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In this paper we study some important aspects of the Kies distribution by deriving expressions for its percentile measures, raw moments, reliability measures etc. The maximum likelihood estimation of the parameters of the distribution have been discussed and the distribution has been fitted to certain real life data sets. The asymptotic behaviour of maximum likelihood estimators are also studied by...
We consider the general situation of fitting an assumed nonlinear regression model which is possibly misspecified. The minimax designs for both response prediction and extrapolation in biased nonlinear regression models are discussed. We extend previous work of others from linear response or a given function of linear response to intrinsically nonlinear response. Several examples are illustrated such...
In this paper we develop some natural “goodness-of-fit” tests for the Gompertz growth curve model (GGCM) based on the empirical estimate of relative growth rate (RGR). Existing approaches of goodness-of-fit tests for growth curve models are mainly based on finite differences of the size data (Bhattacharya et al., Commun Stat Theory Methods 38:340–363, 2009). In growth curve studies the underlying...
It is natural to assume for rating data an ordinal scale consisting of $$k$$ k categories (in ascending order of satisfaction). At first glance, ratings can be summarized by a location index (as the median), resulting in a synthesis that takes into account the ordinal nature of data. On the other hand, ratings are often converted into scores and treated as a quantitative variable. More generally,...
In this paper, and based on records of a sequence of iid random variables from the generalized exponential distribution, we consider the problem of the existence of the maximum likelihood estimates of the shape and scale parameters. Existence and uniqueness of the MLE’s are proved. Different transforming based estimates and confidence intervals of these parameters are then derived. The performances...
The original paper entitled “Delle relazioni tra gli indici di variabilità (Nota I)” by Gaetano Pietra was first published in Atti del Reale Istituto Veneto di Scienze, Lettere e Arti. 1915, Vol. LXXIV, Part I, pages 775–792. We thank the Istituto Veneto di Scienze Lettere e Arti that kindly permitted the publication of this translation. The paper was translated by Pierpaolo Brutti and Stefania Gubbiotti...
The main objective of present paper is to consider robust Bayesian analysis of the Weibull failure model under an $$\varepsilon $$ ε -contamination class of priors for the parameters. The Bayes estimators for the mean life, reliability function and failure rate are obtained under the squared error loss function and LINEX loss function. For numerical illustrations we present simulation study...
Complex models typically involve intractable likelihood functions which, from a Bayesian perspective, lead to intractable posterior distributions. In this context, Approximate Bayesian computation (ABC) methods can be used in order to obtain a valid posterior approximation. However, when simulation from the model is computationally demanding, then the ABC approach may be cumbersome. We discuss an...
Consider a linear semiparametric regression model with normal errors in which the mean function depends on two parameters, a p-dimensional regression parameter, which is the parameter of interest, and an unknown function, which is a nuisance parameter. We consider estimation of the parameter of interest using an integrated likelihood function, in which the nuisance parameter is eliminated from the...
In multiple regression under the normal linear model, the presence of multicollinearity is well known to lead to unreliable and unstable maximum likelihood estimates. This can be particularly troublesome for the problem of variable selection where it becomes more difficult to distinguish between subset models. Here we show how adding a spike-and-slab prior mitigates this difficulty by filtering the...
Empirical Bayes methods are often thought of as a bridge between classical and Bayesian inference. In fact, in the literature the term empirical Bayes is used in quite diverse contexts and with different motivations. In this article, we provide a brief overview of empirical Bayes methods highlighting their scopes and meanings in different problems. We focus on recent results about merging of Bayes...
We discuss two challenging scenarios for frequentist and/or Bayesian inference for categorical data. First, for parameter space regions described by order restrictions, frequentist methods are less straightforward than Bayesian methods, especially for interval estimation. Second, for marginal modeling, frequentist inference is currently feasible only in relatively simplistic settings and Bayesian...
A scoring rule $$S(x; q)$$ S ( x ; q ) provides a way of judging the quality of a quoted probability density $$q$$ q for a random variable $$X$$ X in the light of its outcome $$x$$ x . It is called proper if honesty is your best policy, i.e., when you believe $$X$$ X has density $$p$$ p , your expected score is optimised by the choice $$q =...
The aim of this contribution is to discuss approximate Bayesian computation based on the asymptotic theory of modified likelihood roots and log-likelihood ratios. Results on third-order approximations for univariate posterior distributions, also in the presence of nuisance parameters, are reviewed and the computation of asymptotic credible sets for a vector parameter of interest is illustrated. All...
Experimental design represents the typical context in which the interplay between Bayesian and frequentist methodology is natural and useful. Before the data are observed, it is licit and unavoidable even for a Bayesian statistician to take into account sample variability for the evaluation of statistical procedures and for decision making. At the same time, design planning fatally involves a number...
The occurrence of instantaneous or early failures is a common phenomenon observed in life testing experiments. Such failures are called inliers. In this article, an attempt has been made to model inliers using Rayleigh distribution. We propose the estimation procedures and tests of hypothesis of the parameters in the model. The validity of the model is studied using Goodness-of-fit testing and other...
In the present work we study the asymptotic distribution of the age and residual life in a renewal process. The bivariate distribution so derived is Schur-constant with marginal distributions as equilibrium discuss the reliability properties and the copula. The bivariate ageing properties and some stochastic orders connecting them are explored. It is shown that various time dependent measures of association...
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