Showing papers on "Sampling distribution published in 1974"

Biostatistics: A Foundation for Analysis in the Health Sciences

Abstract: Introduction to Biostatistics Descriptive Statistics Some Basic Probability Concepts Probability Distributions Some Important Sampling Distributions Estimation Hypothesis Testing Analysis of Variance Simple Linear Regression and Correlation Multiple Regression and Correlation Regression Analysis - Some Additional Techniques The Chi-Square Distribution and the Analysis of Frequencies Nonparametric and Distribution-Free Statistics Vital Statistics.

Statistical techniques in business and economics

Abstract: What is statistics? summarizing data - frequency distributions and graphic presentation describing data - measure of central tendency measures of dispersion and skewness a survey of probability concepts discrete probability distributions the normal probability distribution sampling methods and sampling distributions tests of hypotheses - large samples tests of hypotheses - small samples analysis of variance linear regression and correlation multiple regression and correlation nonparametric methods - chi square applications nonparametric methods - analysis of ranked data statistical quality control index numbers time series and forecasting an introduction to decision making under uncertainty.

Subjective sampling distributions and the additivity of estimates

Abstract: .— Previous studies of sampling distributions have been conducted almost exclusively under the assumption that persons behave in accordance with the “fundamental convention” of probability, i.e. that the sum of all probability estimates will equal 1. When this assumption was tested by asking subjects to give “unrestricted” probability estimates of all possible outcomes of samples from a given population, a general tendency of overestimation made the sum of all probabilities exceed 1 to a considerable extent. The subjective sampling distributions appeared to be unaffected by sample size (N=5 or 10) and number of outcomes, and were flatter than the corresponding “objective” sampling distributions.

Algorithm 488: A Gaussian pseudo-random number generator

Abstract: The algorithm calculates the exact cumulative distribution of the two-sided Kolmogorov-Smirnov statistic for samples with few observations. The general problem for which the formula is needed is to assess the probability that a particular sample comes from a proposed distribution. The problem arises specifically in data sampling and in discrete system simulation. Typically, some finite number of observations are available, and some underlying distribution is being considered as characterizing the source of the observations.

Large Sample Theory of Some Measures of Income Inequality

Abstract: THE MEASUREMENT of economic inequality is a timely and important topic. Often the Gini index or the entire Lorenz curve is used; however, the relative mean deviation (or Pietra ratio) has been used by Schutz [9] and Budd [1] to study United States data. Eltet6 and Frigyes [2] developed new measures to aid in their analysis of Hungary's income distribution, and Kondor [6] has shown that these new indices are related to the relative mean deviation. In order to draw valid conclusions from actual samples, one needs to know the sampling distribution of the statistic used to estimate the measure of inequality. The purpose of the present paper is to adapt methods used by the author [3 and 4] in another context to obtain the large sample theory of the mean deviation, Pietra ratio, and the measures of Eltet6 and Frigyes. Since several of these measures estimate some parameters of the underlying income distribution function, the asymptotic theory of the estimators is more complicated than might appear at first glance.

A Decision-Theoretic Approach to Defining Variables Sampling Plans for Finite Lots: Single Sampling for Exponential and Gaussian Processes

Abstract: A decision-theoretic approach is used to derive a variables sampling plan applicable to finite lots. A sampling distribution is derived for a general manufacturing process, and one-sided acceptance regions are determined for the particular cases in which the manufacturing process is described by either a normal distribution or an exponential distribution. Comparisons show that for a given risk level, a substantial savings in sample sizes can be effected over those required by previously available procedures (hypergeometric plans or variables plans with an infinite lot assumption).

The convergence of Bhattacharyya bounds

Abstract: SUMMARY Bhattacharyya bounds are considered for the unbiased estimation of a parametric function when the sampling distribution is a member of an exponential family of distributions. It is shown that the Bhattacharyya bounds converge to the variance of the best unbiased estimator. The application of this result to variance determination is demonstrated with examples from the negative binomial distribution and from the exponential distribution in a reliability theory context.

The asymptotic distributions of the conditional error rate and risk in discriminant analysis

Abstract: SUMMARY The distributions of the conditional error rate and risk associated with Anderson's classification statistic in the context of the two-population discrimination problem with different means and common covariance matrix are studied. For the most general case where all three population parameters are unknown, the distributions are able to be approximated in the form of asymptotic expansions of degrees higher than previously available. Some key word8: Anderson's classification statistic; Asymptotic distribution; Conditional error rate and risk in discriminant analysis.

