Using characterization conditions of continuous distributions in terms of moments of order statistics given in [12], [23], [6] and [7] we present new goodness-of-fit techniques.
In this paper a new family of statistics based on -divergence for testing goodness-of-fit under composite null hypotheses are considered. The asymptotic distribution of this test is obtained when the unspecified parameters are estimated by maximum likelihood as well as minimum -divergence.
Using characterization conditions of continuous distributions in terms of moments of order statistics and moments of record values we present new goodness-of-fit techniques.
Using the Bahadur representation of a sample quantile for m-dependent and strong mixing random variables, we establish the asymptotic distribution of the Hurwicz estimator for the coefficient of autoregression in a linear process with innovations belonging to the domain of attraction of an α-stable law (1 < α < 2). The present paper extends Hurwicz's result to the autoregressive model.
En este trabajo se describe la implementación de un algoritmo para el cálculo de polinomios zonales, así como dos aplicaciones explícitas de éstos en el ámbito del análisis multivariante. Concretamente, esta implementación permite obtener resultados de sumación aproximados para funciones hipergeométricas de argumento matricial que, a su vez, pueden utilizarse en la génesis de distribuciones multivariantes discretas con frecuencias simétricas. De igual forma, se pone en práctica un conocido resultado...
For data generated by stationary Markov chains there are considered estimates of chain parameters minimizing –divergences between theoretical and empirical distributions of states. Consistency and asymptotic normality are established and the asymptotic covariance matrices are evaluated. Testing of hypotheses about the stationary distributions based on –divergences between the estimated and empirical distributions is considered as well. Asymptotic distributions of –divergence test statistics are...
Studentization and analysis of variance are simple in Gaussian families because X̅ and S² are independent random variables. We exploit the independence of the spacings in exponential populations with location λ and scale δ to develop simple ways of dealing with inference on the location parameter, namely by developing an analysis of scale in the homocedastic independent k-sample problem.
2000 Mathematics Subject Classification: 33C90, 62E99.The Fisher information matrix for three generalized beta distributions are derived.
An alternative classification of the Pearson family of probability densities is related to the orthogonality of the corresponding Rodrigues polynomials. This leads to a subset of the ordinary Pearson system, the so-called Integrated Pearson Family. Basic properties of this family are discussed and reviewed, and some new results are presented. A detailed comparison between the Integrated Pearson Family and the ordinary Pearson system is presented, including an algorithm that enables one to decide...
In this paper it is proved that the distribution of the logarithmic series is not invertible while it is found to be invertible if corrected by a suitable affinity. The inverse distribution of the corrected logarithmic series is then derived. Moreover the asymptotic behaviour of the variance function of the logarithmic distribution is determined. It is also proved that the variance function of the inverse distribution of the corrected logarithmic distribution has a cubic asymptotic behaviour.
We derive the two-sample Kolmogorov-Smirnov type test when a nuisance linear regression is present. The test is based on regression rank scores and provides a natural extension of the classical Kolmogorov-Smirnov test. Its asymptotic distributions under the hypothesis and the local alternatives coincide with those of the classical test.