Statistical concepts and methods

XV. 629 hlm. : - ; 21 cm

Some new constructions of bivariate Weibull models

Bivariate Weibull, bivariate exponential, Weibull minimum, random hazards, quadrant dependence, independence representation, moments,

Statistics: principles and methods

ix+501hlm.;26c

Statistical Concepts and Methods

X, 639 tr.; 23 cm

Asymptotic properties of estimators in a binomial reliability growth model and its continuous-time analog

This article deals with a nonhomogeneous binomial (NHB) model where the probability of failure at the ith trial has the functional form μ[iβ - (i) - 1)β], 0 < μ < 1, 0 < β < 1. The model arises in the context of reliability growth of a one-shot system during the successive stages of its development, and is a discrete analog of a continuous-time growth model based on a nonhomogeneous Poisson process (NHPP) with Weibull intensity. Asymptotic properties of the 'continuous analog estimators' (CAE's) are compared with those of the maximum likelihood estimators (MLE's) in the continuous-time growth model. Unlike the NHPP model, the MLE's in the NHB model are not available in closed forms, and derivation of their asymptotic properties confronts the fundamental difficulty that the appropriately scaled information matrix is asymptotically singular. To get around this difficulty, we first link the CAE's to the maximization of a certain pseudo-likelihood, examine the corresponding Taylor expansion, and relate that to the expansion of the correct NHB likelihood. The closeness of the two expansions is then used to establish consistency and asymptotic normality of the MLE's and asymptotic equivalence with the CAE's

Inference procedures for bivariate exponential model of Gumbel

In this article, statistical properties of an absolutely continuous bivariate exponential model due to Gumbel (1960) are examined and the Fisher information matrix is derived. Simple estimators are motivated from a structural representation of the model and are compared both in terms of asymptotic efficiency and finite sample simulation. Besides their good performance, some of the simple estimators lead to exact or nearly exact confidence interval and hypotheses test procedures. The proposed methods are illustrated by reanalyzing a data set to which asymptotic methods were employed by Gross and Lam (1981) under a different bivariate exponential model.Dependent lifetimes Fisher information simple estimators asymptotic efficiency confidence intervals simulation

Student study guide: to accompany statistics principles and methods

v, 16-3 hlm. : ilus. ; 21 cm