Analyzing the Busy Period of the M/M/1 Queue via Order Statistics and Record Values

2021 ◽  
Author(s):  
Pierre M. Fiorini
Keyword(s):  
Order Statistics ◽  
Busy Period ◽  
Record Values

scholarly journals Some Characterizations of the Distribution of the Condition Number of a Complex Gaussian Matrix

2020 ◽  
Vol 8 (1) ◽  
pp. 22-35
Author(s):  
M. Shakil ◽  
M. Ahsanullah
Keyword(s):  
Order Statistics ◽  
Condition Number ◽  
Record Values ◽  
Distributional Properties ◽  
Upper Record Values ◽  
Upper Record

AbstractThe objective of this paper is to characterize the distribution of the condition number of a complex Gaussian matrix. Several new distributional properties of the distribution of the condition number of a complex Gaussian matrix are given. Based on such distributional properties, some characterizations of the distribution are given by truncated moment, order statistics and upper record values.

scholarly journals Nonparametric Prediction Intervals of generalized order statistics from two independent sequences

2016 ◽  
Vol 4 (1) ◽  
pp. 36 ◽  
Author(s):  
Mostafa Mohie El-Din ◽  
Walid Emam
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Prediction Intervals ◽  
Generalized Order Statistics ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
Nonparametric Prediction ◽  
Nonparametric Prediction Intervals ◽  
Generalized Order

<p>This paper, discusses the problem of predicting future a generalized order statistic of an iid sequence sample was drawn from an arbitrary unknown distribution, based on observed also generalized order statistics from the same population. The coverage probabilities of these prediction intervals are exact and free of the parent distribution F(). Prediction formulas of ordinary order statistics and upper record values are extracted as special cases from the productive results. Finally, numerical computations on several models of ordered random variables are given to illustrate the proposed procedures.</p>

Likelihood ratio comparisons and logconvexity properties of p-spacings from generalized order statistics

2021 ◽  
pp. 1-20
Author(s):  
Mahdi Alimohammadi ◽  
Maryam Esna-Ashari ◽  
Jorge Navarro
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Stochastic Comparisons ◽  
Sequential Order Statistics ◽  
Progressive Type ◽  
Likelihood Ratio Ordering ◽  
Generalized Order

Due to the importance of generalized order statistics (GOS) in many branches of Statistics, a wide interest has been shown in investigating stochastic comparisons of GOS. In this article, we study the likelihood ratio ordering of $p$ -spacings of GOS, establishing some flexible and applicable results. We also settle certain unresolved related problems by providing some useful lemmas. Since we do not impose restrictions on the model parameters (as previous studies did), our findings yield new results for comparison of various useful models of ordered random variables including order statistics, sequential order statistics, $k$ -record values, Pfeifer's record values, and progressive Type-II censored order statistics with arbitrary censoring plans. Some results on preservation of logconvexity properties among spacings are provided as well.

A point-process approach to almost-sure behaviour of record values and order statistics

1996 ◽  
Vol 28 (02) ◽  
pp. 426-462 ◽  
Author(s):  
Charles M. Goldie ◽  
Ross A. Maller
Keyword(s):  
Order Statistics ◽  
Point Process ◽  
Relative Stability ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Record Values ◽  
Process Approach ◽  
Integral Conditions ◽  
Comprehensive Investigation ◽  
Trimmed Sums

Point-process and other techniques are used to make a comprehensive investigation of the almost-sure behaviour of partial maxima(the rth largest among a sample ofni.i.d. random variables), partial record valuesand differences and quotients involving them. In particular, we obtain characterizations of such asymptotic properties asa.s. for some finite constantc, ora.s. for some constantcin [0,∞], which tell us, in various ways, how quickly the sequences increase. These characterizations take the form of integral conditions on the tail ofF,which furthermore characterize such properties as stability and relative stability of the sequence of maxima. We also develop their relation to the large-sample behaviour of trimmed sums, and discuss some statistical applications.

EXTREMES: A CONTINUOUS-TIME PERSPECTIVE

2005 ◽  
Vol 19 (3) ◽  
pp. 289-308 ◽  
Author(s):  
Iddo Eliazar
Keyword(s):  
Order Statistics ◽  
Continuous Time ◽  
Time Perspective ◽  
Record Values ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Record Times ◽  
Multidimensional Distribution ◽  
Simple Simulation ◽  
Entire Sequence

We consider a generic continuous-time system in which events of random magnitudes occur stochastically and study the system's extreme-value statistics. An event is described by a pair (t,x) of coordinates, wheretis the time at which the event took place andxis the magnitude of the event. The stochastic occurrence of the events is assumed to be governed by a Poisson point process.We study various issues regarding the system's extreme-value statistics, including (i) the distribution of the largest-magnitude event, the distribution of thenth “runner-up” event, and the multidimensional distribution of the “topn” extreme events, (ii) the internal hierarchy of the extreme-value events—how large are their magnitudes when measured relative to each other, and (iii) the occurrence of record times and record values. Furthermore, we unveil a hidden Poissonian structure underlying the system's sequence of order statistics (the largest-magnitude event, the second largest event, etc.). This structure provides us with a markedly simple simulation algorithm for the entire sequence of order statistics.

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