Asymptotic Results for Inference Procedures Based on the $r$ Smallest Observations

Abstract: We consider procedures for statistical inference based on the smallest $r$ observations from a random sample. This method of sampling is of importance in life testing. Under weak regularity conditions which include the existence of a q.m. derivative for the square root of the ratio of densities, we obtain an approximation to the likelihood and establish the asymptotic normality of the approximation. This enables us to reach several important conclusions concerning the asymptotic properties of point estimators and of tests of hypotheses which follow directly from recent developments in large sample theory. We also give a result for expected values which has importance in the theory of rank tests for censored data.

Robustness of the studentized range statistic

Abstract: SUMMARY The effects of heterogeneity of variance and nonnormality of population distribution on the sampling distribution of the studentized range are investigated.

The Exact Finite Sample Distribution of Theil's Compatibility Test Statistic and its Application

Abstract: In this article we derive the exact finite sample distribution of a statistic utilized by Theil [10] to test whether sample and prior information are in conflict with each other. A weighted estimator for the slope coefficient in a simple regression equation with one independent variable is obtained by using weights which are determined by the observed value of Theil's test statistic. This weighted estimator is particularly useful when we are uncertain about the compatibility of prior information with sample information.

Statistics of Three-Body Experiments

Abstract: A large number of three-body interactions involving one initial binary have been studied by a numerical regularization technique. In each set of experiments some parameters have fixed values, whereas others are selected by uniform sampling of the corresponding distribution functions. Similar statistical results are obtained for different random number sequences at a lower integration accuracy. This experimental approach permits an approximate determination of the final distributions of eccentricity, velocity and lifetime. These results show a strong dependence on the total angular momentum, total energy and the mass range, whereas other parameters are usually of secondary importance.

Some remarks on structural inference applied to weibull distribution

Abstract: The structural probability distribution of the parameters of the two-parameter Weibull distribution is derived directly from considerations of the group structure of its density function. In the process we compare the structural method of inference with the confidence interval approach and reveal their similarities and differences. Structural prediction densities of arbitrary ordered statistics from Weibull distributions are also given to complement a previous work by Bury and Burnholtz.

On accuracy in reliability estimation

Abstract: This study in parametric test theory deals with the statistics of reliability estimation when scores on two parts of a test follow a binormal distribution with equal (Case 1) or unequal (Case 2) expectations. In each case biased maximum-likelihood estimators of reliability are obtained and converted into unbiased estimators. Sampling distributions are derived. Second moments are obtained and utilized in calculating mean square errors of estimation as a measure of accuracy. A rank order of four estimators is established. There is a uniformly best estimator. Tables of absolute and relative accuracies are provided for various reliability parameters and sample sizes.

On inference about the mean in the presence of correlation

Abstract: The problem considered in this paper is that of developing a mode of inference about the population mean from a sample (from a normal distribution) which are correlated, using structural methods of statistical inference. The result for the general correlation model has been applied to the intraclass correlation model and the first order auto-regressive model.

Some sampling distributions

Abstract: Probably the basic problem in statistical work, both applied and theoretical, is the relationship between the population and samples from it. For this, one can simply categorize the people of the population into say male and female, or under 30 years of age, and 30 or over. It is of great importance in all statistical applications that samples be properly chosen. In general the basic aim is to avoid sample bias insofar as possible. For this the most common technique is to choose sample at random from the population. By definition this means that for a finite collection of people, say, one selects the sample in such a way that each person has the same probability of being chosen in the sample. If the selection is made one at a time, then for those people in the population not yet drawn for the sample, each is to have the same chance of being drawn next. This is the way to draw a sample randomly. To accomplish such drawing with equal probability, the standard approach is to use a table of random numbers.

Some results in statistical inference

Abstract: This thesis presents two main bodies of work. First a comparison is made of tests of composite statistical hypotheses using the optimal C(a) tests developed in Neyman [4], Buhler and Puri [2] and Bartoo and Puri [7] and the Wald statistic based on maximum likelihood estimators (Wald, [6]). These comparisons are carried out in the case where the parameter under test is interior to open sets in parameter space. It is also shown that the two test procedures are asymptotically equivalent in this case. In particular the problem of constructing tests associated with a mixture of two normal components with one component known is treated in detail. The problem arises out of studies of Down's Syndrome considered in Penrose and Smith [5] and Moran [3],

Approximate Sampling Distributions And Other Statistical Aspects Of Spectral Analysis

Abstract: This chapter deals with two essential problems. First, if we are free to choose our sample, how many “observations” should we collect and how are the “observations” to be obtained? Second, once we have a sample, how can we make a reasoned determination as to how to process the data? Earlier we gave some rough criteria by which one could discriminate among the several lag window generators proposed. In this chapter, the development of some sampling distribution theory will enhance our discriminating ability.