Parameter Estimation For The Lognormal Distribution

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Entropy-Based Parameter Estimation in Hydrology

Author : Vijay Singh
Publisher : Springer Science & Business Media
ISBN 13 : 9780792352242
Total Pages : 400 pages
Book Rating : 4.3/5 (522 download)

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Book Synopsis Entropy-Based Parameter Estimation in Hydrology by : Vijay Singh

Download or read book Entropy-Based Parameter Estimation in Hydrology written by Vijay Singh and published by Springer Science & Business Media. This book was released on 1998-10-31 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering work of Shannon in the late 1940's on the development of the theory of entropy and the landmark contributions of Jaynes a decade later leading to the development of the principle of maximum entropy (POME), the concept of entropy has been increasingly applied in a wide spectrum of areas, including chemistry, electronics and communications engineering, data acquisition and storage and retreival, data monitoring network design, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, image processing, management sciences, operations research, pattern recognition and identification, photogrammetry, psychology, physics and quantum mechanics, reliability analysis, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, and so on. New areas finding application of entropy have since continued to unfold. The entropy concept is indeed versatile and its applicability widespread. In the area of hydrology and water resources, a range of applications of entropy have been reported during the past three decades or so. This book focuses on parameter estimation using entropy for a number of distributions frequently used in hydrology. In the entropy-based parameter estimation the distribution parameters are expressed in terms of the given information, called constraints. Thus, the method lends itself to a physical interpretation of the parameters. Because the information to be specified usually constitutes sufficient statistics for the distribution under consideration, the entropy method provides a quantitative way to express the information contained in the distribution.

Parameter Estimation in Reliability and Life Span Models

Author : A Clifford Cohen
Publisher : CRC Press
ISBN 13 : 1000147231
Total Pages : 312 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Parameter Estimation in Reliability and Life Span Models by : A Clifford Cohen

Download or read book Parameter Estimation in Reliability and Life Span Models written by A Clifford Cohen and published by CRC Press. This book was released on 2020-07-26 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an applications-oriented treatment of parameter estimation from both complete and censored samples; contains notations, simplified formats for estimates, graphical techniques, and numerous tables and charts allowing users to calculate estimates and analyze sample data quickly and easily. Anno

Progressive Censoring

Author : N. Balakrishnan
Publisher : Springer Science & Business Media
ISBN 13 : 1461213347
Total Pages : 255 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Progressive Censoring by : N. Balakrishnan

Download or read book Progressive Censoring written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book offers a guide to the theory and methods of progressive censoring. In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early. Progressive Censoring first introduces progressive sampling foundations, and then discusses various properties of progressive samples. The book points out the greater efficiency gained by using this scheme instead of classical right-censoring methods.

Lognormal Distributions

Author : Crow
Publisher : CRC Press
ISBN 13 : 9780824778033
Total Pages : 412 pages
Book Rating : 4.7/5 (78 download)

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Book Synopsis Lognormal Distributions by : Crow

Download or read book Lognormal Distributions written by Crow and published by CRC Press. This book was released on 1987-12-29 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding reference encompasses the most-up-to-date advances in lognormal distributions in thorough, detailed contributions by specialists in statistics, business and economics, industry, biology, ecology, geology, and meteorology.

Statistical Methods for Reliability Data

Author : William Q. Meeker
Publisher : John Wiley & Sons
ISBN 13 : 1118594487
Total Pages : 708 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Statistical Methods for Reliability Data by : William Q. Meeker

Download or read book Statistical Methods for Reliability Data written by William Q. Meeker and published by John Wiley & Sons. This book was released on 2022-01-24 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative guide to the most recent advances in statistical methods for quantifying reliability Statistical Methods for Reliability Data, Second Edition (SMRD2) is an essential guide to the most widely used and recently developed statistical methods for reliability data analysis and reliability test planning. Written by three experts in the area, SMRD2 updates and extends the long- established statistical techniques and shows how to apply powerful graphical, numerical, and simulation-based methods to a range of applications in reliability. SMRD2 is a comprehensive resource that describes maximum likelihood and Bayesian methods for solving practical problems that arise in product reliability and similar areas of application. SMRD2 illustrates methods with numerous applications and all the data sets are available on the book’s website. Also, SMRD2 contains an extensive collection of exercises that will enhance its use as a course textbook. The SMRD2's website contains valuable resources, including R packages, Stan model codes, presentation slides, technical notes, information about commercial software for reliability data analysis, and csv files for the 93 data sets used in the book's examples and exercises. The importance of statistical methods in the area of engineering reliability continues to grow and SMRD2 offers an updated guide for, exploring, modeling, and drawing conclusions from reliability data. SMRD2 features: Contains a wealth of information on modern methods and techniques for reliability data analysis Offers discussions on the practical problem-solving power of various Bayesian inference methods Provides examples of Bayesian data analysis performed using the R interface to the Stan system based on Stan models that are available on the book's website Includes helpful technical-problem and data-analysis exercise sets at the end of every chapter Presents illustrative computer graphics that highlight data, results of analyses, and technical concepts Written for engineers and statisticians in industry and academia, Statistical Methods for Reliability Data, Second Edition offers an authoritative guide to this important topic.

