Estimating The Parameters Of Normal Distribution From Imprecise Data
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| Author | : Abbas Pak |
| Publisher | : |
| Total Pages | : 14 |
| Release | : 2018 |
| Genre | : Distribution (Probability theory) |
| ISBN | : |
In the literature, conventional statistical analyses of normal distribution are provided by using precise. However, in real-world situations, the results of an experimental performance can not always be in the form of exact numbers, and the measurements may be described by means of fuzzy samples. In this article, assuming that the available data are reported by fuzzy values, we extend the classical procedures of the estimation for the two-parameter normal distribution. First, we use a Newton-Raphson method to determine maximum likelihood estimates of parameters. Then, an approximation based on the Laplace approximation is used to calculate the Bayes estimates of the unknown parameters. Also, to compute the moment estimates of the parameters, an iterative numerical procedure is proposed. Finally, simulation studies are conducted in order to evaluate the performances of the proposed estimators and an analysis of one real data set is provided.
| Author | : Marwa K. Hassan |
| Publisher | : Infinite Study |
| Total Pages | : 16 |
| Release | : 2024-01-01 |
| Genre | : Mathematics |
| ISBN | : |
A neutrosophic statistic is a random variable and it has a neutrosophic probability distribution. So, in this paper, we introduce the new neutrosophic Birnbaum–Saunders distribution. Some statistical properties are derived, using Mathematica 13.1.1 and R-Studio Software. Two different estimation methods for parameters estimation are introduced for new distribution: maximum likelihood estimation method and Bayesian estimation method. A Monte-Carlo simulation study is used to investigate the behavior of parameters estimates of new distribution, compare the performance of different estimates, and compare between our distribution and the classical version of Birnbaum-Saunders. Finally, study the validity of our new distribution in real life.
| Author | : F. E. Rogers |
| Publisher | : |
| Total Pages | : 14 |
| Release | : 1978 |
| Genre | : Fire insurance |
| ISBN | : |
| Author | : Regina C. Elandt |
| Publisher | : |
| Total Pages | : 62 |
| Release | : 1961 |
| Genre | : Gaussian distribution |
| ISBN | : |
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.
| Author | : Marcos von Sperling |
| Publisher | : IWA Publishing |
| Total Pages | : 668 |
| Release | : 2020-01-15 |
| Genre | : Science |
| ISBN | : 1780409311 |
This book presents the basic principles for evaluating water quality and treatment plant performance in a clear, innovative and didactic way, using a combined approach that involves the interpretation of monitoring data associated with (i) the basic processes that take place in water bodies and in water and wastewater treatment plants and (ii) data management and statistical calculations to allow a deep interpretation of the data. This book is problem-oriented and works from practice to theory, covering most of the information you will need, such as (a) obtaining flow data and working with the concept of loading, (b) organizing sampling programmes and measurements, (c) connecting laboratory analysis to data management, (e) using numerical and graphical methods for describing monitoring data (descriptive statistics), (f) understanding and reporting removal efficiencies, (g) recognizing symmetry and asymmetry in monitoring data (normal and log-normal distributions), (h) evaluating compliance with targets and regulatory standards for effluents and water bodies, (i) making comparisons with the monitoring data (tests of hypothesis), (j) understanding the relationship between monitoring variables (correlation and regression analysis), (k) making water and mass balances, (l) understanding the different loading rates applied to treatment units, (m) learning the principles of reaction kinetics and reactor hydraulics and (n) performing calibration and verification of models. The major concepts are illustrated by 92 fully worked-out examples, which are supported by 75 freely-downloadable Excel spreadsheets. Each chapter concludes with a checklist for your report. If you are a student, researcher or practitioner planning to use or already using treatment plant and water quality monitoring data, then this book is for you! 75 Excel spreadsheets are available to download.
