Likelihood Estimators In Terms Research Articles

Bayesian estimation for median discrete Weibull regression model

<abstract><p>The discrete Weibull model can be adapted to capture different levels of dispersion in the count data. This paper takes into account the direct relationship between explanatory variables and the median of discrete Weibull response variable. Additionally, it provides the Bayesian estimate of the discrete Weibull regression model using the random walk Metropolis algorithm. The prior distributions of the coefficient predictors were carried out based on the uniform non-informative, normal and Laplace distributions. The performance of the Bayes estimators was also compared with the maximum likelihood estimator in terms of the mean square error and the coverage probability through the Monte Carlo simulation study. Meanwhile, a real data set was analyzed to show how the proposed model and the methods work in practice.</p></abstract>

A simulation study on the insurance claims distribution using Weibull distribution

<p style="text-align:justify"><span style="font-size:10.5pt"><span style="font-family:等线"><span dir="ltr" lang="EN-US" style="font-family:"Cambria",serif"><span style="color:black">The Weibull distribution is extensively useful in the field of finance, insurance and natural disasters. Recently, It has been considered as one of the most frequently used statistical distributions in modelling and analyzing stock pricing movement and uncertain prediction in financial and investment data sets, such as insurance claims distribution. It is well known that the Bayes estimators of the two-parameter Weibull distribution do not have a compact form and the closed-form expression of the Bayes estimators cannot be obtained. In this paper and the Bayesian setting, it is assumed that the scale parameter of the Weibull model has a gamma prior under the assumption that its shape parameter is known. A simulation study is performed using random claims amount to compare the performance of the Bayesian approach with traditional maximum likelihood estimators in terms of Root Mean Square Errors (RMSE) and Mean Absolute Error (MAE) for different sample sizes, with specific values of the scale parameter and shape parameters. The results have been compared with the estimated result via the maximum likelihood method. The result revealed that the Bayesian approach behaves similarly to the maximum likelihood method when the sample size is small. Nevertheless, in all cases for both methods, the RMSE and MAE decrease as the sample size increases. Finally, applications of the proposed model to the insurance claim data set have been presented.</span></span></span></span></p>

A Bayesian Framework for Estimating Weibull Distribution Parameters: Applications in Finance, Insurance, and Natural Disaster Analysis

This research presents a Bayesian framework for parameter estimation in the two-parameter Weibull distribution, with applications in finance and investment data analysis. The Weibull distribution is widely used for modeling stock pricing movements and making uncertain predictions in financial datasets. The proposed Bayesian approach assumes a gamma prior distribution for the scale parameter, with a known shape parameter. A simulation study using simulated financial data compares the Bayesian method with maximum likelihood estimators in terms of accuracy, error accumulation, and computational time across various sample sizes and parameter values. Results indicate the Bayesian approach performs similarly to maximum likelihood for small samples, while demonstrating computational efficiency for larger financial datasets. The proposed Bayesian model's application to simulated financial data showcases its practical relevance in real-world scenarios. This Bayesian framework offers a valuable tool for handling uncertainty and making informed decisions in financial data analysis, providing robust parameter estimation and uncertainty quantification in finance and investment domains.

A new Jackknifing ridge estimator for logistic regression model

The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The logistic regression model is a well-known model in application when the response variable is binary data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the logistic regression coefficients. To address this problem, a logistic ridge estimator has been proposed by numerous researchers. In this paper, a new Jackknifing logistic ridge estimator (NLRE) is proposed and derived. The idea behind the NLRE is to get diagonal matrix with small values of diagonal elements that leading to decrease the shrinkage parameter and, therefore, the resultant estimator can be better with small amount of bias. Our Monte Carlo simulation results suggest that the NLRE estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the NLRE estimator outperforms both logistic ridge estimator and maximum likelihood estimator in terms of predictive performance.

Modified Profile Likelihood Estimation in the Lomax Distribution

In this paper, we consider improving maximum likelihood inference for the scale parameter of the Lomax distribution. The improvement is based on using modifications to the maximum likelihood estimator based on the Barndorff-Nielsen modification of the profile likelihood function. We apply these modifications to obtain improved estimators for the scale parameter of the Lomax distribution in the presence of a nuisance shape parameter. Due to the complicated expression for the Barndorff-Nielsen's modification, several approximations to this modification are considered in this paper, including the modification based on the empirical covariances and the approximation based on using suitably derived approximate ancillary statistics. We obtained the approximations for the Lomax profile likelihood function and the corresponding modified maximum likelihood estimators. They are not available in simple closed forms and can be obtained numerically as roots of some complicated likelihood equations. Comparisons between maximum profile likelihood estimator and modified profile likelihood estimators in terms of their biases and mean squared errors were carried out using simulation techniques. We found that the approximation based on the empirical covariances to have the best performance according to the criteria used. Therefore we recommend to use this modified version of the maximum likelihood estimator for the Lomax scale parameter, especially for small sample sizes with heavy censoring, which is quite common in industrial life testing experiments and reliability studies. An example based on real data is given to illustrate the methods considered in this paper.

