A note on various holding probabilities for random lazy random walks on finite groups
type: Item
instance of: scholarly article
title: A note on various holding probabilities for random lazy random walks on finite groups
zbMATH Open document ID: 1001.60050
DOI: 10.1016/S0167-7152(01)00188-2
published in: Statistics \& Probability Letters
publication date: 2002-09-05T00:00:00Z
review text: For \(a, b > 0\), let \(F(x)=\int^x_0 y^{a-1}(1 - y)^{b-1}dy/B(a,b)\), \(0\leq x\leq 1\), denote the beta distribution function, and set \(G(y) = F^{-1}(y)\), \(0\leq y\leq 1\). The author calls \(G\) the complementary beta distribution function. He derives some attractive properties of \(G\), most ones being complementary to those of \(F\). For example, let \(X_{i:n}\) denote the \(i\)th order statistic from an i.i.d. sample of size \(n\) from the distribution function \(G\). Then the expectation of the spacing \(S_{i:n}=X_{i+1:n}- X_{i:n}\) is \(E(S_{i:n}) = {n\choose i}B(a+i, b+n-i)/B(a,b)\). Good measures of the skewness and kurtosis of \(G\) are also provided.
reviewed by: Aurel Spătaru
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 1796679
zbMATH Keywords: complementary beta distribution function
zbMATH Keywords: expectation of the spacing
zbMATH Keywords: measures of the skewness and kurtosis
author: Martin V. Hildebrand
MaRDI profile type: Publication
cites work: Q3660628
cites work: Random walks arising in random number generation
cites work: Comparison theorems for reversible Markov chains
cites work: Probabilistic methods in group theory
cites work: Q5538132
cites work: Random lazy random walks on arbitrary finite groups
cites work: Random walks on finite groups with few random generators
cites work: A comparison theorem on convergence rates of random walks on groups
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description: scientific article; zbMATH DE number 1796679