A PASCAL program for simulating stable random variates

The purposes of this paper are twofold: (1) To correct two errors in the FORTRAN program accompanying a very important algorithm for the generation of random stable variates, and (2) To present a Pascal translation of that FORTRAN program     

Exact Confidence Intervals,Based on the Z Statistic,for the Difference Between Two Proportions

We show that the confidence interval version of the extended exact unconditional Z test of Suissa and Shuster (1985) for testing the equality of two binomial proportions is due to general results of Buehler (1957), Sudakov and references cited there (1974), and Harris and Soms (1984). We apply these results to obtain exact unconditional confidence intervals for the difference between two proportions, deriving an explicit solution for the “best” outcome, make some comments on Buehler's (1957) method and give a numerical example. The Appendix contains a listing of the necessary FORTRAN programs.     

Implementation of fortran random number generators on computers with one's complement arithmetic †

Random number generators can be programmed in FORTRAN using several methods on 1's complement machines. We have presented several methods for the SRU 1107–1108 and CDC 6000 and CYBER series, the two most popular that utilize 1's complement arithmetic. We believe the logical mask method to be the most efficient technique based on execution time on both machines. This method requires only a little more than one-half the time of the signed residue method on the SRU 1107–1108 and a little more than two thirds the time of the unsigned residue method on the CDC 6000–CYBER. A fast composite generator in FORTRAN uses the logical mask merhod combined with the FLD function to implement the table approach of MacLaren and Marsaglia (1965). This generator proves to be more than twice as fast as a previous one for the SRU 1108, Marsaglia and Bray (1968)     

基于平均自下而上时间的两种分类方法的比较

内容提要：诸如疾病分类系统的预后预测和分类方法,常可用于帮助进行临床管理决策。同一疾病总体常可得到多种分类方法,因此有必要比较这些方法以确定最优分类,或者寻找不逊于最优分类的替代方法。本文基于约束平均寿命引入分离度指标来度量分类方法的预后分类效率,这个指标可用来比较以生存时间为结局的两种分类方法的功效,特别是用于非劣性和等效性检验。我们给出了基于配对数据的两个分离度的估计与检验方法。模拟结果提示,检验方法在适当的样本量条件下能够控制第一类错误,两个实例表明在医学临床中的应用。     

Some recent results for series system reliability

Asymptotic properties of key test results ate obtained. Some further results on the Lindstrom-Madden method are given, including a binomial-Poisson inequality, together with some numerical examples. Simplified proofs of some results of Pledger and Proschan (1971) and Nevius, Proschan and Sethuraman (1977) are provided and the listing of a FORTRAN program to calculate a lower bound to the 1-α lower confidence limit on the system reliability is given.     

An algorithm for computing nonparametric estimators of change‐points

An efficient FORTRAN subroutine for computing three nonparametric point estimators of change-points is offered. Estimates computed from the subroutine are obtained for two classical data sets     

Elimination of computer — induced errors

Computer solutions obtained in certain statistical applications can be seriously distorted because of the inability of the hardware to represent all numbers exactly. In this paper the author discusses a software system which eliminates that problem. The system is written in ASA standard FORTRAN, and hence is efficient and portable. A built-in preprocessor makes it possible to invoke the system automatically; the user need only write normal FORTRAN arithmetic expressions.     

Maximum likelihood estimation in the proportional hazards model of random censorship

The maximum likelihood estimator (MLE) for the survival function S_Tunder the proportional hazards model of censorship is derived and shown to differ from the Abdushukurov-Cheng-Lin estimator when the class of allowable distributions includes all continuous and discrete distributions. The estimators are compared via an example. The MLE is calculated using a Newton-Raphson iterative procedure and implemented via a FORTRAN algorithm.     

An improved comorbidity summary score for measuring disease burden and predicting mortality with applications to two national cohorts

Abstract

Research involving administrative healthcare data to study patient outcomes requires the investigator to account for the patient’s disease burden in order to reduce the potential for biased results. Here we develop a comorbidity summary score based on variable importance measures derived from several statistical and machine learning methods and show it has superior predictive performance to the Elixhauser and Charlson indices when used to predict 1-year, 5-year, and 10-year mortality. We used two large Veterans Administration cohorts to develop and validate the summary score and compared predictive performance using the area under ROC curve (AUC) and the Brier score.     

Computing nonparametric functional estimates in semiparametric problems

The purpose of this note is to provide a brief account of available FORTRAN Routines for computing nonparametric functional estimates, Frequently used in semiparametric problems, evaluated at each data point. Then semiparametric estimates can be computed employing the use-favored economic software.     

Computing nonparametric functional estimates in semiparametric problems

The purpose of this note is to provide a brief account of available FORTRAN Routines for computing nonparametric functional estimates, Frequently used in semiparametric problems, evaluated at each data point. Then semiparametric estimates can be computed employing the use-favored economic software.     

Computing factors for exact two-sided tolerance limits for a normal distribution

A self-contained FORTRAN subroutine is provided which computes factors for Wald-Wolfowitz type tolerance limits allowing arbitrary combinations of sample size n and degrees of freedom ν. The exact calculations from our program reveal inadequacies of two existing approximations, especially when ν ? n. Numerous applications where ν ≠ n ? 1 are cited; two of these are discussed and illustrated.     

