We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix ...We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.展开更多
The aim of this paper is to present generalized log-Lindely (GLL) distribution, as a new model, and find doubly truncated generalized log-Lindely (DTGLL) distribution, truncation in probability distributions may occur...The aim of this paper is to present generalized log-Lindely (GLL) distribution, as a new model, and find doubly truncated generalized log-Lindely (DTGLL) distribution, truncation in probability distributions may occur in many studies such as life testing, and reliability. We illustrate the applicability of GLL and DTGLL distributions by Real data application. The GLL distribution can handle the risk rate functions in the form of panich and increase. This property makes GLL useful in survival analysis. Various statistical and reliability measures are obtained for the model, including hazard rate function, moments, moment generating function, mean and variance, quantiles function, Skewness and kurtosis, mean deviations, mean inactivity time and strong mean inactivity time. The estimation of model parameters is justified by the maximum Likelihood method. An application to real data shows that DTGLL distribution can provide better suitability than GLL and some other known distributions.展开更多
In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and sta...In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.展开更多
文摘We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.
文摘The aim of this paper is to present generalized log-Lindely (GLL) distribution, as a new model, and find doubly truncated generalized log-Lindely (DTGLL) distribution, truncation in probability distributions may occur in many studies such as life testing, and reliability. We illustrate the applicability of GLL and DTGLL distributions by Real data application. The GLL distribution can handle the risk rate functions in the form of panich and increase. This property makes GLL useful in survival analysis. Various statistical and reliability measures are obtained for the model, including hazard rate function, moments, moment generating function, mean and variance, quantiles function, Skewness and kurtosis, mean deviations, mean inactivity time and strong mean inactivity time. The estimation of model parameters is justified by the maximum Likelihood method. An application to real data shows that DTGLL distribution can provide better suitability than GLL and some other known distributions.
文摘In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.
