A multivariate zero-inflated binomial model for the analysis of correlated proportional data

In this paper, a new multivariate zero-inflated binomial (MZIB) distribution is proposed to analyse the correlated proportional data with excessive zeros. The distributional properties of purposed model are studied. The Fisher scoring algorithm and EM algorithm are given for the computation of estimates of parameters in the proposed MZIB model with/without covariates. The score tests and the likelihood ratio tests are derived for assessing both the zero-inflation and the equality of multiple binomial probabilities in correlated proportional data. A limited simulation study is performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates and to compare the nominal levels and powers of both score tests and likelihood ratio tests. The whitefly data is used to illustrate the proposed methodologies.     

On weighted Renyi’s entropy for double-truncated distribution

In a recent paper, Nourbakhsh and Yari (2017 Nourbakhsh, M., and G. Yari. 2017. Weighted Renyi’s entropy for lifetime distributions. Communications in Statistics—Theory and Methods 46 (14):7085–98.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) introduce the weighted version of Renyi’s entropy for left/right truncated random variables and studied their properties in context of reliability analysis. In the present communication we extend the notion of weighted Renyi’s entropy for two-sided truncated random variable. In reliability theory and survival analysis, this measure may help to study the quantitative-qualitative information spectrum of a system/component when it fails between two time points. Various aspects of weighted Renyi’s interval entropy have been discussed and some mistakes in the preceding literature have also been corrected. These results generalize and enhance the related existing results that are developed based on weighted Renyi’s entropy for one-sided truncated random variable. Finally, a simulation study is added to provide the estimates of the proposed measure and to demonstrate the performance of the estimates.     

Asymptotic normality of conditional density estimation under truncated,censored and dependent data

Abstract

In this paper, we focus on the left-truncated and right-censored model, and construct the local linear and Nadaraya-Watson type estimators of the conditional density. Under suitable conditions, we establish the asymptotic normality of the proposed estimators when the observations are assumed to be a stationary α-mixing sequence. Finite sample behavior of the estimators is investigated via simulations too.     

Reliability analysis for stress-strength model from a general family of truncated distributions under censored data

Abstract

Under progressive Type-II censoring, inference of stress-strength reliability (SSR) is studied for a general family of lower truncated distributions. When the lifetime models of the strength and stress variables have arbitrary and common parameters, maximum likelihood and pivotal quantities based generalized estimators of SSR are established, respectively. Confidence intervals are constructed based on generalized pivotal quantities and bootstrap technique under different parameter cases as well. In addition, to compare the equivalence of the strength and stress parameters, likelihood ratio testing of interested parameters is provided as a complementary. Simulation studies and two real-life data examples are provided to investigate the performance of proposed methods.     

On a class of bivariate mixed Sarmanov distributions

Multivariate distributions are more and more used to model the dependence encountered in many fields. However, classical multivariate distributions can be restrictive by their nature, while Sarmanov's multivariate distribution, by joining different marginals in a flexible and tractable dependence structure, often provides a valuable alternative. In this paper, we introduce some bivariate mixed Sarmanov distributions with the purpose to extend the class of bivariate Sarmanov distributions and to obtain new dependency structures. Special attention is paid to the bivariate mixed Sarmanov distribution with Poisson marginals and, in particular, to the resulting bivariate Sarmanov distributions with negative binomial and with Poisson‐inverse Gaussian marginals; these particular types of mixed distributions have possible applications in, for example modelling bivariate count data. The extension to higher dimensions is also discussed. Moreover, concerning the dependency structure, we also present some correlation formulas.     

Waiting time paradox and size biased sampling

Feller's (1971) 'Waiting time for the bus paradox1 is explained by the fact that the long Interarrival times have a better chance of covering an arbitrary point in time than do short interarrival times, This gives rise to size biased sampling and the length of the Interarrival time that contains the arbitrary point has a moment distribution, This paper deals with the characterization of the exponential distribution based on this 'Waiting time paradox'. Similar characterizations of the binomial, the negative binomial, the Poisson and the geometric distributions are obtained.     

Minicommnications

This section of the periodical is reserved for Conclusions (Results), Comments, Conjectures, and Microcommunications.     

Comparison of proportions with asymmetric prior information

In this paper a Bayesian model is developed for comparing two binomial proportions. A two stage hierarchical prior distribution is used to represent prior dependence. Prior exchangeability and independence are shown to be but special cases. The relevant distributions have to be computed numerically and some examples are presented.     

Interval estimation of the negative binomial dispersion parameter

Inference concerning the negative binomial dispersion parameter, denoted by c, is important in many biological and biomedical investigations. Properties of the maximum-likelihood estimator of c and its bias-corrected version have been studied extensively, mainly, in terms of bias and efficiency [W.W. Piegorsch, Maximum likelihood estimation for the negative binomial dispersion parameter, Biometrics 46 (1990), pp. 863–867; S.J. Clark and J.N. Perry, Estimation of the negative binomial parameter κ by maximum quasi-likelihood, Biometrics 45 (1989), pp. 309–316; K.K. Saha and S.R. Paul, Bias corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics 61 (2005), pp. 179–185]. However, not much work has been done on the construction of confidence intervals (C.I.s) for c. The purpose of this paper is to study the behaviour of some C.I. procedures for c. We study, by simulations, three Wald type C.I. procedures based on the asymptotic distribution of the method of moments estimate (mme), the maximum-likelihood estimate (mle) and the bias-corrected mle (bcmle) [K.K. Saha and S.R. Paul, Bias corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics 61 (2005), pp. 179–185] of c. All three methods show serious under-coverage. We further study parametric bootstrap procedures based on these estimates of c, which significantly improve the coverage probabilities. The bootstrap C.I.s based on the mle (Boot-MLE method) and the bcmle (Boot-BCM method) have coverages that are significantly better (empirical coverage close to the nominal coverage) than the corresponding bootstrap C.I. based on the mme, especially for small sample size and highly over-dispersed data. However, simulation results on lengths of the C.I.s show evidence that all three bootstrap procedures have larger average coverage lengths. Therefore, for practical data analysis, the bootstrap C.I. Boot-MLE or Boot-BCM should be used, although Boot-MLE method seems to be preferable over the Boot-BCM method in terms of both coverage and length. Furthermore, Boot-MLE needs less computation than Boot-BCM.     

On some properties of variable size simple random sampling and a limit theorem

This paper introduces a sampling plan for finite populations herein called “variable size simple random sampling” and compares properties of estimators based on it with results from the usual fixed size simple random sampling without replacement. Necessary and sufficient conditions (in the spirit of Hajek (1960)) for the limiting distribution of the sample total (or sample mean) to be normal are given.