The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance

Springer Science & Business Media
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The aim of this monograph is quite modest: It attempts to be a systematic exposition of all that appeared in the literature and was known to us by the end of the 20th century about the Laplace distribution and its numerous generalizations and extensions. We have tried to cover both theoretical developments and applications. There were two main reasons for writing this book. The first was our conviction that the areas and situations where the Laplace distribution naturally occurs is so extensive that tracking the original sources is unfeasible. The second was our observation of the growing demand for statistical distributions having properties tangent to those exhibited by the Laplace laws. These two "necessary" conditions justified our efforts that led to this book. Many details are arranged primarily for reference, such as inclusion of the most commonly used terminology and notation. In several cases, we have proposed unification to overcome the ambiguity of notions so often present in this area. Personal taste may have done some injustice to the subject matter by omitting or emphasizing certain topics due to space limitations. We trust that this feature does not constitute a serious drawback-in our literature search we tried to leave no stone unturned (we collected over 400 references).
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Publisher
Springer Science & Business Media
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Published on
Dec 6, 2012
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Pages
349
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ISBN
9781461201731
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Best For
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Language
English
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Genres
Business & Economics / Statistics
Mathematics / Applied
Mathematics / General
Mathematics / Probability & Statistics / General
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Content Protection
This content is DRM protected.
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Charles Wheelan
“Brilliant, funny . . . the best math teacher you never had.”—San Francisco Chronicle Once considered tedious, the field of statistics is rapidly evolving into a discipline Hal Varian, chief economist at Google, has actually called “sexy.” From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. How can we catch schools that cheat on standardized tests? How does Netflix know which movies you’ll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more.

For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.

And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.

Samuel Kotz
Cathy O'Neil
Longlisted for the National Book Award
New York Times Bestseller

A former Wall Street quant sounds an alarm on the mathematical models that pervade modern life — and threaten to rip apart our social fabric

We live in the age of the algorithm. Increasingly, the decisions that affect our lives—where we go to school, whether we get a car loan, how much we pay for health insurance—are being made not by humans, but by mathematical models. In theory, this should lead to greater fairness: Everyone is judged according to the same rules, and bias is eliminated.

But as Cathy O’Neil reveals in this urgent and necessary book, the opposite is true. The models being used today are opaque, unregulated, and uncontestable, even when they’re wrong. Most troubling, they reinforce discrimination: If a poor student can’t get a loan because a lending model deems him too risky (by virtue of his zip code), he’s then cut off from the kind of education that could pull him out of poverty, and a vicious spiral ensues. Models are propping up the lucky and punishing the downtrodden, creating a “toxic cocktail for democracy.” Welcome to the dark side of Big Data.

Tracing the arc of a person’s life, O’Neil exposes the black box models that shape our future, both as individuals and as a society. These “weapons of math destruction” score teachers and students, sort résumés, grant (or deny) loans, evaluate workers, target voters, set parole, and monitor our health.

O’Neil calls on modelers to take more responsibility for their algorithms and on policy makers to regulate their use. But in the end, it’s up to us to become more savvy about the models that govern our lives. This important book empowers us to ask the tough questions, uncover the truth, and demand change.

— Longlist for National Book Award (Non-Fiction)
— Goodreads, semi-finalist for the 2016 Goodreads Choice Awards (Science and Technology)
— Kirkus, Best Books of 2016
— New York Times, 100 Notable Books of 2016 (Non-Fiction)
— The Guardian, Best Books of 2016
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Book 470
A comprehensive account of economic size distributions around the world and throughout the years

In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions.

Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include:

Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions

Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.

Book 470
A comprehensive account of economic size distributions around the world and throughout the years

In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions.

Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include:

Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions

Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.

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