General results for the Kumaraswamy-G distribution

For any continuous baseline G distribution [G.M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883–898], proposed a new generalized distribution (denoted here with the prefix ‘Kw-G’ (Kumaraswamy-G)) with two extra positive parameters. They studied some of its mathematical properties and presented special sub-models. We derive a simple representation for the Kw-G density function as a linear combination of exponentiated-G distributions. Some new distributions are proposed as sub-models of this family, for example, the Kw-Chen [Z.A. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), pp. 155–161], Kw-XTG [M. Xie, Y. Tang, and T.N. Goh, A modified Weibull extension with bathtub failure rate function, Reliab. Eng. System Safety 76 (2002), pp. 279–285] and Kw-Flexible Weibull [M. Bebbington, C.D. Lai, and R. Zitikis, A flexible Weibull extension, Reliab. Eng. System Safety 92 (2007), pp. 719–726]. New properties of the Kw-G distribution are derived which include asymptotes, shapes, moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, reliability, Rényi entropy and Shannon entropy. New properties of the order statistics are investigated. We discuss the estimation of the parameters by maximum likelihood. We provide two applications to real data sets and discuss a bivariate extension of the Kw-G distribution.     

Asymptotically optimal shrinkage estimates for non-normal data

Motivated by several practical issues, we consider the problem of estimating the mean of a p-variate population (not necessarily normal) with unknown finite covariance. A quadratic loss function is used. We give a number of estimators (for the mean) with their loss functions admitting expansions to the order of p ^?1/2 as p→∞. These estimators contain Stein's [Inadmissibility of the usual estimator for the mean of a multivariate normal population, in Proceedings of the Third Berkeley Symposium in Mathematical Statistics and Probability, Vol. 1, J. Neyman, ed., University of California Press, Berkeley, 1956, pp. 197–206] estimate as a particular case and also contain ‘multiple shrinkage’ estimates improving on Stein's estimate. Finally, we perform a simulation study to compare the different estimates.     

Estimation of weibull location

A simulation study was carried out to compare the performances of two different simple estimators of the location parameter for a three-parameter Weibull distribution Both Estimators have been suggested by recent paper in the literature. Bras and mean square error are examined for many different sample-size and shape-parameter-value combinations. Strong evidence of the domination of one estimator over the other is found.     

Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields

We investigate the asymptotic behaviour of binned kernel density estimators for dependent and locally non-stationary random fields converging to stationary random fields. We focus on the study of the bias and the asymptotic normality of the estimators. A simulation experiment conducted shows that both the kernel density estimator and the binned kernel density estimator have the same behavior and both estimate accurately the true density when the number of fields increases. We apply our results to the 2002 incidence rates of tuberculosis in the departments of France.     

Estimating ordered quantiles of two exponential populations with a common minimum guarantee time

The problem of estimating ordered quantiles of two exponential populations is considered, assuming equality of location parameters (minimum guarantee times), using the quadratic loss function. Under order restrictions, we propose new estimators which are the isotonized version of the MLEs, call it, restricted MLE. A sufficient condition for improving equivariant estimators is derived under order restrictions on the quantiles. Consequently, estimators improving upon the old estimators have been derived. A detailed numerical study has been done to evaluate the performance of proposed estimators using the Monte-Carlo simulation method and recommendations have been made for the use of the estimators.     

Ridge Regression and Generalized Maximum Entropy: An improved version of the Ridge–GME parameter estimator

In this article, the Ridge–GME parameter estimator, which combines Ridge Regression and Generalized Maximum Entropy, is improved in order to eliminate the subjectivity in the analysis of the ridge trace. A serious concern with the visual inspection of the ridge trace to define the supports for the parameters in the Ridge–GME parameter estimator is the misinterpretation of some ridge traces, in particular where some of them are very close to the axes. A simulation study and two empirical applications are used to illustrate the performance of the improved estimator. A MATLAB code is provided as supplementary material.     

Modeling probability density through ultraspherical polynomial transformations

We present a method for fitting parametric probability density models using an integrated square error criterion on a continuum of weighted Lebesgue spaces formed by ultraspherical polynomials. This approach is inherently suitable for creating mixture model representations of complex distributions and allows fully autonomous cluster analysis of high-dimensional datasets. The method is also suitable for extremely large sets, allowing post facto model selection and analysis even in the absence of the original data. Furthermore, the fitting procedure only requires the parametric model to be pointwise evaluable, making it trivial to fit user-defined models through a generic algorithm.     

Bayesian estimation of rare sensitive attribute

Randomized response models have been used to estimate a population proportion of a sensitive attribute. A randomized device is typically employed to protect respondent's privacy in a survey. In addition, an unrelated question is asked to improve the statistical efficiency. In this article, we propose Bayesian estimation of rare sensitive attribute using randomized response technique, which includes a rare unrelated attribute. Two cases are considered, the proportion of a rare unrelated attribute is known and unknown. A simulation study is conducted to assess the performance of the models using mean absolute error and coverage probability. The results show that the performance depends on the parameters and is robust to priors.     

Inference for Weibull distribution under adaptive Type-I progressive hybrid censored competing risks data

In this paper, a competing risks model is considered under adaptive type-I progressive hybrid censoring scheme (AT-I PHCS). The lifetimes of the latent failure times have Weibull distributions with the same shape parameter. We investigate the maximum likelihood estimation of the parameters. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) techniques to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. To evaluate the performance of the estimators, a simulation study is carried out.