Noninformative priors for linear combinations of normal means with unequal variances

For normal populations with unequal variances, we develop matching priors and reference priors for a linear combination of the means. Here, we find three second-order matching priors: a highest posterior density (HPD) matching prior, a cumulative distribution function (CDF) matching prior, and a likelihood ratio (LR) matching prior. Furthermore, we show that the reference priors are all first-order matching priors, but that they do not satisfy the second-order matching criterion that establishes the symmetry and the unimodality of the posterior under the developed priors. The results of a simulation indicate that the second-order matching prior outperforms the reference priors in terms of matching the target coverage probabilities, in a frequentist sense. Finally, we compare the Bayesian credible intervals based on the developed priors with the confidence intervals derived from real data.     

Economic design of acceptance sampling plans for truncated life test using Frechet distribution

In this article designing of acceptance sampling plans for the truncated life test is proposed using economic approach by assuming that the lifetime of a product follows Frechet distribution based on median. The optimal sampling plans to meet the consumer’s confidence level with minimum total cost are designed. Efficiency of the proposed plan is also analyzed.     

A Bayesian approach to non-parametric monotone function estimation

Summary.  The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate. The small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods. Asymptotic results are also given that show that Bayesian methods provide consistent function estimators for a large class of smooth functions. An example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple-regression model where two functions are constrained to be monotone.     

Probability density function of quotient of order statistics from the pareto,power and weibull distributions

This paper deals with the probability density functions of quotient of order statistics. We use the Mellin transform technique, to find the distribution of the quotient Z= X/Xwhere X.,X(i < j) are the ith and jth order statistics from the Pareto, Power and Weibull distributions     

z Test for the significance of the mean of a stable probability distribution with 1<α≤2

The analysis of data using a stable probability distribution with tail parameter α<2 (sometimes called a Pareto–Levy distribution) seems to have been avoided in the past in part because of the lack of a significance test for the mean, even though it appears to be the correct distribution to use for describing returns in the financial markets. A z test for the significance of the mean of a stable distribution with tail parameter 1<α≤2 is defined. Tables are calculated and displayed for the 5% and 1% significance levels for a range of tail and skew parameters α and β. Through the use of maximum likelihood estimates, the test becomes a practical tool even when α and β are not that accurately determined. As an example, the z test is applied to the daily closing prices for the Dow Jones Industrial average from 2 January 1940 to 19 March 2010.     

Analysis of all-zero binomial outcomes with borderline and equilibrium priors

This article is concerned with the analysis of a random sample from a binomial distribution when all the outcomes are zero (or unity). We discuss how elicitation of the prior can be reduced to asking the expert whether (and which of) the so-called borderline or equilibrium priors are plausible.     

对《劳动合同法》立法宗旨的认识

《劳动合同法》从立法之初,其立法宗旨就引发了社会各界的激烈争论,主要集中在立法根据以及＂单保护＂还是＂双保护＂等问题上。应从倾斜保护的角度认识《劳动合同法》的立法宗旨,即《劳动合同法》既不是＂单保护＂,也不是＂双保护＂,而是在保护劳动者权益的同时,兼顾保护了用人单位的利益。     

A Quality Risk Management Model Approach for Cell Therapy Manufacturing

International regulatory authorities view risk management as an essential production need for the development of innovative, somatic cell‐based therapies in regenerative medicine. The available risk management guidelines, however, provide little guidance on specific risk analysis approaches and procedures applicable in clinical cell therapy manufacturing. This raises a number of problems. Cell manufacturing is a poorly automated process, prone to operator‐introduced variations, and affected by heterogeneity of the processed organs/tissues and lot‐dependent variability of reagent (e.g., collagenase) efficiency. In this study, the principal challenges faced in a cell‐based product manufacturing context (i.e., high dependence on human intervention and absence of reference standards for acceptable risk levels) are identified and addressed, and a risk management model approach applicable to manufacturing of cells for clinical use is described for the first time. The use of the heuristic and pseudo‐quantitative failure mode and effect analysis/failure mode and critical effect analysis risk analysis technique associated with direct estimation of severity, occurrence, and detection is, in this specific context, as effective as, but more efficient than, the analytic hierarchy process. Moreover, a severity/occurrence matrix and Pareto analysis can be successfully adopted to identify priority failure modes on which to act to mitigate risks. The application of this approach to clinical cell therapy manufacturing in regenerative medicine is also discussed.     

Exact likelihood inference for Laplace distribution based on Type-II censored samples

We develop exact inference for the location and scale parameters of the Laplace (double exponential) distribution based on their maximum likelihood estimators from a Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Upon conditioning first on the number of observations that are below the population median, exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. Tables of quantiles are presented for the complete sample case.     

Bayesian predictive densities based on latent information priors

Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data is assumed to belong to a parametric submodel of a multinomial model. Future observables and data are possibly dependent. The discrepancy of a predictive density to the true conditional density of future observables given observed data is evaluated by the Kullback-Leibler divergence. It is proved that limits of Bayesian predictive densities form an essentially complete class. Latent information priors are defined as priors maximizing the conditional mutual information between the parameter and the future observables given the observed data. Minimax predictive densities are constructed as limits of Bayesian predictive densities based on prior sequences converging to the latent information priors.