Probability Distributions Used in Reliability Engineering

Author : Andrew N O'Connor
Publisher : RIAC
ISBN 13 : 1933904062
Total Pages : 220 pages
Book Rating : 4.9/5 (339 download)

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Book Synopsis Probability Distributions Used in Reliability Engineering by : Andrew N O'Connor

Download or read book Probability Distributions Used in Reliability Engineering written by Andrew N O'Connor and published by RIAC. This book was released on 2011 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.

Loss Models

Author : Stuart A. Klugman
Publisher : John Wiley & Sons
ISBN 13 : 0470391332
Total Pages : 758 pages
Book Rating : 4.4/5 (73 download)

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Book Synopsis Loss Models by : Stuart A. Klugman

Download or read book Loss Models written by Stuart A. Klugman and published by John Wiley & Sons. This book was released on 2012-01-25 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: An update of one of the most trusted books on constructing and analyzing actuarial models Written by three renowned authorities in the actuarial field, Loss Models, Third Edition upholds the reputation for excellence that has made this book required reading for the Society of Actuaries (SOA) and Casualty Actuarial Society (CAS) qualification examinations. This update serves as a complete presentation of statistical methods for measuring risk and building models to measure loss in real-world events. This book maintains an approach to modeling and forecasting that utilizes tools related to risk theory, loss distributions, and survival models. Random variables, basic distributional quantities, the recursive method, and techniques for classifying and creating distributions are also discussed. Both parametric and non-parametric estimation methods are thoroughly covered along with advice for choosing an appropriate model. Features of the Third Edition include: Extended discussion of risk management and risk measures, including Tail-Value-at-Risk (TVaR) New sections on extreme value distributions and their estimation Inclusion of homogeneous, nonhomogeneous, and mixed Poisson processes Expanded coverage of copula models and their estimation Additional treatment of methods for constructing confidence regions when there is more than one parameter The book continues to distinguish itself by providing over 400 exercises that have appeared on previous SOA and CAS examinations. Intriguing examples from the fields of insurance and business are discussed throughout, and all data sets are available on the book's FTP site, along with programs that assist with conducting loss model analysis. Loss Models, Third Edition is an essential resource for students and aspiring actuaries who are preparing to take the SOA and CAS preliminary examinations. It is also a must-have reference for professional actuaries, graduate students in the actuarial field, and anyone who works with loss and risk models in their everyday work. To explore our additional offerings in actuarial exam preparation visit www.wiley.com/go/actuarialexamprep.

Statistical Distributions

Author : Nick T. Thomopoulos
Publisher : Springer
ISBN 13 : 3319651129
Total Pages : 176 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Statistical Distributions by : Nick T. Thomopoulos

Download or read book Statistical Distributions written by Nick T. Thomopoulos and published by Springer. This book was released on 2017-10-10 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a description of the group of statistical distributions that have ample application to studies in statistics and probability. Understanding statistical distributions is fundamental for researchers in almost all disciplines. The informed researcher will select the statistical distribution that best fits the data in the study at hand. Some of the distributions are well known to the general researcher and are in use in a wide variety of ways. Other useful distributions are less understood and are not in common use. The book describes when and how to apply each of the distributions in research studies, with a goal to identify the distribution that best applies to the study. The distributions are for continuous, discrete, and bivariate random variables. In most studies, the parameter values are not known a priori, and sample data is needed to estimate parameter values. In other scenarios, no sample data is available, and the researcher seeks some insight that allows the estimate of the parameter values to be gained. This handbook of statistical distributions provides a working knowledge of applying common and uncommon statistical distributions in research studies. These nineteen distributions are: continuous uniform, exponential, Erlang, gamma, beta, Weibull, normal, lognormal, left-truncated normal, right-truncated normal, triangular, discrete uniform, binomial, geometric, Pascal, Poisson, hyper-geometric, bivariate normal, and bivariate lognormal. Some are from continuous data and others are from discrete and bivariate data. This group of statistical distributions has ample application to studies in statistics and probability and practical use in real situations. Additionally, this book explains computing the cumulative probability of each distribution and estimating the parameter values either with sample data or without sample data. Examples are provided throughout to guide the reader. Accuracy in choosing and applying statistical distributions is particularly imperative for anyone who does statistical and probability analysis, including management scientists, market researchers, engineers, mathematicians, physicists, chemists, economists, social science researchers, and students in many disciplines.

