Identifiability of differentiable bayes estimators of the uniform scale parameter

The problem of estimating the uniform scale parameter under the squared error loss function is investigated from a Bayesian viewpoint. A complete characterization of differentiable Bayes estimators and generalized Bayes estimators is given. The solution determines a family of prior measures both proper and improper, involving densities whose support is the whole parameter space, i.e, the interval (0,00)' Relations between degrees of smoothness of the estimators and the priors are investigated. We will also consider sequences, depending on the sample size, of Bayes (generalized Bayes) estimators with a fixed structure which are generated from a unique prior measure. They will be named strong Bayes sequences or strong generalized Bayes sequences. We characterize this type of Bayes estimation which is more restrictive than the usual one. As a consequence oithe characterization results, we will prove that strong Bayes sequences of polynomial form are not possible for the uniform scale parameter. Moreover we will show that the sequence whose components are the minimum risk equivariant estimator for each sample size is the best strong generalized Bayes sequence of polynomial form

Note on characterization problem of Nagaraja and Nevzorov

In this note a conjecture of Nagaraja and Nevzorov (1997) concerning the characterization of distributions functions by a convex conditional mean function is proved. It is not neccesary furthermore to suppose that the c.d. f. is continuous and the characterization does hold without assumptions considered in the result of the above reference. The present note gives a general theorem of characterization in terms of the convex conditional mean function introduced by Nagaraja and Nevzorov (1997) determining explicitly the distribution function associated with each one

Characterizations involving conditional expectations based on a functional derivative approach

We introduce a notion of the derivative with respect to a distribution function, not relating necessarily to probability, which generalizes the concept of the derivative as proposed by Lebesgue (1973). The differential calculus required to solve the linear differential equation involved in this notion of the derivative is included in the paper. The definition given here may also be considered as the inverse operator of a modified notion of the Riemmann--Stieltjes integral. Both this unified approach and the results of differential calculus allow us to characterize distributions in terms of three different types of conditional expectations. In applying these results, a test of goodness-of-fit is also indicated. Finally, two characterizations of a general Poisson process are included, based on conditional expectations. Specifically, a useful result for the homogeneous Poisson process is generalized to a general context

On the Conjecture of Kochar and Korwar

In this paper, we solve for some cases a conjecture by Kochar and Korwar (1996) in relation with the normalized spacings of the order statistics related to a sample of independent exponential random variables with different scale parameter. In the case of a sample of size n=3, they proved the ordering of the normalized spacings and conjectured that result holds for all n. We give the proof of this conjecture for n=4 and for both spacing and normalized spacings. We also generalize some results to n>

Comparisons among spacings from two populations

In this work, we obtain some new results in the area of stochastic comparisons of simple and normalized spacings from two heterogeneous populations. We also show some applications of our results to multiple-outlier models

On identifiability of MAP processes

Two types of transitions can be found in the Markovian Arrival process or MAP: with and without arrivals. In transient transitions the chain jumps from one state to another with no arrival; in effective transitions, a single arrival occurs. We assume that in practice, only arrival times are observed in a MAP. This leads us to define and study the Effective Markovian Arrival process or E-MAP. In this work we define identifiability of MAPs in terms of equivalence between the corresponding E-MAPs and study conditions under which two sets of parameters induce identical laws for the observable process, in the case of 2 and 3-states MAP. We illustrate and discuss our results with examples

Allocation policies of redundancies in two-parallel-series and two-series-parallel systems

In this paper comparisons of allocation policies of components in two-parallel-series systems with two types of components are provided with respect to both, the hazard rate and the reversed hazard rate orders. The main results indicate that the life of this kind of system is stochastically maximized by unbalancing as much as possible the two classes of components. We only assume that the two distributions implied in the model have proportional hazard rates. The same type of comparisons are also given for the dual model, the two-series-parallel systems but assuming that the distributions implied in the model have proportional reversed hazard rates, and therefore the final conclusion is the opposite; that is, the reliability of the system improves as the similarity between the two parallel subsystems increasesThe authors of the paper would like to acknowledge the financial support by MEC project ECO2012-38442 and the project 2009/00035/00

Los estadísticos dan guerra

Audiovisuales. Concurso Stat Wars. Disponible en http://www.youtube.com/watch?v=1a6J9KXyoQo .El pasado 13 de noviembre, en el marco de la Semana de la Ciencia, el departamento organizó la competición Stats Wars, una batalla estadística que congregó a mil asistentes, casi todos estudiantes de secundaria y bachillerato, en el auditorio de Leganés. El día 29, la universidad acogerá la jornada de Estadística de Leganés, que contará con otro concurso, Stats&Google, para estudiantes de grado.Contiene: ¿Es el año de la Estadística? Probablemente, sí (p.6) .-- Ser estadístico importa / Rosa Lillo (p.7) .-- Stat Wars,: que empiece el espectáculo (pp. .8-9) .-- La importancia de la estadística en lo cotidiano / Ignacio Cascos (p.9)

Clustering and classifying images with local and global variability

A procedure for clustering and classifying images determined by three classification variables is presented. A measure of global variability based on the singular value decomposition of the image matrices, and two average measures of local variability based on spatial correlation and spatial changes. The performance of the procedure is compared using three different databases

Bayesian estimation for the M/G/1 queue using a phase type approximation

This article deals with Bayesian inference and prediction for M/G/1 queueing systems. The general service time density is approximated with a class of Erlang mixtures which are phase type distributions. Given this phase type approximation, an explicit evaluation of measures such as the stationary queue size, waiting time and busy period distributions can be obtained. Given arrival and service data, a Bayesian procedure based on reversible jump Markov Chain Monte Carlo methods is proposed to estimate system parameters and predictive distributions