scholarly journals New Closed-Form Results on Ordered Statistics of Partial Sums of Gamma Random Variables and Its Application to Performance Evaluation in the Presence of Nakagami Fading

IEEE Access ◽  
2017 ◽  
Vol 5 ◽  
pp. 12820-12832 ◽  
Author(s):  
Sung Sik Nam ◽  
Young-Chai Ko ◽  
Mohamed-Slim Alouini
Keyword(s):  
Performance Evaluation ◽  
Closed Form ◽  
Random Variables ◽  
Partial Sums ◽  
Nakagami Fading ◽  
Ordered Statistics

scholarly journals ON THE REPRESENTATION OF THE NESTED LOGIT MODEL

2021 ◽  
pp. 1-11
Author(s):  
Alfred Galichon
Keyword(s):  
Closed Form ◽  
Logit Model ◽  
Random Variables ◽  
Nested Logit ◽  
Random Utility ◽  
Nested Logit Model ◽  
Utility Representation ◽  
Phd Thesis ◽  
Closed Form Formula

In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

A note on Spitzer's lemma and its application to the maximum of partial sums of dependent random variables

1976 ◽  
Vol 13 (2) ◽  
pp. 361-364 ◽  
Author(s):  
M. E. Solari ◽  
J. E. A. Dunnage
Keyword(s):  
Infinite Sequence ◽  
Random Variables ◽  
Finite Sequence ◽  
Partial Sums ◽  
Dependent Random Variables ◽  
Finite Segment ◽  
Exchangeable Random Variables ◽  
Partial Sum

We give an expression for the expectation of max (0, S1, …, Sn) where Sk is the kth partial sum of a finite sequence of exchangeable random variables X1, …, Xn. When the Xk are also independent, the formula we give has already been obtained by Spitzer; and when the sequence is a finite segment of an infinite sequence of exchangeable random variables, it is a consequence of a theorem of Hewitt.

On the ordered partial sums of real random variables

1977 ◽  
Vol 14 (1) ◽  
pp. 75-88 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Variables ◽  
Partial Sums ◽  
Markov Sequence ◽  
Stieltjes Transforms ◽  
Independent And Identically Distributed

In 1952 Pollaczek discovered a remarkable formula for the Laplace-Stieltjes transforms of the distributions of the ordered partial sums for a sequence of independent and identically distributed real random variables. In this paper Pollaczek's result is proved in a simple way and is extended for a semi-Markov sequence of real random variables.

scholarly journals On the Density Functions of Integrals of Gaussian Random Fields

2013 ◽  
Vol 45 (02) ◽  
pp. 398-424 ◽  
Author(s):  
Jingchen Liu ◽  
Gongjun Xu
Keyword(s):  
Closed Form ◽  
Random Fields ◽  
Random Variables ◽  
Gaussian Random Fields ◽  
Density Functions ◽  
Exponential Functions ◽  
Asymptotic Bounds

In the paper we consider the density functions of random variables that can be written as integrals of exponential functions of Gaussian random fields. In particular, we provide closed-form asymptotic bounds for the density functions and, under smoothness conditions, we derive exact tail approximations of the density functions.

scholarly journals First-crossing and ballot-type results for some nonstationary sequences

2007 ◽  
Vol 39 (02) ◽  
pp. 492-509 ◽  
Author(s):  
Claude Lefèvre
Keyword(s):  
Time Distribution ◽  
Numerical Evaluation ◽  
Random Variables ◽  
Parametric Family ◽  
Partial Sums ◽  
Variable Parameters ◽  
Type Formula ◽  
Polynomial Structure ◽  
Crossing Time ◽  
First Crossing Time

In this paper we consider the problem of first-crossing from above for a partial sums process m+S t , t ≥ 1, with the diagonal line when the random variables X t , t ≥ 1, are independent but satisfying nonstationary laws. Specifically, the distributions of all the X t s belong to a common parametric family of arithmetic distributions, and this family of laws is assumed to be stable by convolution. The key result is that the first-crossing time distribution and the associated ballot-type formula rely on an underlying polynomial structure, called the generalized Abel-Gontcharoff structure. In practice, this property advantageously provides simple and efficient recursions for the numerical evaluation of the probabilities of interest. Several applications are then presented, for constant and variable parameters.

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