented inverse probability-weighted (IPW) semiparametric estimator performed best among candidate estimators that were not omnisciently correct. In one setting, the augmented IPW estimator reduced the standard error by nearly 30%, compared with a standard Horvitz-Thompson IPW estimator; such a standard error reduction is equivalent to doubling the sample size. These results highlight the gains and losses that can be incurred when model assumptions are made in any analysis.

Study of modal parameter estimation of time-varying mechanical system in time-frequency domain based on output-only method

With increasing mobile instrument inspection systems like mobile inspection cameras applied in modern industrial automation lines, their time-varying modal parameters need to be thoroughly studied since they are operating under various random vibration excitations which are mostly unpredictable and unrepeatable. This paper investigates modal parameter identification of time-varying mobile mechanical systems through a poly-reference expansion based on output-only method in time-frequency domain. The poly-reference parametric model is presented through a time-frequency-domain right matrix fraction description. Based on the poly-reference parametric model, a poly-reference least square estimator and a poly-reference maximum likelihood estimator of modal parameters of time-varying systems are developed. For the case of only one batch of measurements, a novel approach to estimate the covariance matrix for the poly-reference maximum likelihood estimator by non-repeatable measurement is also proposed in this paper. A numerical example demonstrates the advantageous performance of the proposed estimators, such as the estimation of the close-coupled modes. Finally, a laboratory experiment validates these proposed estimators via a comparative way.

Alchemical transformations for concerted hydration free energy estimation with explicit solvation.

We present a family of alchemical perturbation potentials that enable the calculation of hydration free energies of small- to medium-sized molecules in a single concerted alchemical coupling step instead of the commonly used sequence of two distinct coupling steps for Lennard-Jones and electrostatic interactions. The perturbation potentials we employ are non-linear functions of the solute-solvent interaction energy designed to focus sampling near entropic bottlenecks along the alchemical pathway. We present a general framework to optimize the parameters of alchemical perturbation potentials of this kind. The optimization procedure is based on the λ-function formalism and the maximum-likelihood parameter estimation procedure we developed earlier to avoid the occurrence of multi-modal distributions of the coupling energy along the alchemical path. A novel soft-core function applied to the overall solute-solvent interaction energy rather than individual interatomic pair potentials critical for this result is also presented. Because it does not require modifications of core force and energy routines, the soft-core formulation can be easily deployed in molecular dynamics simulation codes. We illustrate the method by applying it to the estimation of the hydration free energy in water droplets of compounds of varying size and complexity. In each case, we show that convergence of the hydration free energy is achieved rapidly. This work paves the way for the ongoing development of more streamlined algorithms to estimate free energies of molecular binding with explicit solvation.

A new BISARMA time series model for forecasting mortality using weather and particulate matter data

AbstractThe Birnbaum–Saunders (BS) distribution is a model that frequently appears in the statistical literature and has proved to be very versatile and efficient across a wide range of applications. However, despite the growing interest in the study of this distribution and the development of many articles, few of them have considered data with a dependency structure. To fill this gap, we introduce a new class of time series models based on the BS distribution, which allows modeling of positive and asymmetric data that have an autoregressive structure. We call these BS autoregressive moving average (BISARMA) models. Also included is a thorough study of theoretical properties of the proposed methodology and of practical issues, such as maximum likelihood parameter estimation, diagnostic analytics, and prediction. The performance of the proposed methodology is evaluated using Monte Carlo simulations. An analysis of real‐world data is performed using the methodology to show its potential for applications. The numerical results report the excellent performance of the BISARMA model, indicating that the BS distribution is a good modeling choice when dealing with time series data with positive support and asymmetrically distributed. Hence, it can be a valuable addition to the toolkit of applied statisticians and data scientists.

A non-elliptical orthogonal GARCH model for portfolio selection under transaction costs

Covariance matrix forecasts for portfolio optimization have to balance sensitivity to new data points with stability in order to avoid excessive rebalancing. To achieve this, a new orthogonal GARCH model for a multivariate set of non-Gaussian asset returns is proposed. The conditional return distribution is multivariate generalized hyperbolic and the dispersion matrix dynamics are driven by the leading factors in a principal component decomposition. Each of these leading factors is endowed with a univariate GARCH structure, while the remaining eigenvalues are kept constant over time. Joint maximum likelihood estimation of all model parameters is performed via an expectation maximization algorithm, and is applicable in high dimensions. The new model generates realistic correlation forecasts even for large asset universes and captures rising pairwise correlations in periods of market distress better than numerous competing models. When applied to portfolio optimization, it generates strategies with lower turnover and maximum drawdown, and superior risk-adjusted returns net of transaction costs. Moreover, unlike its competitors, it performs well in the sudden market downturn triggered by the global COVID-19 pandemic.