A Bayes Estimation for the Parameters of Misclassified Size-biased Poisson Lindley Distribution and its Application

This paper introduces a misclassified size-biased Poisson-Lindley distribution by compounding the size-biased Poisson distribution with the size-biased Lindley distribution. The Bayes estimation for the misclassified size-biased Poisson-Lindley distribution is investigated and compared with the Maximum Likelihood estimation. A real dataset is discussed to demonstrate the suitability and applicability of the proposed distribution in the modeling count dataset. Finally, a Monte Carlo simulation study of 100000 simulated data is presented to investigate and compare the Bayes estimators and Maximum Likelihood estimators in terms of simulated risk for different sample sizes and varying parameters value

Almost unbiased ridge estimator in the count data regression models

The ridge estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The Poisson regression negative binomial regression models are well-known model in application when the response variable is count data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the count regression coefficients. To address this problem, a count data ridge estimator has been proposed by numerous researchers. In this paper, an almost unbiased regression estimator is proposed and derived. Our Monte Carlo simulation results suggest that the proposed estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the proposed estimator outperforms both negative binomial ridge regression and maximum likelihood estimators in terms of predictive performance.

The Generalized Odd Generalized Exponential Family of Distributions: Properties, Characterizations and Application

We introduce a new class of distributions called the generalized odd generalized exponential family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, R𝑒́nyi, Shannon and q-entropies, order statistics and probability weighted moments are derived. We also propose bivariate generalizations. We constructed a simple type Copula and intro-duced a useful stochastic property. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors via a simulation study.

Some Theoretical and Computational Aspects of the Inverse Generalized Power Weibull Distribution

This paper introduces a new three-parameter distribution called inverse generalized power Weibull distribution. This distribution can be regarded as a reciprocal of the generalized power Weibull distribution. The new distribution is characterized by being a general formula for some well-known distributions, namely inverse Weibull, inverse exponential, inverse Rayleigh and inverse Nadarajah-Haghighi distributions. Some of the mathematical properties of the new distribution including the quantile, density, cumulative distribution functions, moments, moments generating function and order statistics are derived. The model parameters are estimated using the maximum likelihood method. The Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators in terms of mean squared errors. Two real datasets are used to demonstrate the flexibility of the new distribution as well as to demonstrate its applicability.

Identification without assuming mean stationarity: quasi–maximum likelihood estimation of dynamic panel models with endogenous regressors

SummaryLinear generalised method of moments (GMM) estimators for dynamic panel models with predetermined or endogenous regressors suffer from a weak instruments problem when the data are highly persistent. In this paper, we propose new random- and fixed-effects limited-information quasi–maximum likelihood estimators (LIQMLEs) for such models. We also discuss LIQMLEs for models that contain time-varying individual effects. Unlike system GMM estimators, the LIQMLEs do not require mean stationarity conditions for consistency. Such conditions often do not hold for the models we consider. Our LIQMLEs are based on a two-step control function approach that includes the first-stage model residuals for a predetermined or endogenous regressor in the outcome equation. The LIMLEs are more precise than nonlinear GMM estimators that are based on the original outcome equation. The LIQMLEs also compare favourably to various alternative (quasi–) maximum likelihood estimators in terms of precision, robustness, and/or ease of computation.

Estimation from cross-sectional data under a semiparametric truncation model

Summary Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper, we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family. We examine two methods of estimating both the truncation and the lifetime distributions. We obtain asymptotic representations of the estimators for the lifetime distribution and establish their weak convergence. Both of the proposed estimators perform better than Wang’s (1991) nonparametric maximum likelihood estimator in terms of the integrated mean squared error, when the parametric family for the truncation is sufficiently close to its true distribution. The full likelihood approach is preferable to the conditional likelihood approach in estimating the lifetime distribution, though not necessarily the truncation distribution. In an application to Alzheimer’s disease data, hypothesis tests reject the uniform truncation distribution, but several other parametric models lead to similar behaviour of the truncation and lifetime distributions after disease onset.

The Hjorth’s IDB Generator of Distributions: Properties, Characterizations, Regression Modeling and Applications

We introduce a new flexible class of continuous distributions via the Hjorth’s IDB model. We provide some mathematical properties of the new family. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. The maximum likelihood method is used for estimating the model parameters. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of the simulation study. A new regression model as well as residual analysis are presented. Finally, the usefulness of the family is illustrated by means of four real data sets. The new model provides consistently better fits than other competitive models for these data sets.

