Distributions of Runs Revisited

Distributions of runs have important applications in many fields, including biological sequence analysis. The generating function (GF) method provides a unified approach to tackle different run-related problems in multistate trials. By utilizing this method, various run-related distributions are derived in a systematic way for both conditional and unconditional models. The GF approach also naturally yields the asymptotic distributions. For all the distributions considered, the limiting distributions are Gaussian, with mean, variance, and covariance linear functions in the size of the system.     

The effect of parameter estimation on the performance of one-sided Shewhart control charts for zero-inflated processes

ABSTRACT

Zero-inflated probability models are used to model count data that have an excessive number of zeros. Shewhart-type control charts have been proposed for the monitoring of zero-inflated processes. Usually their performance is evaluated under the assumption of known process parameters. However, in practice, their values are rarely known and they have to be estimated from an in-control historical Phase I sample. In the present paper, we investigate the performance of Shewhart-type control charts for zero-inflated processes with estimated parameters and propose practical guidelines for the statistical design of the examined charts, when the size of the preliminary sample is predetermined.     

On generalized hyper-Poisson distribution of order k and its application

ABSTRACT

Here we introduce a new class of distributions namely the generalized hyper-Poisson distribution of order k (GHPD(k)) as an order k version of the alpha-generalized hyper-Poisson distribution of Kumar and Nair (Statistica, 2014b Kumar, C.S., Nair, B.U. (2014b). A three parameter hyper-Poisson distribution and some of its properties. Statistica. 74(2):183–198. [Google Scholar]). Several properties of the GHPD(k) are derived and the estimation of the parameters of the distribution by the method of mixed moments and the method of maximum likelihood is discussed. Certain testing procedures are suggested and all these estimation and testing procedures are illustrated with the help of a real-life data set. Further a simulation study is conducted.     

An introduction to designh optimality with an overview of the literature

A brief introduction to oprimal design theorv is given for those who are not familiar with the subject. A list of 312 selected articles on the theory of optimal design is provided. The bibliography should be sufficiently thorough to be of use to researchers in the field.     

Bayesian prediction for two-parameter weibull lifetime models

Prediction methods for the two-parameter Weibull distribution are computationally complicated. This paper shows how an approximate Bayesian method can be used to simplify the computation and presents a simpler alternative for computing prediction bounds derived classically by Lawless (1973).     

General Saddlepoint Approximation for Testing Separate Location-Scale Families of Hypotheses

For testing separate families of hypotheses, the likelihood ratio test does not have the usual asymptotic properties. This paper considers the asymptotic distribution of the ratio of maximized likelihoods (RML) statistic in the special case of testing separate scale or location-scale families of distributions. We derive saddlepoint approximations to the density and tail probabilities of the log of the RML statistic. These approximations are based on the expansion of the log of the RML statistic up to the second order, which is shown not to depend on the location and scale parameters. The resulting approximations are applied in several cases, including normal versus Laplace, normal versus Cauchy, and Weibull versus log-normal. Our results show that the saddlepoint approximations are satisfactory, even for fairly small sample sizes, and are more accurate than normal approximations and Edgeworth approximations, especially for tail probabilities that are the values of main interest in hypothesis testing problems.     

基于最大梅森素数的随机数

研究表明梅森素数的数字分布是均匀的,由此产生了服从各类分布的随机数．本文就基于最大的梅森素数2^43112609-1产生均匀分布随机数,对其进行了检验并给出简单应用．     

对《中医基础理论》五行学说概念的不同理解

传统教材中对五行和五行学说的解释围绕木火土金水五种物质,认为五行是五种物质及其运动变化,五行学说认为世界是物质的,是由木火土金水五种基本物质构成,并且由五种物质之间的运动变化而生成。对此提出疑问并追溯五行思想的根源,认为五行和五行学说与太阳-月亮-地球母系统的内在规律———生长化收藏有关,并且以这个内在规律为核心轴,将母系统与地球上各种事物和现象构成的诸多子系统相关联,构成五行系统的同构系统。     

General mathematical properties,regression and applications of the log-gamma-generated family

The construction of some wider families of continuous distributions obtained recently has attracted applied statisticians due to the analytical facilities available for easy computation of special functions in programming software. We study some general mathematical properties of the log-gamma-generated (LGG) family defined by Amini, MirMostafaee, and Ahmadi (2014 Amini, M., S. M. T. K. MirMostafaee, and J. Ahmadi. 2014. Log-gamma-generated families of distributions. Statistics 48:913–32.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). It generalizes the gamma-generated class pioneered by Risti? and Balakrishnan (2012 Risti?, M. M., and N. Balakrishnan. 2012. The gamma exponentiated exponential distribution. Journal of Statistical Computation and Simulation 82:1191–206.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). We present some of its special models and derive explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, Shannon entropy, Rényi entropy, reliability, and order statistics. Models in this family are compared with nested and non nested models. Further, we propose and study a new LGG family regression model. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models and therefore can be used more effectively in the analysis of survival data. We prove that the proposed models can provide consistently better fits in some applications to real data sets.