Transcription of Univariate Distribution Relationships
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Univariate Distribution Relationships
Univariate Distribution RelationshipsLawrence M. LEEMISand Jacquelyn T. MCQUESTONP robability distributions are traditionally treated separately inintroductory mathematical statistics textbooks. A figure is pre-sented here that shows properties that individual distributionspossess and many of the Relationships between these WORDS: Asymptotic Relationships ; Distribution proper-ties; Limiting distributions; Stochastic parameters; INTRODUCTIONI ntroductory probability and statistics textbooks typically in-troduce common Univariate distributions individually, and sel-dom report all of the Relationships between these article contains an update of a figure presented by Leemis(1986) that shows the properties of and Relationships betweenseveral common Univariate distributions. More detail concern-ing these distributions is given by Johnson, Kotz, and Balakrish-nan (1994, 1995) and Johnson, Kemp, and Kotz (2005).
from a distribution comes from the same distribution fam-ily. Example: If X i ∼standard power (β i) for i =1,2,...,n, and X 1, X 2, ..., X n are independent, then max{X 1,X 2,...,X n}∼standard power Xn i=1 β i!. •The forgetfulness property (F), more commonly known as the memoryless property, indicates that the conditional dis-
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