The problem to be analyzed in this paper deals with the finding of n values x1, x2, ..., xn ∈ R which minimize the function:E [míni=1,...,n c (ξ - xi)]where ξ is a one-dimensional random variable with known distribution function φ and c is a measurable and positive function.First, conditions on c in order to ensure the existence of a solution to this problem are determined. Next, necessary conditions to be satisfied by the point (x1, x2, ..., xn) in which the function attains the minimum are looked...

The problem of nonparametric estimation of a survival function based on a partially censored on the right sample is established in a Bayesian context, using parametric Bayesian techniques. Estimates are obtained considering neutral to the right processes, they are particularized to some of them, and their asymptotic properties are studied from a Bayesian point of view. Finally, an application to a Dirichlet process is simulated.

The minimum variance unbiased, the maximum likelihood, the Bayes, and the naive estimates of the reliability function of a normal distribution are studied. Their asymptotic normality is proved and asymptotic expansions for both the expectation and the mean squared error are derived. The estimates are then compared using the concept of deficiency. In the end an extensive Monte Carlo study of the estimates in small samples is given.

The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.

The shape parameter of the Topp-Leone distribution is estimated from classical and Bayesian points of view based on Type I censored samples. The maximum likelihood and the approximate maximum likelihood estimates are derived. The Bayes estimate and the associated credible interval are approximated by using Lindley's approximation and Markov Chain Monte Carlo using the importance sampling technique. Monte Carlo simulations are performed to compare the performances of the proposed methods. Real and...

The minimum variance linear unbiased estimators (MVLUE), the best linear invariant estimators (BLIE) and the maximum likelihood estimators (MLE) based on m selected kth record values are presented for the parameters of the Gumbel and Burr distributions.

Evolutionary computation is a discipline that has been emerging for at least 40 or 50 years. All methods within this discipline are characterized by maintaining a set of possible solutions (individuals) to make them successively evolve to fitter solutions generation after generation. Examples of evolutionary computation paradigms are the broadly known Genetic Algorithms (GAs) and Estimation of Distribution Algorithms (EDAs). This paper contributes to the further development of this discipline by...

In this paper we focus on the problem of using a genetic algorithm for model selection within a Bayesian framework. We propose to reduce the model selection problem to a search problem solved using evolutionary computation to explore a posterior distribution over the model space. As a case study, we introduce ELeaRNT (Evolutionary Learning of Rich Neural Network Topologies), a genetic algorithm which evolves a particular class of models, namely, Rich Neural Networks (RNN), in order to find an optimal...

Generalized length biased distribution is defined as $h\left(x\right)={\phi }_r\left(x\right)f\left(x\right),x>0$, where $f\left(x\right)$ is a probability density function, ${\phi }_r\left(x\right)$ is a polynomial of degree $r$, that is, ${\phi }_r\left(x\right)=a_1(x/{\mu }_1^{\text{'}})+...+a_r(x^r/{\mu }_r^{\text{'}})$, with $a_i>0,i=1,...,r,a_1+...+a_r=1,{\mu }_i^{\text{'}}=E\left(x^i\right)$ for $f\left(x\right),i=1,2...,r$. If $r=1$, we have the simple length biased distribution of Gupta and Keating [1]. First, characterizations of exponential, uniform and beta distributions are given in terms of simple length biased distributions. Next, for the case of generalized distribution, the distribution of the sum of $n$ independent variables is put in the closed form when $f\left(x\right)$...

An adaptive output regulation design method is proposed for a class of output feedback systems with nonlinear exosystem and unknown parameters. A new nonlinear internal model approach is developed in the present study that successfully converts the global robust output regulation problem into a robust adaptive stabilization problem for the augmented system. Moreover, an output feedback controller is achieved based on a type of state filter which is designed for the transformed augmented system....

We construct a new class of data driven tests for uniformity, which have greater average power than existing ones for finite samples. Using a simulation study, we show that these tests as well as some "optimal maximum test" attain an average power close to the optimal Bayes test. Finally, we prove that, in the middle range of the power function, the loss in average power of the "optimal maximum test" with respect to the Neyman-Pearson tests, constructed separately for each alternative, in the Gaussian...