Lectures on Probability Theory and Mathematical Statistics - 3rd Edition

Author : Marco Taboga
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781981369195
Total Pages : 670 pages
Book Rating : 4.3/5 (691 download)

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Book Synopsis Lectures on Probability Theory and Mathematical Statistics - 3rd Edition by : Marco Taboga

Download or read book Lectures on Probability Theory and Mathematical Statistics - 3rd Edition written by Marco Taboga and published by Createspace Independent Publishing Platform. This book was released on 2017-12-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: it contains several results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books. The topics covered by the book are as follows. PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions. PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions. PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions. PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart. PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions. PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutsky's Theorem. PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.

Nonparametric Econometrics

Author : Qi Li
Publisher : Princeton University Press
ISBN 13 : 1400841062
Total Pages : 769 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Nonparametric Econometrics by : Qi Li

Download or read book Nonparametric Econometrics written by Qi Li and published by Princeton University Press. This book was released on 2011-10-09 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, up-to-date textbook on nonparametric methods for students and researchers Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data—nominal and ordinal—in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types—continuous, nominal, and ordinal—within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.

Handbook of Mathematical Geosciences

Author : B.S. Daya Sagar
Publisher : Springer
ISBN 13 : 3319789996
Total Pages : 911 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Handbook of Mathematical Geosciences by : B.S. Daya Sagar

Download or read book Handbook of Mathematical Geosciences written by B.S. Daya Sagar and published by Springer. This book was released on 2018-06-25 with total page 911 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences.

Entropy-Based Parameter Estimation in Hydrology

Author : V.P. Singh
Publisher : Springer Science & Business Media
ISBN 13 : 9401714312
Total Pages : 382 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Entropy-Based Parameter Estimation in Hydrology by : V.P. Singh

Download or read book Entropy-Based Parameter Estimation in Hydrology written by V.P. Singh and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering work of Shannon in the late 1940's on the development of the theory of entropy and the landmark contributions of Jaynes a decade later leading to the development of the principle of maximum entropy (POME), the concept of entropy has been increasingly applied in a wide spectrum of areas, including chemistry, electronics and communications engineering, data acquisition and storage and retreival, data monitoring network design, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, image processing, management sciences, operations research, pattern recognition and identification, photogrammetry, psychology, physics and quantum mechanics, reliability analysis, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, and so on. New areas finding application of entropy have since continued to unfold. The entropy concept is indeed versatile and its applicability widespread. In the area of hydrology and water resources, a range of applications of entropy have been reported during the past three decades or so. This book focuses on parameter estimation using entropy for a number of distributions frequently used in hydrology. In the entropy-based parameter estimation the distribution parameters are expressed in terms of the given information, called constraints. Thus, the method lends itself to a physical interpretation of the parameters. Because the information to be specified usually constitutes sufficient statistics for the distribution under consideration, the entropy method provides a quantitative way to express the information contained in the distribution.

Handbook of Tables for Order Statistics from Lognormal Distributions with Applications

Author : N. Balakrishnan
Publisher : Springer Science & Business Media
ISBN 13 : 1461553091
Total Pages : 873 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Handbook of Tables for Order Statistics from Lognormal Distributions with Applications by : N. Balakrishnan

Download or read book Handbook of Tables for Order Statistics from Lognormal Distributions with Applications written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lognormal distributions are one of the most commonly studied models in the sta tistical literature while being most frequently used in the applied literature. The lognormal distributions have been used in problems arising from such diverse fields as hydrology, biology, communication engineering, environmental science, reliability, agriculture, medical science, mechanical engineering, material science, and pharma cology. Though the lognormal distributions have been around from the beginning of this century (see Chapter 1), much of the work concerning inferential methods for the parameters of lognormal distributions has been done in the recent past. Most of these methods of inference, particUlarly those based on censored samples, involve extensive use of numerical methods to solve some nonlinear equations. Order statistics and their moments have been discussed quite extensively in the literature for many distributions. It is very well known that the moments of order statistics can be derived explicitly only in the case of a few distributions such as exponential, uniform, power function, Pareto, and logistic. In most other cases in cluding the lognormal case, they have to be numerically determined. The moments of order statistics from a specific lognormal distribution have been tabulated ear lier. However, the moments of order statistics from general lognormal distributions have not been discussed in the statistical literature until now primarily due to the extreme computational complexity in their numerical determination.

