scholarly journals Efficient Optimal Approximation of Discrete Random Variables for Estimation of Probabilities of Missing Deadlines

2019 ◽  
Vol 33 ◽  
pp. 7809-7815
Author(s):  
Liat Cohen ◽  
Gera Weiss
Keyword(s):  
Computational Complexity ◽  
Efficient Algorithm ◽  
Empirical Evaluation ◽  
Random Variable ◽  
Optimal Approximation ◽  
Discrete Random Variable ◽  
Kolmogorov Distance ◽  
Main Application ◽  
Discrete Random Variables ◽  
In Series

We present an efficient algorithm that, given a discrete random variable X and a number m, computes a random variable whose support is of size at most m and whose Kolmogorov distance from X is minimal. We present some variants of the algorithm, analyse their correctness and computational complexity, and present a detailed empirical evaluation that shows how they performs in practice. The main application that we examine, which is our motivation for this work, is estimation of the probability of missing deadlines in series-parallel schedules. Since exact computation of these probabilities is NP-hard, we propose to use the algorithms described in this paper to obtain an approximation.

A FUZZY RELIABILITY ANALYSIS BASED ON THE TRANSFORMATION BETWEEN DISCRETE FUZZY VARIABLES AND DISCRETE RANDOM VARIABLES

2006 ◽  
Vol 13 (01) ◽  
pp. 25-35 ◽  
Author(s):  
YUGE DONG ◽  
AINAN WANG
Keyword(s):  
Reliability Analysis ◽  
Fuzzy Variable ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Fuzzy Information ◽  
Discrete Random Variable ◽  
Fuzzy Reliability ◽  
Fuzzy Variables ◽  
Discrete Random Variables ◽  
Fuzzy Random

When fuzzy information is taken into consideration in design, it is difficult to analyze the reliability of machine parts because we usually must deal with random information and fuzzy information simultaneously. Therefore, in order to make it easy to analyze fuzzy reliability, this paper proposes the transformation between discrete fuzzy random variable and discrete random variable based on a fuzzy reliability analysis when one of the stress and strength is a discrete fuzzy variable and the other is a discrete random variable. The transformation idea put forwards in this paper can be extended to continuous case, and can also be used in the fuzzy reliability analysis of repairable system.

A storage process by semi-Markov input

1975 ◽  
Vol 7 (4) ◽  
pp. 830-844 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Recurrence Formula ◽  
Random Variables ◽  
Random Variable ◽  
Discrete Random Variable ◽  
Storage Process ◽  
Markov Sequence ◽  
Discrete Random Variables ◽  
Matrix Factorisation

A sequence of random variables η0, η1, …, ηn, … is defined by the recurrence formula ηn = max (ηn–1 + ξn, 0) where η0 is a discrete random variable taking on non-negative integers only and ξ1, ξ2, … ξn, … is a semi-Markov sequence of discrete random variables taking on integers only. Define Δ as the smallest n = 1, 2, … for which ηn = 0. The random variable ηn can be interpreted as the content of a dam at time t = n(n = 0, 1, 2, …) and Δ as the time of first emptiness. This paper deals with the determination of the distributions of ηn and Δ by using the method of matrix factorisation.

Peluang, Peubah Acak Diskrit, dan Sebaran Peluang Peubah Acak Diskrit

2020 ◽  
Author(s):  
Ahmad Sudi Pratikno
Keyword(s):  
Probability Distribution ◽  
Random Variables ◽  
Random Variable ◽  
Discrete Random Variable ◽  
Discrete Random Variables

Probability to learn someone's chance in getting or winning an event. In the discrete random variable is more identical to repeated experiments, to form a pattern. Discrete random variables can be calculated as the probability distribution by calculating each value that might get a certain probability value.

A storage process by semi-Markov input

1975 ◽  
Vol 7 (04) ◽  
pp. 830-844
Author(s):  
Lajos Takács
Keyword(s):  
Recurrence Formula ◽  
Random Variables ◽  
Random Variable ◽  
Discrete Random Variable ◽  
Storage Process ◽  
Markov Sequence ◽  
Discrete Random Variables ◽  
Matrix Factorisation

A sequence of random variables η 0, η 1, …, ηn , … is defined by the recurrence formula ηn = max (η n–1 + ξn , 0) where η 0 is a discrete random variable taking on non-negative integers only and ξ 1, ξ 2, … ξn , … is a semi-Markov sequence of discrete random variables taking on integers only. Define Δ as the smallest n = 1, 2, … for which ηn = 0. The random variable ηn can be interpreted as the content of a dam at time t = n(n = 0, 1, 2, …) and Δ as the time of first emptiness. This paper deals with the determination of the distributions of ηn and Δ by using the method of matrix factorisation.

