Bayesian Design of Special Type of Double Sampling Plans for Compliance Testing

Bayesian acceptance sampling plans, which utilize prior information on the process variation, can be employed as an alternative to conventional types of plans for taking decisions on the disposition of submitted lots. A special type of double sampling inspection plans by attributes with small acceptance numbers using Bayesian methodology is presented in this paper emphasizing its significance over small acceptance number single sampling plans. The procedures for designing such sampling plans for specified degree of discrimination which would ensure protection to the producer and consumer are discussed with illustrations under the conditions for the application of gamma-Poisson distribution.     

Numerical computation of exact moments of the least squares estimator in a first-order stationary autoregressive model

This paper examines the least squares estimator of the autoregressive coefficient in a first-order sta¬tionary autoregressive model. Exact lower-order moments are computed by numerical integrations. From the study of moment values, it is found that the exact distribution of the least squares estimator may be well approximated by a beta distribution.     

Dependency and truncated forms of combinations in multivariate combination-based permutation tests and ordered categorical variables

ABSTRACT

Quite an important problem usually occurs in several multi-dimensional hypotheses testing problems when variables are correlated. In this framework the non-parametric combination (NPC) of a finite number of dependent permutation tests is suitable to cover almost all real situations of practical interest since the dependence relations among partial tests are implicitly captured by the combining procedure itself without the need to specify them [Pesarin F, Salmaso L. Permutation tests for complex data: theory, applications and software. Chichester: Wiley; 2010a]. An open problem related to NPC-based tests is the impact of the dependency structure on combined tests, especially in the presence of categorical variables. This paper’s goal is firstly to investigate the impact of the dependency structure on the possible significance of combined tests in cases of ordered categorical responses using Monte Carlo simulations, then to propose some specific procedures aimed at improving the power of multivariate combination-based permutation tests. The results show that an increasing level of correlation/association among responses negatively affects the power of combination-based multivariate permutation tests. The application of special forms of combination functions based on the truncated product method [Zaykin DV, Zhivotovsky LA, Westfall PH, Weir BS. Truncated product method for combining p-values. Genet Epidemiol. 2002;22:170–185; Dudbridge F, Koeleman BPC. Rank truncated product of p-values, with application to genomewide association scans. Genet Epidemiol. 2003;25:360–366] or on Liptak combination allowed us, using Monte Carlo simulations, to demonstrate the possibility of mitigating the negative effect on power of combination-based multivariate permutation tests produced by an increasing level of correlation/association among responses.     

Goodness—of—fit for the two—parameter weibull distribution with estimated parameters

Goodness—of—fit statistics based on the empirical distribution function (EDF) are not distribution—free when parameters for the hypothesized distribution are estimated. Tables are percentile values of several EDF statistics are available for the two—parameter Weibull distribution when parameters are estimated by maximum likelihood. To determine how these tabled values change when simpler estimators are employed, percentile scores for EDF goodness—of—fit tests were obtained by Monte—Carlo simulation for maximum likelihood estimators (MLEs), good linear unbiased estimators (GLUEs), and modified Cramer—von Mises, Anderson—Darling, and Watson statistics are presented for GLUEs for both complete and censored samples. Critical values for Kolmogorov—Smirnov statistics were less affected by the method of estimation than were closer for MLEs and MGLUEs than for MGLUEs and GLUEs. On the other hand, MGLUE and GLUE results were much more similar to each other than to the MLE results when censoring was light and sample sizes were large.     

Time series models based on the unrestricted skew-normal process

The standard location and scale unrestricted (or unified) skew-normal (SUN) family studied by Arellano-Valle and Genton [On fundamental skew distributions. J Multivar Anal. 2005;96:93–116] and Arellano-Valle and Azzalini [On the unification of families of skew-normal distributions. Scand J Stat. 2006;33:561–574], allows the modelling of data which is symmetrically or asymmetrically distributed. The family has a number of advantages suitable for the analysis of stochastic processes such as Auto-Regressive Moving-Average (ARMA) models, including being closed under linear combinations, being able to satisfy the consistency condition of Kolmogorov’s theorem and providing the guarantee of the existence of such a SUN stochastic process. The family is able to be represented in a hierarchical form which can be used for the ease of simulation. In addition, it facilitates an EM-type algorithm to estimate the model parameters. The performances and suitability of the proposed model are demonstrated on simulations and using two real data sets in applications.     

Estimation of weibull location

A simulation study was carried out to compare the performances of two different simple estimators of the location parameter for a three-parameter Weibull distribution Both Estimators have been suggested by recent paper in the literature. Bras and mean square error are examined for many different sample-size and shape-parameter-value combinations. Strong evidence of the domination of one estimator over the other is found.     

Odd-Burr generalized family of distributions with some applications

We study a new family of continuous distributions with two extra shape parameters called the Burr generalized family of distributions. We investigate the shapes of the density and hazard rate function. We derive explicit expressions for some of its mathematical quantities. The estimation of the model parameters is performed by maximum likelihood. We prove the flexibility of the new family by means of applications to two real data sets. Furthermore, we propose a new extended regression model based on the logarithm of the Burr generalized distribution. This model can be very useful to the analysis of real data and provide more realistic fits than other special regression models.     

Bayesian estimation of rare sensitive attribute

Randomized response models have been used to estimate a population proportion of a sensitive attribute. A randomized device is typically employed to protect respondent's privacy in a survey. In addition, an unrelated question is asked to improve the statistical efficiency. In this article, we propose Bayesian estimation of rare sensitive attribute using randomized response technique, which includes a rare unrelated attribute. Two cases are considered, the proportion of a rare unrelated attribute is known and unknown. A simulation study is conducted to assess the performance of the models using mean absolute error and coverage probability. The results show that the performance depends on the parameters and is robust to priors.     

Corrected maximum likelihood estimators in heteroscedastic symmetric nonlinear models

In this article, we derive general matrix formulae for second-order biases of maximum likelihood estimators (MLEs) in a class of heteroscedastic symmetric nonlinear regression models, thus generalizing some results in the literature. This class of regression models includes all symmetric continuous distributions, and has a wide range of practical applications in various fields such as engineering, biology, medicine and economics, among others. The variety of distributions with different kurtosis coefficients than the normal may give more flexibility in the choice of an appropriate distribution, particularly to accommodate outlying and influential observations. We derive a joint iterative process for estimating the mean and dispersion parameters. We also present simulation studies for the biases of the MLEs.     

On the reciprocity of connections in weighted and unweighted networks

Bivariate Bernoulli and bivariate geometric distributions are proposed to model reciprocity in weighted and unweighted networks. Sampling properties of commonly used reciprocity measures are studied, under both presence and absence of reciprocity. Extensions to situations where link parameters depend on outgoing and incoming nodes are investigated. Results are illustrated with a data set, on 50 anesthesia providers at a hospital, that describes the number of times an anesthesia provider starting an operation transfers his/her responsibilities to another anesthesia provider.