The Multivariate Normal Distribution最新文献

Review 审查

The Multivariate Normal Distribution Pub Date : 2020-01-21 DOI: 10.5194/gmd-2019-294-rc2

K. Hass, Lisanne Walma

{"title":"Review","authors":"K. Hass, Lisanne Walma","doi":"10.5194/gmd-2019-294-rc2","DOIUrl":"https://doi.org/10.5194/gmd-2019-294-rc2","url":null,"abstract":"Freitag expands more on the regulation of space and the implementation of law and order in this changing cosmopolitan city. In this chapter, she returns to her initial discussion of managing difference in Jeddah, highlighting how the Saudi state consolidated power through legal codes that both segregated and removed cosmopolitan difference. As a foundational study on Jeddah, Freitag illuminates the city’s trajectory of development from the 1800s into the contemporary era. While the book provides the reader with a comprehensive overview of Jeddah during the modern period, this macro view of the city lacks the voices of locals outside the elite class. As a study examining the development of Jeddah primarily from 1840 to 1947, the city and its spaces hold the book together, while the changes occurring during this time challenge the authors’ ability to convey individual stories outside of those who left a mark on imperial sources. However, Freitag’s limited discussion of additional Ottoman archives and court records leaves more layers to uncover for other scholars. As a result of this limited source material and due to space constraints, Freitag offers only brief extrapolations of experiences of women, poorer classes, and Bedouin. She also leaves Indian Ocean and Bedouin connections unexplored. Indeed, this book pairs well with M. Christopher Low’s recent book, Imperial Mecca. Set against the backdrop of recent national discussions and Jeddah’s place on the UNESCO World Heritage List, Freitag provides readers with a glimpse of historical Jeddah. Freitag’s book adds to the growing scholarship that seeks to illuminate life on the periphery of the Ottoman Empire. Refreshingly, she is honest and clear about the archival and thematic gaps in the history of Jeddah as she welcomes other contributions towards elucidating Jeddah’s history. This study would be a welcome addition to a graduate seminar on Saudi Arabia, the Ottoman Empire, or urban history in the Middle East. For that, the book delivers foundational research that allows the reader to better understand the role of Jeddah and its people in the history of the region.","PeriodicalId":399073,"journal":{"name":"The Multivariate Normal Distribution","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131537358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Limit Theorems 极限定理

The Multivariate Normal Distribution Pub Date : 2018-10-08 DOI: 10.1002/9781118344972.ch8

J. Peterson

{"title":"Limit Theorems","authors":"J. Peterson","doi":"10.1002/9781118344972.ch8","DOIUrl":"https://doi.org/10.1002/9781118344972.ch8","url":null,"abstract":"Inequalities Proposition 1 (Markov Inequality) If X is a nonnegative random variable with mean µ, then for any a > 0, P(X ≥ a) ≤ µ a. Proposition 2 (Chebyshev Inequality) If X is a random variable with mean µ and variance σ 2 , then for any a > 0, P(|X − µ| ≥ a) ≤ σ 2 a 2. Example 3 Suppose that it is known that the number of items produced in a factory during a week is a random variable with mean 50. (a) What can be said about the probability that this week's production will exceed 75? (b) If the variance of a weeks production is known to be 25, what can be said about the probability that this week's production will between 40 and 60? Limit Theorems Theorem 4 (Weak Law of Large Numbers) Let X 1 , X 2 ,. .. be a sequence of independent and identically distributed random variables with common mean µ. Then for any > 0, lim n→∞ P X 1 + · · · + X n n − µ ≥ = 0. Proof We will prove this theorem under the additional assumption that random variables has a finite variance σ 2. Theorem 5 (Strong Law of Large Numbers) Let X 1 , X 2 ,. .. be a sequence of independent and identically distributed random variables with common mean µ. Then, P lim n→∞ X 1 + · · · + X n n = µ = 1. Theorem 6 (Central Limit Theorem) Let X 1 , X 2 ,. .. be a sequence of independent and identically distributed random variables with common mean µ and common variance σ 2. Then the distribution of X 1 + · · · + X n − nµ σ √ n","PeriodicalId":399073,"journal":{"name":"The Multivariate Normal Distribution","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122875595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 20

The Univariate Normal Distribution 单变量正态分布

The Multivariate Normal Distribution Pub Date : 2008-11-10 DOI: 10.1002/9780470473900.CH2

K. Krishnamoorthy, T. Mathew

引用次数: 4

Bivariate and Trivariate Normal Distributions 二元和三元正态分布

The Multivariate Normal Distribution Pub Date : 2005-01-28 DOI: 10.1002/0471722065.CH46

S. Kotz, N. Balakrishnan, N. L. Johnson

引用次数: 27

Some Applications of the Multivariate Normal Distribution in Science and Engineering 多元正态分布在科学与工程中的一些应用

The Multivariate Normal Distribution Pub Date : 1900-01-01 DOI: 10.1142/9789811235290_0010

引用次数: 1

Probability, Historical Survey, and Discussion 概率，历史调查和讨论

The Multivariate Normal Distribution Pub Date : 1900-01-01 DOI: 10.1142/9789811235290_0008

引用次数: 0

BACK MATTER 回到问题

The Multivariate Normal Distribution Pub Date : 1900-01-01 DOI: 10.1142/9789811235290_bmatter

引用次数: 0

Complements and Supplementary Information 补充信息

The Multivariate Normal Distribution Pub Date : 1900-01-01 DOI: 10.1142/9789811235290_0013

引用次数: 0

FRONT MATTER 前页

The Multivariate Normal Distribution Pub Date : 1900-01-01 DOI: 10.1142/9789811235290_fmatter

引用次数: 0

Bayes Approach in Applied Probability 应用概率中的贝叶斯方法

The Multivariate Normal Distribution Pub Date : 1900-01-01 DOI: 10.1142/9789811235290_0006

引用次数: 0