scholarly journals Multiple buying or selling with vector offers

1997 ◽  
Vol 34 (4) ◽  
pp. 959-973 ◽  
Author(s):  
F. Thomas Bruss ◽  
Thomas S. Ferguson
Keyword(s):  
Decision Maker ◽  
Stopping Rules ◽  
Random Vectors ◽  
Second Moments ◽  
Constant Cost ◽  
Independent Identically Distributed

We consider a generalization of the house-selling problem to selling k houses. Let the offers, X1, X2, · ··, be independent, identically distributed k-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneously k stopping rules, N1, · ··, Nk, one for each component. The payoff is the sum over j of the jth component of minus a constant cost per observation until all stopping rules have stopped. Simple descriptions of the optimal rules are found. Extension is made to problems with recall of past offers and to problems with a discount.

scholarly journals Multiple buying or selling with vector offers

1997 ◽  
Vol 34 (04) ◽  
pp. 959-973 ◽  
Author(s):  
F. Thomas Bruss ◽  
Thomas S. Ferguson
Keyword(s):  
Decision Maker ◽  
Stopping Rules ◽  
Random Vectors ◽  
Second Moments ◽  
Constant Cost ◽  
Independent Identically Distributed

We consider a generalization of the house-selling problem to sellingkhouses. Let the offers,X1,X2, · ··,be independent, identically distributedk-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneouslykstopping rules,N1, · ··,Nk,one for each component. The payoff is the sum overjof thejth component ofminus a constant cost per observation until all stopping rules have stopped. Simple descriptions of the optimal rules are found. Extension is made to problems with recall of past offers and to problems with a discount.

scholarly journals The asymptotic expansions of the distribution function and of density function for the sums of independent identically distributed random vectors

1968 ◽  
Vol 8 (3) ◽  
pp. 405-422
Author(s):  
A. Bikelis
Keyword(s):  
Distribution Function ◽  
Density Function ◽  
Asymptotic Expansions ◽  
Random Vectors ◽  
Independent Identically Distributed

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: А. Бикялис. Асимптотические разложения для плотностей и распределений сумм независимых одинаково распределенных случайных векторов A. Bikelis. Nepriklausomų vienodai pasiskirsčiusių atsitiktinių vektorių sumų tankių ir pasiskirstymo funkcijų asimptotiniai išdėstymai

scholarly journals On Second Moments of Stopping Rules

1966 ◽  
Vol 37 (2) ◽  
pp. 388-392 ◽  
Author(s):  
Y. S. Chow ◽  
H. Teicher
Keyword(s):  
Stopping Rules ◽  
Second Moments

scholarly journals Improved Approximation of the Sum of Random Vectors by the Skew Normal Distribution

2014 ◽  
Vol 51 (2) ◽  
pp. 466-482 ◽  
Author(s):  
Marcus C. Christiansen ◽  
Nicola Loperfido
Keyword(s):  
Normal Distribution ◽  
Normal Approximation ◽  
Distribution Functions ◽  
Skew Normal Distribution ◽  
Random Vectors ◽  
Multivariate Distributions ◽  
Uniform Distance ◽  
Special Case ◽  
Independent Identically Distributed ◽  
Skew Normal

We study the properties of the multivariate skew normal distribution as an approximation to the distribution of the sum of n independent, identically distributed random vectors. More precisely, we establish conditions ensuring that the uniform distance between the two distribution functions converges to 0 at a rate of n-2/3. The advantage over the corresponding normal approximation is particularly relevant when the summands are skewed and n is small, as illustrated for the special case of exponentially distributed random variables. Applications to some well-known multivariate distributions are also discussed.

scholarly journals Two-choice optimal stopping

2004 ◽  
Vol 36 (04) ◽  
pp. 1116-1147 ◽  
Author(s):  
David Assaf ◽  
Larry Goldstein ◽  
Ester Samuel-Cahn
Keyword(s):  
Distribution Function ◽  
Asymptotic Behaviour ◽  
Large Class ◽  
Optimal Stopping ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Indicator Function ◽  
Stopping Rules ◽  
A Value ◽  
Independent Identically Distributed

Let X n ,…,X 1 be independent, identically distributed (i.i.d.) random variables with distribution function F. A statistician, knowing F, observes the X values sequentially and is given two chances to choose Xs using stopping rules. The statistician's goal is to stop at a value of X as small as possible. Let equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behaviour of the sequence for a large class of Fs belonging to the domain of attraction (for the minimum) 𝒟(G α), where G α(x) = [1 - exp(-x α)]1(x ≥ 0) (with 1(·) the indicator function). The results are compared with those for the asymptotic behaviour of the classical one-choice value sequence , as well as with the ‘prophet value’ sequence

scholarly journals Improved Approximation of the Sum of Random Vectors by the Skew Normal Distribution

2014 ◽  
Vol 51 (02) ◽  
pp. 466-482 ◽  
Author(s):  
Marcus C. Christiansen ◽  
Nicola Loperfido
Keyword(s):  
Normal Distribution ◽  
Normal Approximation ◽  
Distribution Functions ◽  
Skew Normal Distribution ◽  
Random Vectors ◽  
Multivariate Distributions ◽  
Uniform Distance ◽  
Special Case ◽  
Independent Identically Distributed ◽  
Skew Normal

We study the properties of the multivariate skew normal distribution as an approximation to the distribution of the sum of n independent, identically distributed random vectors. More precisely, we establish conditions ensuring that the uniform distance between the two distribution functions converges to 0 at a rate of n -2/3. The advantage over the corresponding normal approximation is particularly relevant when the summands are skewed and n is small, as illustrated for the special case of exponentially distributed random variables. Applications to some well-known multivariate distributions are also discussed.

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