Fitting a Three-parameter Lognormal Distribution with Applications to Hydrogeochemical Data from the National Uranium Resource Evaluation Program

Download Fitting a Three-parameter Lognormal Distribution with Applications to Hydrogeochemical Data from the National Uranium Resource Evaluation Program PDF Online Free

Author : V. E. Kane
Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Fitting a Three-parameter Lognormal Distribution with Applications to Hydrogeochemical Data from the National Uranium Resource Evaluation Program by : V. E. Kane

Download or read book Fitting a Three-parameter Lognormal Distribution with Applications to Hydrogeochemical Data from the National Uranium Resource Evaluation Program written by V. E. Kane and published by . This book was released on 1979 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Simulating Data with SAS

Author : Rick Wicklin
Publisher : SAS Institute
ISBN 13 : 1612903320
Total Pages : 363 pages
Book Rating : 4.6/5 (129 download)

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Book Synopsis Simulating Data with SAS by : Rick Wicklin

Download or read book Simulating Data with SAS written by Rick Wicklin and published by SAS Institute. This book was released on 2013 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data simulation is a fundamental technique in statistical programming and research. Rick Wicklin's Simulating Data with SAS brings together the most useful algorithms and the best programming techniques for efficient data simulation in an accessible how-to book for practicing statisticians and statistical programmers. This book discusses in detail how to simulate data from common univariate and multivariate distributions, and how to use simulation to evaluate statistical techniques. It also covers simulating correlated data, data for regression models, spatial data, and data with given moments. It provides tips and techniques for beginning programmers, and offers libraries of functions for advanced practitioners. As the first book devoted to simulating data across a range of statistical applications, Simulating Data with SAS is an essential tool for programmers, analysts, researchers, and students who use SAS software. This book is part of the SAS Press program.

Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications

Author : Wayne B. Nelson
Publisher : SIAM
ISBN 13 : 0898715229
Total Pages : 157 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications by : Wayne B. Nelson

Download or read book Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications written by Wayne B. Nelson and published by SIAM. This book was released on 2003-01-01 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survival data consist of a single event for each population unit, namely, end of life, which is modeled with a life distribution. However, many applications involve repeated-events data, where a unit may accumulate numerous events over time. This applied book provides practitioners with basic nonparametric methods for such data.

Using the Weibull Distribution

Author : John I. McCool
Publisher : John Wiley & Sons
ISBN 13 : 1118351983
Total Pages : 366 pages
Book Rating : 4.1/5 (183 download)

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Book Synopsis Using the Weibull Distribution by : John I. McCool

Download or read book Using the Weibull Distribution written by John I. McCool and published by John Wiley & Sons. This book was released on 2012-08-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand and utilize the latest developments in Weibull inferential methods While the Weibull distribution is widely used in science and engineering, most engineers do not have the necessary statistical training to implement the methodology effectively. Using the Weibull Distribution: Reliability, Modeling, and Inference fills a gap in the current literature on the topic, introducing a self-contained presentation of the probabilistic basis for the methodology while providing powerful techniques for extracting information from data. The author explains the use of the Weibull distribution and its statistical and probabilistic basis, providing a wealth of material that is not available in the current literature. The book begins by outlining the fundamental probability and statistical concepts that serve as a foundation for subsequent topics of coverage, including: • Optimum burn-in, age and block replacement, warranties and renewal theory • Exact inference in Weibull regression • Goodness of fit testing and distinguishing the Weibull from the lognormal • Inference for the Three Parameter Weibull Throughout the book, a wealth of real-world examples showcases the discussed topics and each chapter concludes with a set of exercises, allowing readers to test their understanding of the presented material. In addition, a related website features the author's own software for implementing the discussed analyses along with a set of modules written in Mathcad®, and additional graphical interface software for performing simulations. With its numerous hands-on examples, exercises, and software applications, Using the Weibull Distribution is an excellent book for courses on quality control and reliability engineering at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for engineers, scientists, and business analysts who gather and interpret data that follows the Weibull distribution