Estimation of distributions with the new better than used in expectation property

2013 ◽  
Vol 83 (5) ◽  
pp. 1346-1352 ◽  
Author(s):  
Edgardo Lorenzo ◽  
Ganesh Malla ◽  
Hari Mukerjee
Keyword(s):  
New Better Than Used ◽  
Estimation Of Distributions ◽  
Better Than

Tail of compound distributions and excess time

1996 ◽  
Vol 33 (01) ◽  
pp. 184-195 ◽  
Author(s):  
Xiaodong Lin
Keyword(s):  
Size Distribution ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Claim Size ◽  
Compound Distributions ◽  
Fundamental Identity ◽  
Claim Size Distribution ◽  
Simple Bounds ◽  
New Better Than Used ◽  
Better Than

Bounds on the tail of compound distributions are considered. Using a generalization of Wald's fundamental identity, we derive upper and lower bounds for various compound distributions in terms of new worse than used (NWU) and new better than used (NBU) distributions respectively. Simple bounds are obtained when the claim size distribution is NWUC, NBUC, NWU, NBU, IMRL, DMRL, DFR and IFR. Examples on how to use these bounds are given.

CLASSIFICATION OF MULTIVARIATE LIFE DISTRIBUTIONS BASED ON PARTIAL ORDERING

2002 ◽  
Vol 16 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Present Article ◽  
Failure Rate ◽  
Partial Ordering ◽  
Increasing Failure Rate ◽  
Multivariate Generalization ◽  
Partial Orderings ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

Barlow and Proschan presented some interesting connections between univariate classifications of life distributions and partial orderings where equivalent definitions for increasing failure rate (IFR), increasing failure rate average (IFRA), and new better than used (NBU) classes were given in terms of convex, star-shaped, and superadditive orderings. Some related results are given by Ross and Shaked and Shanthikumar. The introduction of a multivariate generalization of partial orderings is the object of the present article. Based on that concept of multivariate partial orderings, we also propose multivariate classifications of life distributions and present a study on more IFR-ness.

scholarly journals Relating Time and Customer Averages for Queues Using ‘forward’ Coupling from the Past

2008 ◽  
Vol 45 (02) ◽  
pp. 568-574
Author(s):  
Erol A. Peköz ◽  
Sheldon M. Ross
Keyword(s):  
Queueing System ◽  
Steady State Distribution ◽  
State Distribution ◽  
The Past ◽  
Coupling From The Past ◽  
Poisson Arrivals ◽  
Time Averages ◽  
Time Average ◽  
New Better Than Used ◽  
Better Than

We give a new method for simulating the time average steady-state distribution of a continuous-time queueing system, by extending a ‘read-once’ or ‘forward’ version of the coupling from the past (CFTP) algorithm developed for discrete-time Markov chains. We then use this to give a new proof of the ‘Poisson arrivals see time averages’ (PASTA) property, and a new proof for why renewal arrivals see either stochastically smaller or larger congestion than the time average if interarrival times are respectively new better than used in expectation (NBUE) or new worse than used in expectation (NWUE).

On the dependence structure of hitting times of univariate processes

1988 ◽  
Vol 25 (02) ◽  
pp. 355-362 ◽  
Author(s):  
Nader Ebrahimi ◽  
T. Ramalingam
Keyword(s):  
Brownian Motion ◽  
Structural Properties ◽  
Hitting Times ◽  
Dependence Structure ◽  
Special Case ◽  
New Better Than Used ◽  
Better Than

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

A class of correlated cumulative shock models

1985 ◽  
Vol 17 (2) ◽  
pp. 347-366 ◽  
Author(s):  
Ushio Sumita ◽  
J. George Shanthikumar
Keyword(s):  
Failure Time ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Random Variables ◽  
System Failure ◽  
Shock Models ◽  
The Times ◽  
New Better Than Used ◽  
Better Than

In this paper we define and analyze a class of cumulative shock models associated with a bivariate sequence {Xn, Yn}∞n=0 of correlated random variables. The {Xn} denote the sizes of the shocks and the {Yn} denote the times between successive shocks. The system fails when the cumulative magnitude of the shocks exceeds a prespecified level z. Two models, depending on whether the size of the nth shock is correlated with the length of the interval since the last shock or with the length of the succeeding interval until the next shock, are considered. Various transform results and asymptotic properties of the system failure time are obtained. Further, sufficient conditions are established under which system failure time is new better than used, new better than used in expectation, and harmonic new better than used in expectation.

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