A New Ridge Estimator for the Poisson Regression Model

The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The Poisson regression model is a well-known model in application when the response variable is count data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the Poisson regression coefficients. To address this problem, a Poisson ridge regression model has been proposed by numerous researchers. In this paper, a new Poisson ridge estimator (NPRRM) is proposed and derived. The idea behind the NPRRM is to get diagonal matrix with small values of diagonal elements that leading to decrease the shrinkage parameter, and therefore, the resultant estimator can be better with small amount of bias. Our Monte Carlo simulation results suggest that the NPRRM estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the NPRRM estimator outperforms both Poisson ridge regression and maximum likelihood estimators in terms of predictive performance.

Estimation of the Exponential Distribution under Generalized Multiply Hybrid Censored Competing Risks Data

The disadvantages of the multiply censoring scheme are that the experiment may be very long if the items are highly reliable. Because of that, multiply hybrid censoring scheme was introduced. But, one limitation of the multiply hybrid censoring scheme (MHCS) is that it cannot be applied when very few failures may occur before pre-fixed time. In this reason, we propose a generalized multiply hybrid censoring scheme, which allows us to observe a pre-specified number of failures. Also, we derive the maximum likelihood estimators and Bayes estimators of parameters based on exponential distribution with competing risks data under generalized multiply hybrid censoring scheme. Lindley’s approximation method (LAM) is used to compute these Bayes estimators. The Bayes estimators of parameters are better than the respective maximum likelihood estimators in terms of mean squared errors and biases. The choice of SEL seems to be a reasonable for Bayes estimation method of parameters. Also, a real data analysis has been provided.

Random-effects meta-analysis of few studies involving rare events.

Meta-analyses of clinical trials targeting rare events face particular challenges when the data lack adequate numbers of events for all treatment arms. Especially when the number of studies is low, standard random-effects meta-analysis methods can lead to serious distortions because of such data sparsity. To overcome this, we suggest the use of weakly informative priors (WIPs) for the treatment effect parameter of a Bayesian meta-analysis model, which may also be seen as a form of penalization. As a data model, we use a binomial-normal hierarchical model (BNHM) that does not require continuity corrections in case of zero counts in one or both arms. We suggest a normal prior for the log-odds ratio with mean 0 and standard deviation 2.82, which is motivated (a) as a symmetric prior centered around unity and constraining the odds ratio within a range from 1/250 to 250 with 95% probability and (b) as consistent with empirically observed effect estimates from a set of 37 773 meta-analyses from the Cochrane Database of Systematic Reviews. In a simulation study with rare events and few studies, our BNHM with a WIP outperformed a Bayesian method without a WIP and a maximum likelihood estimator in terms of smaller bias and shorter interval estimates with similar coverage. Furthermore, the methods are illustrated by a systematic review in immunosuppression of rare safety events following pediatric transplantation. A publicly available R package, MetaStan, is developed to automate a Bayesian implementation of meta-analysis models using WIPs.

The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications

A new family of distributions called the Topp-Leone generalized odd log-logistic-G family is introduced and studied. We provide some mathematical properties of the new family including ordinary and incomplete moments, generating function and order statistics. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. Finally, the usefulness of the family is illustrated by means of two real data sets. The new model provides consistently better fits than other competitive models for these data sets.

Type II General Exponential Class of Distributions

In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution. Some special models are presented. Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived. Characterizations of this family are obtained based on truncated moments, hazard function, conditional expectation of certain functions of the random variable are obtained. The performance of the maximum likelihood estimators in terms of biases, mean squared errors and confidence interval length is examined by means of a simulation study. Two real data sets are used to illustrate the application of the proposed class.

The Zografos-Balakrishnan Odd Log-Logistic Generalized Half-Normal Distribution with Mathematical Properties and Simulations

In this paper, A new class of distributions called the Zografos-Balakrishnan odd log-logistic Generalized half-normal (ZOLL-GHN) family with four parameters is introduced and studied. Useful representations and some mathematical properties of the new family include moments, quantile function, moment Generating function are investigated. The maximum likelihood equations for estimating the parameters based on real data are given. Different methods have been used to estimate its parameters such as maximum likelihood, Least squares, weighted least squares, Crammer-von-Misers,Anderson-Darling and right-tailed Anderson-Darling methods. We assesses the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. Finally, the usefulness of the family and fitness capability of this model, are illustrated by means of two real data sets.

The Exponentiated Burr XII Power Series Distribution: Properties and Applications

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

Modified profile likelihood estimation for the Weibull regression models in survival analysis

In this study, adjustment of profile likelihood function of parameter of interest in presence of many nuisance parameters is investigated for survival regression models. Our objective is to extend the Barndorff–Nielsen’s technique to Weibull regression models for estimation of shape parameter in presence of many nuisance and regression parameters. We conducted Monte-Carlo simulation studies and a real data analysis, all of which demonstrate and suggest that the modified profile likelihood estimators outperform the profile likelihood estimators in terms of three comparison criterion: mean squared errors, bias and standard errors.