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Stochastic Orders

Part of the Springer Series in Statistics Book Series

Editors: Shaked, Moshe; Shanthikumar, J. George

DOI: 10.1007/978-0-387-34675-5

ISBN: 978-0-387-32915-4

Publisher: Springer New York - Springer Journals

Jan 1, 2007

1 - 9 of 9 Chapters

LitStream

Chapter 1Univariate Stochastic Orders

Pages: 3 –79

[In this chapter we study stochastic orders that compare the “location” or the “magnitude” of random variables. The most important and common orders that are considered in this chapter are the usual stochastic order ≤st, the hazard rate order ≤hr, and the likelihood ratio order ≤lr. Some...
LitStream

Chapter 2Mean Residual Life Orders

Pages: 81 –108

[In this chapter we study two orders that are based on comparisons of functionals of mean residual lives. Like the orders in Chapter 1, the purpose of the orders here is to compare the “location” or the “magnitude” of random variables. Among other things, the relationship between the orders of...
LitStream

Chapter 3Univariate Variability Orders

Pages: 109 –179

[In this chapter we study stochastic orders that compare the “variability” or the “dispersion” of random variables. The most important and common orders that are studied in this chapter are the convex and the dispersive orders. We also study in this chapter the excess wealth order (which is also...
LitStream

Chapter 4Univariate Monotone Convex and Related Orders

Pages: 181 –232

[In Chapter 1 we studied orders that compare random variables according to their “magnitude”. In Chapter 3 the studied orders compare random variables according to their “variability”. The orders that are discussed in this chapter compare random variables according to both their “location” and...
LitStream

Chapter 5The Laplace Transform and Related Orders

Pages: 233 –263

[The most important common order that is studied in this chapter is the Laplace transform order. Like the orders that were discussed in Chapter 4, the Laplace transform order compares random variables according to both their “location” and their “spread”. Two other useful orders, based on ratios...
LitStream

Chapter 6Multivariate Stochastic Orders

Pages: 265 –322

[In this chapter we describe various extensions, of the univariate stochastic orders in Chapters 1 and 2, to the multivariate case. The most important common orders that are studied in this chapter are the multivariate stochastic orders ≤st and ≤lr. Multivariate extensions of the orders ≤hr and...
LitStream

Chapter 7Multivariate Variability and Related Orders

Pages: 323 –356

[In this chapter we describe various extensions, of the univariate variability orders in Chapters 3 and 4, to the multivariate case. The most important common orders that are studied in this chapter are the increasing and the directional convex and concave orders. Multivariate extensions of the...
LitStream

Chapter 8Stochastic Convexity and Concavity

Pages: 357 –385

[In this chapter we study stochastic monotonicities of parametric families of distributions with respect to various stochastic orders. We have already encountered stochastic monotonicities earlier in this book. For example, condition (1.A.13) in Theorem 1.A.6, condition (3.A.47) in Theorem...
LitStream

Chapter 9Positive Dependence Orders

Pages: 387 –430

[Notions of positive dependence of two random variables X1 and X2 have been introduced in the literature in an effort to mathematically describe the property that “large (respectively, small) values of X1 tend to go together with large (respectively, small) values of X2.” Many of the notions of...

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