Current status data with two competing risks and missing failure types: a parametric approach

ABSTRACT Missing cause of failure is a common problem in competing risks data. Here we consider a general missing pattern in which one observes a set of possible causes containing the true cause. In this work, we focus on the parametric analysis of current status data with two competing risks and the above-mentioned missing pattern. We make some simpler assumptions on the conditional probability of observing a set of possible causes of failure given the true cause and carry out maximum-likelihood estimation of the model parameters. Asymptotic properties of the maximum-likelihood estimators are also discussed. Simulation studies are performed to study the finite sample properties of the estimators and also to investigate the role of the monitoring time distribution. Finally, the method is illustrated through the analysis of a real data set.

A new extended alpha power transformed family of distributions: properties, characterizations and an application to a data set in the insurance sciences

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformedWeibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions

Mixture of linear experts (MoE) model is one of the widespread statistical frameworks for modeling, classification, and clustering of data. Built on the normality assumption of the error terms for mathematical and computational convenience, the classical MoE model has two challenges: (1) it is sensitive to atypical observations and outliers, and (2) it might produce misleading inferential results for censored data. The aim is then to resolve these two challenges, simultaneously, by proposing a robust MoE model for model-based clustering and discriminant censored data with the scale-mixture of normal (SMN) class of distributions for the unobserved error terms. An analytical expectation–maximization (EM) type algorithm is developed in order to obtain the maximum likelihood parameter estimates. Simulation studies are carried out to examine the performance, effectiveness, and robustness of the proposed methodology. Finally, a real dataset is used to illustrate the superiority of the new model.

Using Entropy and Linear Exponential Loos Function Estimators the Parameter and Reliability Function of Inverse Rayleigh Distribution

This paper is devoted to compare the performance of non-Bayesian estimators represented by the Maximum likelihood estimator of the scale parameter and reliability function of inverse Rayleigh distribution with Bayesian estimators obtained under two types of loss function specifically; the linear, exponential (LINEX) loss function and Entropy loss function, taking into consideration the informative and non-informative priors. The performance of such estimators assessed on the basis of mean square error (MSE) criterion. The Monte Carlo simulation experiments are conducted in order to obtain the required results. 

Meta-analysis of a step-stress experiment under Weibull distribution

ABSTRACT In this article, we mainly focus on the meta-analysis of several simple step-stress experimental data sets. It is assumed that independent data sets are obtained from s simple step-stress experiments. It is further assumed that the lifetime of the experimental units follow two parameter Weibull distribution with different shape and scale parameters at different stress levels. The classical and Bayesian inference of the model parameters have been provided. Since the closed-form solution of maximum-likelihood estimators of the model parameters do not exist, asymptotic properties of the estimators have been used to construct confidence intervals. On the other hand, Gibbs sampling technique has been used to obtain the Bayes estimates and the associated credible intervals of the model parameters. Extensive simulation experiments have been performed to assess the performance of the proposed methods, and the analyses of two data sets have been presented for illustrative purpose.

An Over and Underdispersed Biparametric Extension of the Waring Distribution

A new discrete distribution for count data called extended biparametric Waring (EBW) distribution is developed. Its name is related to the fact that, in a specific configuration of its parameters, it can be seen as a biparametric version of the univariate generalized Waring (UGW) distribution, a well-known model for the variance decomposition into three components: randomness, liability and proneness. Unlike the UGW distribution, the EBW can model both overdispersed and underdispersed data sets. In fact, the EBW distribution is a particular case of a UWG distribution when its first parameter is positive; otherwise, it is a particular case of a Complex Triparametric Pearson (CTP) distribution. Hence, this new model inherits most of their properties and, moreover, it helps to solve the identification problem in the variance components of the UGW model. We compare the EBW with the UGW by a simulation study, but also with other over and underdispersed distributions through the Kullback-Leibler divergence. Additionally, we have carried out a simulation study in order to analyse the properties of the maximum likelihood parameter estimates. Finally, some application examples are included which show that the proposed model provides similar or even better results than other models, but with fewer parameters.

The Marshall-Olkin-Gompertz-G family of distributions: properties and applications

We develop a new generalized family of the Gompertz-G distribution, namely, the Marshall-Olkin-Gompertz-G distribution. Statistical properties of the new proposed model are presented. Some special cases of the new family of distributions are presented. Maximum likelihood estimates of the model parameters are also determined. A simulation study was conducted to assess the performance of the maximum likelihood estimates. Applications to demonstrate the usefulness of the Marshall-Olkin-Gompertz-Weibull distribution to real data examples are provided.

