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Inference under progressively type II right censored sampling for certain lifetime distributions
In this paper, estimation of the parameters of a certain family of two-parameter lifetime
distributions based on progressively Type II right censored samples (including ordinary Type II right censoring) is studied. This family, of reverse hazard distributions, includes the Weibull, Gompertz and Lomax distributions. A new type of parameter estimation, named inverse estimation, is introduced for both parameters. Exact confidence intervals for one of the parameters and generalized confidence intervals for the other are explored; inference for the first parameter can be accomplished by our
methodology independently of the unknown value of the other parameter in this family of distributions. Derivation of the estimation method uses properties of order statistics.
A simulation study in the particular context of the Weibull distribution illustrates the accuracy of these confidence intervals and compares inverse estimators favorably with maximum likelihood estimators. A numerical example is used to illustrate the proposed procedures
Categorical data analysis using a skewed Weibull regression model
In this paper, we present a Weibull link (skewed) model for categorical
response data arising from binomial as well as multinomial model. We show that,
for such types of categorical data, the most commonly used models (logit,
probit and complementary log-log) can be obtained as limiting cases. We further
compare the proposed model with some other asymmetrical models. The Bayesian as
well as frequentist estimation procedures for binomial and multinomial data
responses are presented in details. The analysis of two data sets to show the
efficiency of the proposed model is performed
A Quantile Variant of the EM Algorithm and Its Applications to Parameter Estimation with Interval Data
The expectation-maximization (EM) algorithm is a powerful computational
technique for finding the maximum likelihood estimates for parametric models
when the data are not fully observed. The EM is best suited for situations
where the expectation in each E-step and the maximization in each M-step are
straightforward. A difficulty with the implementation of the EM algorithm is
that each E-step requires the integration of the log-likelihood function in
closed form. The explicit integration can be avoided by using what is known as
the Monte Carlo EM (MCEM) algorithm. The MCEM uses a random sample to estimate
the integral at each E-step. However, the problem with the MCEM is that it
often converges to the integral quite slowly and the convergence behavior can
also be unstable, which causes a computational burden. In this paper, we
propose what we refer to as the quantile variant of the EM (QEM) algorithm. We
prove that the proposed QEM method has an accuracy of while the MCEM
method has an accuracy of . Thus, the proposed QEM method
possesses faster and more stable convergence properties when compared with the
MCEM algorithm. The improved performance is illustrated through the numerical
studies. Several practical examples illustrating its use in interval-censored
data problems are also provided
Reliability-centered maintenance: analyzing failure in harvest sugarcane machine using some generalizations of the Weibull distribution
In this study we considered five generalizations of the standard Weibull
distribution to describe the lifetime of two important components of harvest
sugarcane machines. The harvesters considered in the analysis does the harvest
of an average of 20 tons of sugarcane per hour and their malfunction may lead
to major losses, therefore, an effective maintenance approach is of main
interesting for cost savings. For the considered distributions, the
mathematical background is presented. Maximum likelihood is used for parameter
estimation. Further, different discrimination procedures were used to obtain
the best fit for each component. At the end, we propose a maintenance
scheduling for the components of the harvesters using predictive analysis
Density Regression Based on Proportional Hazards Family
This paper develops a class of density regression models based on proportional hazards family, namely, Gamma transformation proportional hazard (Gt-PH) model . Exact inference for the regression parameters and hazard ratio is derived. These estimators enjoy some good properties such as unbiased estimation, which may not be shared by other inference methods such as maximum likelihood estimate (MLE). Generalised confidence interval and hypothesis testing for regression parameters are also provided. The method itself is easy to implement in practice. The regression method is also extended to Lasso-based variable selection.National Natural Science Foundation of China (Grant No. 71490725, 71071087 and 11261048
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