6,917 research outputs found
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
Simulation-based Estimation of Mean and Standard Deviation for Meta-analysis via Approximate Bayesian Computation (ABC)
Background: When conducting a meta-analysis of a continuous outcome,
estimated means and standard deviations from the selected studies are required
in order to obtain an overall estimate of the mean effect and its confidence
interval. If these quantities are not directly reported in the publications,
they need to must be estimated from other reported summary statistics, such as
the median, the minimum, the maximum, and quartiles. Methods: We propose a
simulation-based estimation approach using the Approximate Bayesian Computation
(ABC) technique for estimating mean and standard deviation based on various
sets of summary statistics found in published studies. We conduct a simulation
study to compare the proposed ABC method with the existing methods of Hozo et
al. (2005), Bland (2015), and Wan et al. (2014). Results: In the estimation of
the standard deviation, our ABC method performs best in skewed or heavy-tailed
distributions. The average relative error (ARE) approaches zero as sample size
increases. In the normal distribution, our ABC performs well. However, the Wan
et al. method is best since it is based on the normal distribution assumption.
When the distribution is skewed or heavy-tailed, the ARE of Wan et al. moves
away from zero even as sample size increases. In the estimation of the mean,
our ABC method is best since the AREs converge to zero. Conclusion: ABC is a
flexible method for estimating the study-specific mean and standard deviation
for meta-analysis, especially with underlying skewed or heavy-tailed
distributions. The ABC method can be applied using other reported summary
statistics such as the posterior mean and 95% credible interval when Bayesian
analysis has been employed
Estimation of Inverse Weibull Distribution Under Type-I Hybrid Censoring
The hybrid censoring is a mixture of Type I and Type II censoring schemes.
This paper presents the statistical inferences of the Inverse Weibull
distribution when the data are Type-I hybrid censored. First we consider the
maximum likelihood estimators of the unknown parameters. It is observed that
the maximum likelihood estimators can not be obtained in closed form. We
further obtain the Bayes estimators and the corresponding highest posterior
density credible intervals of the unknown parameters under the assumption of
independent gamma priors using the importance sampling procedure. We also
compute the approximate Bayes estimators using Lindley's approximation
technique. We have performed a simulation study and a real data analysis in
order to compare the proposed Bayes estimators with the maximum likelihood
estimators.Comment: This paper is under review in the Austrian Journal of Statistics and
will likely be published ther
An Intuitive Curve-Fit Approach to Probability-Preserving Prediction of Extremes
A method is described for predicting extremes values beyond the span of
historical data. The method - based on extending a curve fitted to a location-
and scale-invariant variation of the double-logarithmic QQ-plot - is simple and
intuitive, yet it preserves probability to a good approximation. The procedure
is developed on the Generalised Pareto Distribution (GPD), but is applicable to
the upper order statistics of a wide class of distributions.Comment: 20 pages, 16 figure
Using weibull mixture distributions to model heterogeneous survival data
In this article we use Bayesian methods to fit a Weibull mixture model with an unknown number of components to possibly right censored survival data. This is done using the recently developed, birth-death MCMC algorithm. We also show how to estimate the survivor function and the expected hazard rate from the MCMA output
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