A Local Search Maximum Likelihood Parameter Estimator of Chirp Signal

A local search Maximum Likelihood (ML) parameter estimator for mono-component chirp signal in low Signal-to-Noise Ratio (SNR) conditions is proposed in this paper. The approach combines a deep learning denoising method with a two-step parameter estimator. The denoiser utilizes residual learning assisted Denoising Convolutional Neural Network (DnCNN) to recover the structured signal component, which is used to denoise the original observations. Following the denoising step, we employ a coarse parameter estimator, which is based on the Time-Frequency (TF) distribution, to the denoised signal for approximate estimation of parameters. Then around the coarse results, we do a local search by using the ML technique to achieve fine estimation. Numerical results show that the proposed approach outperforms several methods in terms of parameter estimation accuracy and efficiency.

Maximum Likelihood Estimation of Parameters for Advanced Continuously Reinforced Concrete Pavement (CRCP) Punchout Calibration Model

Pavement performance prediction is the essential part of the pavement design, which is very important for highway agencies for the purpose of budget allocating. This study introduces a model of local calibration for punchout, which is the major structural distress of continuously reinforced concrete pavement (CRCP). It is assumed that the number of equivalent single axle loads’ (ESALs) leads to punchout follows a Weibull distribution. The parameters of Weibull distribution were estimated by maximum likelihood estimation (MLE). Additionally, an approach of estimating the initial value of the parameters was also presented before applying the Newton method for solving the likelihood equations. The regression result was found to fit the performance‐monitoring data from LTPP very well. The proposed calibration model is capable of describing the punchout and can be employed to predict the failure rate and reliability of CRCP in the pavement design and the arrangement of rehabilitation activities.

A Mixture Model Parameters Estimation Algorithm for Inter-Contact Times in Internet of Vehicles

Communication opportunities among vehicles are important for data transmission over the Internet of Vehicles (IoV). Mixture models are appropriate to describe complex spatial-temporal data. By calculating the expectation of hidden variables in vehicle communication, Expectation Maximization (EM) algorithm solves the maximum likelihood estimation of parameters, and then obtains the mixture model of vehicle communication opportunities. However, the EM algorithm requires multiple iterations and each iteration needs to process all the data. Thus its computational complexity is high. A parameter estimation algorithm with low computational complexity based on Bin Count (BC) and Differential Evolution (DE) (PEBCDE) is proposed. It overcomes the disadvantages of the EM algorithm in solving mixture models for big data. In order to reduce the computational complexity of the mixture models in the IoV, massive data are divided into relatively few time intervals and then counted. According to these few counted values, the parameters of the mixture model are obtained by using DE algorithm. Through modeling and analysis of simulation data and instance data, the PEBCDE algorithm is verified and discussed from two aspects, i.e., accuracy and efficiency. The numerical solution of the probability distribution parameters is obtained, which further provides a more detailed statistical model for the distribution of the opportunity interval of the IoV.

A New Family: Σh Distributions

In this study, a new method is proposed for generating families of the sum of the hazard functions for two distributions named the Σh distributions. This new family will help in the application of a wider range of life time data. Many new distributions, which are members of the family, are presented with emphasis on the Σh Exponential-Lomax distribution. Details and various statistical properties have been introduced. The maximum likelihood estimation for parameters of the Σh Exponential-Lomax distribution has also been discussed alongside Monte Carlo simulation study to assess the accuracy and the performance of the estimation procedure. Finally, the Σh Exponential-Lomax distribution has been fitted to a real data set to provide variability of its applicability.

Kumaraswamy Inverted Topp–Leone Distribution with Applications to COVID-19 Data

In this paper, an attempt is made to discover the distribution of COVID-19 spread in different countries such as; Saudi Arabia, Italy, Argentina and Angola by specifying an optimal statistical distribution for analyzing the mortality rate of COVID-19. A new generalization of the recently inverted Topp Leone distribution, called Kumaraswamy inverted Topp–Leone distribution, is proposed by combining the Kumaraswamy-G family and the inverted Topp–Leone distribution. We initially provide a linear representation of its density function. We give some of its structure properties, such as quantile function, median, moments, incomplete moments, Lorenz and Bonferroni curves, entropies measures and stress-strength reliability. Then, Bayesian and maximum likelihood estimators for parameters of the Kumaraswamy inverted Topp–Leone distribution under Type-II censored sample are considered. Bayesian estimator is regarded using symmetric and asymmetric loss functions. As analytical solution is too hard, behaviours of estimates have been done viz Monte Carlo simulation study and some reasonable comparisons have been presented. The outcomes of the simulation study confirmed the efficiencies of obtained estimates as well as yielded the superiority of Bayesian estimate under adequate priors compared to the maximum likelihood estimate. Application to COVID-19 in some countries showed that the new distribution is more appropriate than some other competitive models.