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We consider first the folded normal probability density function, especially as it relates to the original normal population from which it came. We present some maximum likelihood estimates, followed by other estimating procedures which are simpler to handle...Finally, an example of real camber data is presented with the appropriate estimation of the theoretical distributions. Some remarks of the folded normal and other work being done on this conclude the paper.
Formulae for the asymptotic variances and covariance of the maximum likelihood estimators of the parameters of the folded normal distribution are obtained. Numerical comparisons with the asymptotic variances of moments estimators are made. (Author).
The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.
The general formula for the rth moment of the folded normal distribution is obtained, and formulae for the first four non-central and central moments are calculated explicitly. To illustrate the mode of convergence of teh folded normal to the normal distribution, as [mu]/ơ = [theta] increases, the shape factors ßf1 and ßf2 were calculated and the relationship between them represented graphically. Two methods, one using first and second moments (Method I) and the other using second and fourth moments (Method II) of estimating the parameters of [mu] and ơ of the parent normal distribution are presented and their standard errors calculated. The accuracy of both methods, for various values of [theta], are discussed.
This book describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance.
A common problem is that of describing the probability distribution of a single, continuous variable. A few distributions, such as the normal and exponential, were discovered in the 1800's or earlier. But about a century ago the great statistician, Karl Pearson, realized that the known probability distributions were not sufficient to handle all of the phenomena then under investigation, and set out to create new distributions with useful properties. During the 20th century this process continued with abandon and a vast menagerie of distinct mathematical forms were discovered and invented, investigated, analyzed, rediscovered and renamed, all for the purpose of describing the probability of some interesting variable. There are hundreds of named distributions and synonyms in current usage. The apparent diversity is unending and disorienting. Fortunately, the situation is less confused than it might at first appear. Most common, continuous, univariate, unimodal distributions can be organized into a small number of distinct families, which are all special cases of a single Grand Unified Distribution. This compendium details these hundred or so simple distributions, their properties and their interrelations.
Comprehensive reference for statistical distributions Continuous Univariate Distributions, Volume 2 provides in-depth reference for anyone who applies statistical distributions in fields including engineering, business, economics, and the sciences. Covering a range of distributions, both common and uncommon, this book includes guidance toward extreme value, logistics, Laplace, beta, rectangular, noncentral distributions and more. Each distribution is presented individually for ease of reference, with clear explanations of methods of inference, tolerance limits, applications, characterizations, and other important aspects, including reference to other related distributions.
​The objective of this text is to introduce RStudio to practitioners and students and enable them to use R in their everyday work. It is not a statistical textbook, the purpose is to transmit the joy of analyzing data with RStudio. Practitioners and students learn how RStudio can be installed and used, they learn to import data, write scripts and save working results. Furthermore, they learn to employ descriptive statistics and create graphics with RStudio. Additionally, it is shown how RStudio can be used to test hypotheses, run an analysis of variance and regressions. To deepen the learned content, tasks are included with the solutions provided at the end of the textbook. This textbook has been recommended and developed for university courses in Germany, Austria and Switzerland.
This research monograph gives a unified view of non-standard estimation problems. It provides an overall mathematical framework, but also draws together and studies in detail a large number of practical problems, previously only treated separately, offering solution methods and numerical procedures for each.