Communications in Statistics: Theory and Methods

Ko, Mi-Hwa

doi: 10.1080/03610926.2013.815212pmid: N/A

In this paper we obtain the central limit theorem for weighted sums of the form ∑1 ⩽ i ⩽ nan, iXi, where is an array of non negative numbers such that , max 1 ⩽ i ⩽ nan, i → 0 as n → ∞ and is a field of associated random variables with EXi = 0 and EX2i < ∞. As application, we give a central limit theorem for the partial sum of linear random field .

Fallah, Lida; Golparvar, Leila; Parsian, Ahmad

doi: 10.1080/03610926.2013.815778pmid: N/A

AbstractIn this paper, we assume that the lifetimes have a two-parameter Pareto distribution and discuss some results of progressive Type-II censored sample. We obtain maximum likelihood estimators and Bayes estimators of the unknown parameters under squared error loss and a precautionary loss functions in progressively Type-II censored sample. Robust Bayes estimation of unknown parameters over three different classes of priors under progressively Type-II censored sample, squared error loss, and precautionary loss functions are obtained. We discuss estimation of unknown parameters on competing risks progressive Type-II censoring. Finally, we consider the problem of estimating the common scale parameter of two Pareto distributions when samples are progressively Type-II censored.

Haq, Abdul; Brown, Jennifer; Moltchanova, Elena; Ibrahim Al-Omari, Amer

doi: 10.1080/03610926.2013.818696pmid: N/A

AbstractIn this article, we propose the best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the unknown parameters of location-scale family of distributions based on double-ranked set sampling (DRSS) using perfect and imperfect rankings. These estimators are then compared with the BLUEs and BLIEs based on ranked set sampling (RSS). It is shown that under perfect ranking, the proposed estimators are uniformly better than the BLUEs and BLIEs obtained via RSS. We also propose the best linear unbiased quantile (BLUQ) and the best linear invariant quantile (BLIQ) estimators for normal distribution under DRSS. It is observed that the proposed quantile estimators are more efficient than the BLUQ and BLIQ estimators based on RSS for both perfect and imperfect orderings.

Faliva, M.; Potì, V.; Zoia, M. G.

doi: 10.1080/03610926.2013.818698pmid: N/A

AbstractThis article deals with the problem of tailoring distributions to embody evidence of moments and dependence structure deviating from those of a given parent law. First, we show that finite-moment distributions can be reshaped, to allow for extra kurtosis, asymmetry, and dependence by using orthogonal polynomials. Then, we derive a set of orthogonal polynomials for adjusting any symmetric density to given requirements in terms of moments. Conditions for positiveness of the resulting polynomially modified distribution are further established. This provides a broader approach to reshaping parent distributions by means of polynomial adjustments than that currently found in the literature.

Iwińska, Maria; Szymkowiak, Magdalena

doi: 10.1080/03610926.2013.818699pmid: N/A

AbstractUnder the reliability conditions NBU/NWU or IFRA/DFRA, the exponential distribution is characterized by stochastic ordering properties and by increasing convex ordering properties which link the Pascal compound with record values, spacing between record values and record values with a random index.

Bayoud, Husam Awni

doi: 10.1080/03610926.2013.818700pmid: N/A

AbstractThe shape parameter of Topp–Leone distribution is estimated in this article from the Bayesian viewpoint under the assumption of known scale parameter. Bayes and empirical Bayes estimates of the unknown parameter are proposed under non informative and suitable conjugate priors. These estimates are derived under the assumption of squared and linear-exponential error loss functions. The risk functions of the proposed estimates are derived in analytical forms. It is shown that the proposed estimates are minimax and admissible. The consistency of the proposed estimates under the squared error loss function is also proved. Numerical examples are provided.

Krishnamoorthy, K.; Peng, Jie; Zhang, Dan

doi: 10.1080/03610926.2013.821486pmid: N/A

AbstractInterval estimation procedures for the ratio of two Poisson means, weighted average of Poisson rates, and product of powers of Poisson means are considered. We propose a confidence interval (CI) based on the modified large sample (MLS) approach, and compare with the Cox CIs and the Wilson-score CIs. Our numerical studies indicate that the MLS CI is comparable with the Cox CI, and offers improvement in some cases. We also provide MLS CI for a weighted sum of Poisson means and compare with the available approximate CIs. The methods are illustrated using two examples.

Podgórski, Krzysztof; Wallin, Jonas

doi: 10.1080/03610926.2013.821489pmid: N/A

AbstractIt is rigorously shown that the generalized Laplace distributions and the normal inverse Gaussian distributions are the only subclasses of the generalized hyperbolic distributions that are closed under convolution. The result is obtained by showing that the corresponding two classes of variance mixing distributions—gamma and inverse Gaussian—are the only convolution-invariant classes of the generalized inverse Gaussian distributions.

Kundu, Amarjit; Nanda, Asok K.

doi: 10.1080/03610926.2013.824591pmid: N/A

AbstractRecently, a new class of measure of uncertainty, called “dynamic survival entropy”, has been defined and studied in the literature. Based on this entropy, DSE(α) ordering, IDSE(α), and DDSE(α) classes of life distributions are defined and some results are studied. In this paper, our main aim is to prove some more results of the ordering and the aging classes of life distributions mentioned above. Some important distributions such as exponential, Pareto, Pareto II, and finite range distributions are also characterized. Here we have defined cumulative past entropy and proved some interesting results.

Jose, K. K.; Mariyamma, K. D.

doi: 10.1080/03610926.2013.826979pmid: N/A

AbstractThis paper proposes a new model for autoregressive time series of counts in terms of a convolution of Poisson and negative binomial random variables, known as Poisson–negative binomial (PNB) distribution. The corresponding first-order integer valued time series models are developed and their properties are discussed. The geometric PNB and the geometric semi PNB distributions are also introduced and studied.