جستجوی مقالات مرتبط با کلیدواژه "monte-carlo simulation" در نشریات گروه "ریاضی"

In this paper, the problem of estimating unknown parameters is investigated when lifetime data following Poisson-exponential distribution under classical and Bayesian frameworks based on progressively type-II hybrid censored data. We compute point and associated interval estimates under classical and Bayesian approaches. For point estimates in the problem of estimation, we compute maximum likelihood estimators of model using Expectation-Maximization (EM) and Stochastic Expectation-Maximization (SEM) algorithms under classical approach, these algorithms are easily implemented. We compute Bayes estimates with the help of Lindley and importance sampling technique under informative and non-informative priors using different loss functions namely squared error, LINEX as well as general entropy in Bayesian framework. The associated interval estimates are obtained using the Fisher information matrix and Chen and Shao method respectively under classical and Bayesian approaches. We analysis real data set, and conduct Monte Carlo simulation study for the comparison of various proposed methods. Finally, we present a conclusion.

In reducing the effects of collinearity, the ridge estimator (RE) has been consistently demonstrated to be an attractive shrinkage method. In application, when the response variable is binary data, the logistic regression model (LRM) is a well-known model. However, it is known that collinearity negatively affects the variance of maximum likelihood estimator of the LRM. To address this problem, a logistic ridge estimator was proposed by several authors. In this work, a Jackknifing logistic ridge estimator (NJLRE) is proposed and derived. The Monte Carlo simulation results recommend that the NJLRE estimator can bring significant improvement relative to other existing estimators. Furthermore, the real application results demonstrate that the NJLRE estimator outperforms both LRE and MLE in terms of predictive performance.

The Liu estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of Inter-correlated (multicollinearity). The negative binomial regression model is a well-known model in the application when the response variable is non-negative integers or counts. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator of the negative binomial coefficients. To overcome this problem, a negative binomial Liu estimator has been proposed by numerous researchers. In this paper, a Jackknifed Liu-type negative binomial estimator (JNBLTE) is proposed and derived. The idea behind the JNBLTE is to decrease the shrinkage parameter and, therefore, the resultant estimator can be better with a small amount of bias. Our Monte Carlo simulation results suggest that the JNBLTE estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the JNBLTE estimator outperforms both the negative binomial Liu estimator and maximum likelihood estimators in terms of predictive performance.

Modelling of count data has been of extreme interest to researchers. However, in practice, count data is often identified with overdispersion or underdispersion. The Conway Maxwell Poisson regression model (CMPRE) has been proven powerful in modelling count data with a wide range of dispersion. In regression modeling, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator. To address this problem, shrinkage estimators, such as Liu and Liu-type estimators have been consistently verified to be attractive to decrease the effects of multicollinearity. However, these shrinkage estimators are considered biased estimators. In this study, the jackknife approach and its modified version are proposed for modeling count data with CMPRE. These two estimators are proposed to reduce the effects of multicollinearity and the biasedness of using the Liu-type estimator simultaneously. The results of Monte Carlo simulation and real data recommend that the proposed estimators were significant improvement relative to other competitor estimators, in terms of absolute bias and mean squared error with superiority to the modified jackknifed Liu-type estimator.

It is a challenge in the real application when modelling the relationship between the response variable and several explanatory variables when the existence of collinearity. Traditionally, in order to avoid this issue, several shrinkage estimators are proposed. Among them is the Kibria and Lukman estimator (K-L). In this study, a jackknifed version of the K-L estimator is proposed in the generalized linear model that combines the Jackknife procedure with the K-L estimator to reduce the biasedness. Our Monte Carlo simulation results and the real data application related to the inverse Gaussian regression model suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in terms of absolute bias and mean squared error.

We propose a new class of continuous distributions with two extra shape parameters named the Odd Log-Logistic Poisson-G family. Some of its mathematical properties including moments, quantile, generating functions and order statistics are obtained. We estimate the model parameters by the maximum likelihood method and present a Monte Carlo simulation study. The importance of the proposed family is demonstrated by means of three real data applications. Empirical results indicate that proposed family provides better fits than other well-known classes of distributions in real applications.