On three and four vicious walkers

We establish a reflection principle for three lattice walkers and use this principle to reduce the enumeration of configurations of three vicious walkers to the enumeration of configurations of two vicious walkers. More precisely, the reflection principle leads to a bijection between three walks (L₁, L₂, L₃) such that L₂ intersects both L₁ and L₃ and three walks (L₁, L₂, L₃) such that L₁ intersects L₃. Hence we find a combinatorial interpretation of the formula for the generating function for the number of configurations of three vicious walkers, originally derived by Bousquet-Mélou by using the kernel method, and independently by Gessel by using tableaux and symmetric functions. This answers a question posed by Gessel and Bousquet-Mélou. We also find a reflection principle for four vicious walks that leads to a combinatorial interpretation of a formula derived from Gessel's theorem.     

A statistical signalling model for use in surveillance of adverse drug reaction data

SUMMARY This paper presents a statistically superior lag-adjusted model for detecting increased frequency of reports of adverse drug event (ADE) rates. The effect of a significant lag time between ADE occurrence and report dates is studied. The approach in this paper to analyzing ADE data of this nature involves proposing a statistical model that utilizes a lag density function. The statistical method proposed was the development of an 'exact' procedure to monitor drugs that have a low incidence of ADEs. The approach determines statistically whether a change in the frequency of a specific ADE exists between two predetermined time intervals. There exist immense public health implications associated with the early detection of serious ADEs. The reduced risk of unfavorable outcomes associated with medication therapy is the goal of all involved. Simulated illustrations and discussion are provided, along with a detailed FORTRAN program used to implement the newly suggested lag-adjusted procedure.     

Approximations for the doubly noncentral-F distribution

The approximate normality of the cube root of the noncentral chi-square observed by Aty (1954) and an Edgeworth-series expansion are used to derive an approximation for the doubly noncentral-F distribution. Another approximation in terms of a noncentral-F distribution is also proposed. Both these approximations are seen to compare favorably with some earlier approximations due to Das Gupta (1968) and Tiku (1972). The problem of approximating the cumulants of the doubly noncentral-F variable, which is pivotal in Tiku’s approximation, is examined and use of a noncentral-F distribution is seen to provide a good solution for it. A FORTRAN routine for the Edgeworth-series approximation is given.     

Constructing optimal router bit life sequential experimental designs: New results with a case study

Consider the experiment to improve router bit life as reported in Phadke (1986 Phadke, M. S. 1986. Design optimization case studies. AT &; T Technical Journal 65:51–68.[Crossref], [Web of Science ®] , [Google Scholar]). The goal of the experiment was to increase the life of the router bit before it gets dull, which causes excessive dust formation and consequent expensive cleaning operation to smooth the edges of the boards. A 32-run experimental design was used including seven two-level factors and two four-level factors (cf. Table 1). In this experiment and others, factorial designs with a mixture of two-level and μ( > 2)-level factors may be adopted. Sequential experiments composed of initial experiments and follow-up experiments are widely used to resolve ambiguities involving the aliasing of factorial effects. This article investigates the construction and theoretical properties of optimal designs for sequential experiments with a mixture of α two-level and β μ-level factors for the first time. Constructing optimal design for the router bit life sequential experiment will be discussed for a practical use. From the numerical results, it is found that using a uniform design as the initial experimental design for the router bit life experiment is highly recommended to get an efficient router bit life sequential experimental design. The novelty and significance of the work are evaluated by comparing our results to the existing literature.     

Counting strings at height j in Dyck paths

Let τ be an arbitrary lattice path, called in this context string, consisting of two kinds of steps (rises and falls) and let j be a non-negative integer.In this paper, the explicit formula for the generating function F_j associated with the Dyck path statistic “number of occurrences of τ at height j” is evaluated.For the expression of F_j some basic characteristics of the string are used, namely its number of rises, height, depth and periodicity, as well as the generating function of the Catalan numbers.     

A strong law of large number for negatively dependent and non identical distributed random variables in the framework of sublinear expectation

Abstract

In this article, in the framework of sublinear expectation initiated by Peng, we derive a strong law of large numbers (SLLN) for negatively dependent and non identical distributed random variables. This result includes and extends some existing results. Furthermore, we give two examples of our result for applications.     

Weak and strong laws of large numbers for sub-linear expectation

Abstract

In this paper, we derive a new form of weak laws of large numbers for sub-linear expectation and establish the equivalence relation among this new form and the other two forms of weak laws of large numbers for sub-linear expectation. Moreover, we obtain the strong laws of large numbers for sub-linear expectation under a general moment condition by applying our new weak laws of large numbers.     

Comparison of programs MULT,ESTIMATE and BROWNIE

I describe and compare programs ESTIMATE (one-age class band recovery), BROWNIE (two-age class band recovery) and MULT (one- and two-age class band recovery and extensions). All are easy to use and suited for the purposes for which they were designed. MULT offers considerable advantages over the other two programs, in providing a unified framework for both one- and two-age class band recovery problems, as well as extensions to allow inclusion of a covariate, banding twice per year, unequal intervals between banding periods, and analysis of reward-band data. MULT is menu-driven, and offers additional advantages in terms of ease of input and output and user-modified defaults (e.g. selection or suppression of some printed output). Users seeking additional flexibility are referred to program SURVIV but advised that both user sophistication and software (i.e. a FORTRAN compiler) beyond that required for MULT, ESTIMATE or BROWNIE would be required.