| Author | : F. E. Rogers |
| Publisher | : |
| Total Pages | : 14 |
| Release | : 1978 |
| Genre | : Estimation theory |
| ISBN | : |
| Author | : Dennis R. Helsel |
| Publisher | : John Wiley & Sons |
| Total Pages | : 344 |
| Release | : 2012-02-01 |
| Genre | : Mathematics |
| ISBN | : 0470479884 |
Praise for the First Edition " . . . an excellent addition to an upper-level undergraduate course on environmental statistics, and . . . a 'must-have' desk reference for environmental practitioners dealing with censored datasets." —Vadose Zone Journal Statistics for Censored Environmental Data Using Minitab® and R, Second Edition introduces and explains methods for analyzing and interpreting censored data in the environmental sciences. Adapting survival analysis techniques from other fields, the book translates well-established methods from other disciplines into new solutions for environmental studies. This new edition applies methods of survival analysis, including methods for interval-censored data to the interpretation of low-level contaminants in environmental sciences and occupational health. Now incorporating the freely available R software as well as Minitab® into the discussed analyses, the book features newly developed and updated material including: A new chapter on multivariate methods for censored data Use of interval-censored methods for treating true nondetects as lower than and separate from values between the detection and quantitation limits ("remarked data") A section on summing data with nondetects A newly written introduction that discusses invasive data, showing why substitution methods fail Expanded coverage of graphical methods for censored data The author writes in a style that focuses on applications rather than derivations, with chapters organized by key objectives such as computing intervals, comparing groups, and correlation. Examples accompany each procedure, utilizing real-world data that can be analyzed using the Minitab® and R software macros available on the book's related website, and extensive references direct readers to authoritative literature from the environmental sciences. Statistics for Censored Environmental Data Using Minitab® and R, Second Edition is an excellent book for courses on environmental statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for??environmental professionals, biologists, and ecologists who focus on the water sciences, air quality, and soil science.
| Author | : Frederick Backer (Jr.) |
| Publisher | : |
| Total Pages | : 106 |
| Release | : 1961 |
| Genre | : |
| ISBN | : |
| Author | : Daniel Navarro |
| Publisher | : Lulu.com |
| Total Pages | : 617 |
| Release | : 2013-01-13 |
| Genre | : Computers |
| ISBN | : 1326189727 |
"Learning Statistics with R" covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software and adopting a light, conversational style throughout. The book discusses how to get started in R, and gives an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book. For more information (and the opportunity to check the book out before you buy!) visit http://ua.edu.au/ccs/teaching/lsr or http://learningstatisticswithr.com
| Author | : Matthew A. Barsalou |
| Publisher | : Quality Press |
| Total Pages | : 394 |
| Release | : 2018-12-19 |
| Genre | : Mathematics |
| ISBN | : 1953079067 |
This book was written to provide guidance for those who need to apply statistical methods for practical use. While the book provides detailed guidance on the use of Minitab for calculation, simply entering data into a software program is not sufficient to reliably gain knowledge from data. The software will provide an answer, but the answer may be wrong if the sample was not taken properly, the data was unsuitable for the statistical test that was performed, or the wrong test was selected. It is also possible that the answer will be correct, but misinterpreted. This book provides both guidance in applying the statistical methods described as well as instructions for performing calculations without a statistical software program such as Minitab. One of the authors is a professional statistician who spent nearly 13 years working at Minitab and the other is an experienced and certified Lean Six Sigma Master Black Belt. Together, they strive to present the knowledge of a statistician in a format that can be easily understood and applied by non-statisticians facing real-world problems. Their guidance is provided with the goal of making data analysis accessible and practical. Rather than focusing on theoretical concepts, the book delivers only the information that is critical to success for the practitioner. It is a thorough guide for those who have not yet been exposed to the value of statistics, as well as a reliable reference for those who have been introduced to statistics but are not yet confident in their abilities. Supplemental files available! If you are an instructor who would like to conduct training with this book, please visit this "https://asqassets.widencollective.com/portals/sybdffda/(H1550)AppliedStatisticsManualAGuidetoImprovingandSustainingQualitywithMinitab" access: Course descriptions for one or two semester university courses Chapter descriptions for standalone sessions A data file containing data sets used in the book
