Intermediate Probability: A Computational Approach (Hardcover)
Marc S. Paolella
- 出版商: Wiley
- 出版日期: 2007-10-01
- 售價: $1,750
- 貴賓價: 9.8 折 $1,715
- 語言: 英文
- 頁數: 430
- 裝訂: Hardcover
- ISBN: 0470026375
- ISBN-13: 9780470026373
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商品描述
Description
"Intermediate Probability" is the natural extension of the author's Fundamental Probability. It details several highly important topics, from standard ones such as order statistics, multivariate normal, and convergence concepts, to more advanced ones which are usually not addressed at this mathematical level, or have never previously appeared in textbook form. The author adopts a computational approach throughout, allowing the reader to directly implement the methods, thus greatly enhancing the learning experience and clearly illustrating the applicability, strengths, and weaknesses of the theory. The book places great emphasis on the numeric computation of convolutions of random variables, via numeric integration, inversion theorems, fast Fourier transforms, saddlepoint approximations, and simulation.It provides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra, confluent hypergeometric functions, digamma functions, and Bessel functions. It presents full derivation and numerous computational methods of the stable Paretian and the singly and doubly non-central distributions. A whole chapter is dedicated to mean-variance mixtures, NIG, GIG, generalized hyperbolic and numerous related distributions. A whole chapter is dedicated to nesting, generalizing, and asymmetric extensions of popular distributions, as have become popular in empirical finance and other applications. This book provides all essential programming code in Matlab and R.The user-friendly style of writing and attention to detail means that self-study is easily possible, making the book ideal for senior undergraduate and graduate students of mathematics, statistics, econometrics, finance, insurance, and computer science, as well as researchers and professional statisticians working in these fields.
Table of Contents
Pt. I Sums of random variables 1
1 Generating functions 3
2 Sums and other functions of several random variables 65
3 The multivariate normal distribution 97
Pt. II Asymptotics and other approximations 127
4 Convergence concepts 129
5 Saddlepoint approximations 169
6 Order statistics 203
Pt. III More flexible and advanced random variables 237
7 Generalizing and mixing 239
8 The stable Paretian distribution 277
9 Generalized inverse Gaussian and generalized hyperbolic distributions 299
10 Noncentral distributions 341
A Notation and distribution tables 389
商品描述(中文翻譯)
「中級概率」是作者「基礎概率」的自然延伸。它詳細介紹了幾個非常重要的主題,從標準主題如順序統計量、多變量正態分佈和收斂概念,到更高級的主題,這些主題通常在這個數學水平上不被討論,或者以前從未以教科書形式出現過。作者在整本書中採用了計算方法,讓讀者能夠直接實施這些方法,從而大大增強了學習體驗,並清楚地說明了理論的應用性、優勢和劣勢。本書非常重視通過數值計算隨機變量的卷積,通過數值積分、反演定理、快速傅立葉變換、鞍點近似和模擬等方法。它提供了關於複數、拉普拉斯和傅立葉變換、矩陣代數、共軛超幾何函數、digamma函數和貝塞爾函數等所需數學主題的入門材料。它提供了穩定Paretian分佈和單一和雙非中心分佈的完整推導和多種計算方法。整章專門介紹了均值-方差混合、NIG、GIG、廣義雙曲線和許多相關分佈。整章專門介紹了流行分佈的嵌套、泛化和非對稱擴展,這在實證金融和其他應用中變得流行起來。本書在Matlab和R中提供了所有必要的編程代碼。易於使用的寫作風格和對細節的關注意味著自學非常容易,使本書成為數學、統計學、計量經濟學、金融學、保險學和計算機科學的高年級本科生和研究生,以及在這些領域工作的研究人員和專業統計學家的理想選擇。
目錄:
第一部分 隨機變量的和 1
1 生成函數 3
2 多個隨機變量的和和其他函數 65
3 多變量正態分佈 97
第二部分 漸近和其他近似 127
4 收斂概念 129
5 鞍點近似 169
6 順序統計量 203
第三部分 更靈活和高級的隨機變量 237
7 泛化和混合 239
8 穩定Paretian分佈 277
9 廣義逆高斯分佈和廣義雙曲線分佈 299
10 非中心分佈 341
附錄A 符號和分佈表 389