A Probabilistic Approach to The Moments of Binomial Random Variables and Application

2019 ◽  
pp. 1-3
Author(s):  
Duy Nguyen
Keyword(s):  
Probabilistic Approach ◽  
Random Variables ◽  
Binomial Random Variables

scholarly journals A Concept of Determining the Relation between Load and Wear of Tribological Systems of Ship Main Selfignition Engines by Using Probabilistic Approach

2018 ◽  
Vol 25 (4) ◽  
pp. 130-138
Author(s):  
Jerzy Girtler
Keyword(s):  
Probabilistic Approach ◽  
Random Variables ◽  
Coefficient Of Correlation ◽  
Ship Propulsion ◽  
The Third ◽  
Operational Principle ◽  
External Conditions ◽  
Excessive Load

Abstract This paper presents a proposal of simultaneous consideration of load and wear associated with it , of tribological systems of ship main engines (intended for ship propulsion) . Based on results of investigations it was assumed that both the load Q (i.e. a cause of wear ) and the wear Z (i.e. an effect of load occurrence) considered in a given time t (0 ≤ t ≤ tn) are random variables Qt and Zt ,respectively. There was characterized operational principle of ship main engines in definite external conditions (WZ) as well as consequences of excessive load of engines. Three hypotheses highlighting relations existing between load and wear of the above mentioned systems, have been proposed. The first of them deals with explanation of stochastic relation between load and wear, the second highlights why it is possible to assume that the load Qt and the wear Zt are positively correlated , and the third - why it is possible to assume that coefficient of correlation between Qt and Zt may be taken close to one.

Error Analysis of Cam-Follower Systems: A Probabilistic Approach

1984 ◽  
Vol 198 (3) ◽  
pp. 155-162 ◽  
Author(s):  
S S Rao
Keyword(s):  
Error Analysis ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Stochastic Approach ◽  
Geometrical Parameters ◽  
Manufacturing Costs ◽  
Actual Output ◽  
Analysis And Synthesis ◽  
Cam Follower ◽  
Synthesis Procedure

The actual output kinematic characteristics of a cam-follower system will be different from the theoretical (desired) ones due to errors in manufacture and assembly. A method of evaluating the mechanical error in the kinematic response of cam-follower systems is presented using a stochastic approach. The tolerances on cam profiles and other geometrical parameters are treated as random variables that influence the mechanical error. The equations necessary for the mechanical error analysis of a planar cam-follower system (disc cam with translating roller follower) are derived. The equations for a spatial cam-follower system (globoidal cam with oscillating cylindrical follower) are also given at the end. An optimal synthesis procedure is outlined for the allocation of tolerances so as to minimize the manufacturing costs while satisfying a constraint on the maximum mechanical error in the kinematic response of cam-follower systems. The application of analysis and synthesis procedure is demonstrated with reference to a disc cam with translating roller follower.

Ordering comparison of negative binomial random variables with their mixtures

2008 ◽  
Vol 78 (14) ◽  
pp. 2234-2239 ◽  
Author(s):  
Mohammad Hossein Alamatsaz ◽  
Somayyeh Abbasi
Keyword(s):  
Negative Binomial ◽  
Random Variables ◽  
Binomial Random Variables

scholarly journals Probabilities of Competing Binomial Random Variables

2012 ◽  
Vol 49 (3) ◽  
pp. 731-744
Author(s):  
Wenbo V. Li ◽  
Vladislav V. Vysotsky
Keyword(s):  
Phase Transition ◽  
Fourier Analysis ◽  
Random Variables ◽  
Integral Representations ◽  
Transition Phenomenon ◽  
Convexity Properties ◽  
Binomial Random Variables

Suppose that both you and your friend toss an unfair coin n times, for which the probability of heads is equal to α. What is the probability that you obtain at least d more heads than your friend if you make r additional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function of n, and demonstrate surprising phase transition phenomenon as the parameters d, r, and α vary. Our main tools are integral representations based on Fourier analysis.

COMMENTS ON THE SURVEY BY BALAKRISHNAN AND ZHAO

2013 ◽  
Vol 27 (4) ◽  
pp. 445-449 ◽  
Author(s):  
Moshe Shaked
Keyword(s):  
Order Statistics ◽  
Negative Binomial ◽  
Random Variables ◽  
Hazard Rates ◽  
Proportional Hazard ◽  
Stochastic Comparisons ◽  
Exponential Random Variables ◽  
Binomial Random Variables

N. Balakrishnan and Peng Zhao have prepared an outstanding survey of recent results that stochastically compare various order statistics and some ranges based on two collections of independent heterogeneous random variables. Their survey focuses on results for heterogeneous exponential random variables and their extensions to random variables with proportional hazard rates. In addition, some results that stochastically compare order statistics based on heterogeneous gamma, Weibull, geometric, and negative binomial random variables are also given. In particular, the authors of have listed some stochastic comparisons that are based on one heterogeneous collection of random variables, and one homogeneous collection of random variables. Personally, I find these types of comparisons to be quite fascinating. Balakrishnan and Zhao have done a thorough job of listing all the known results of this kind.

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