Determination of Optimal Reserve between Two Machines in Series with the Repair Time has Change of Distribution after the Truncation Point

GIS Business ◽  
2019 ◽  
Vol 14 (6) ◽  
pp. 577-585
Author(s):  
T. Vivekanandan ◽  
S. Sachithanantham
Keyword(s):  
Real Life ◽  
Random Variable ◽  
Repair Time ◽  
Inventory Level ◽  
Optimal Size ◽  
Truncation Point ◽  
In Series ◽  
Optimal Reserve ◽  
Optimal Inventory Level ◽  
Two Machines

In inventory control, suitable models for various real life systems are constructed with the objective of determining the optimal inventory level.  A new type of inventory model using the so-called change of distribution property is analyzed in this paper. There are two machines M1 and M2  in series and the output of M1 is the input of M2. Hence a reserve inventory between M1 and M2 is to be maintained. The method of obtaining the optimal size of reserve inventory, assuming cost of excess inventory, cost of shortage and when the rate of consumption of M2  is a constant, has already been attempted.  In this paper, it is assumed that the repair time of M1  is a random variable and the distribution of the same undergoes a change of distribution  after the truncation point X0 , which is taken to be a random variable.  The optimal size of the reserve inventory is obtained under the above said  assumption . Numerical illustrations are also provided.

scholarly journals Fast 10-Point DFT Algorithm for Power System Harmonic Analysis

2021 ◽  
Vol 11 (15) ◽  
pp. 7007
Author(s):  
Janusz P. Paplinski ◽  
Aleksandr Cariow
Keyword(s):  
Computational Complexity ◽  
Power System ◽  
Harmonic Analysis ◽  
Efficient Algorithm ◽  
System Analysis ◽  
Spectral Leakage ◽  
Power System Analysis ◽  
Improve Accuracy ◽  
The Cost ◽  
Harmonic Power

This article presents an efficient algorithm for computing a 10-point DFT. The proposed algorithm reduces the number of multiplications at the cost of a slight increase in the number of additions in comparison with the known algorithms. Using a 10-point DFT for harmonic power system analysis can improve accuracy and reduce errors caused by spectral leakage. This paper compares the computational complexity for an L×10M-point DFT with a 2M-point DFT.

scholarly journals Distributional Replication

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1063
Author(s):  
Brendan K. Beare
Keyword(s):  
Hedge Fund ◽  
Minimum Cost ◽  
Random Variable ◽  
Optimal Approximation ◽  
Regularity Conditions ◽  
Return Distribution ◽  
Continuous Random Variable ◽  
Hedge Fund Replication ◽  
Market Index ◽  
Fund Return

A function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under suitable regularity conditions, including a bound on the entropy of the set of candidate approximations, we show that the optimal approximation comes close to achieving distributional replication, and close to achieving the minimum cost among replicating functions. We discuss the relevance of our results to the financial literature on hedge fund replication; in this case, the optimal approximation corresponds to the cheapest portfolio of market index options which delivers the hedge fund return distribution.

scholarly journals A note on characteristic function for Bernstein polynomials involving special numbers and polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 543-549
Author(s):  
Buket Simsek
Keyword(s):  
Characteristic Function ◽  
Binomial Distribution ◽  
Bernstein Polynomials ◽  
Random Variable ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Discrete Random Variable ◽  
Euler Numbers ◽  
Negative Order ◽  
Special Numbers And Polynomials

The aim of this present paper is to establish and study generating function associated with a characteristic function for the Bernstein polynomials. By this function, we derive many identities, relations and formulas relevant to moments of discrete random variable for the Bernstein polynomials (binomial distribution), Bernoulli numbers of negative order, Euler numbers of negative order and the Stirling numbers.

scholarly journals Mining Closed Item sets using Partition based Single Scan Algorithm

2019 ◽  
Vol 8 (2) ◽  
pp. 3885-3889
Keyword(s):  
Efficient Algorithm ◽  
Empirical Evaluation ◽  
Frequent Itemsets ◽  
Frequent Item ◽  
Closed Itemsets ◽  
Frequent Item Sets

Closed item sets are frequent itemsets that uniquely determines the exact frequency of frequent item sets. Closed Item sets reduces the massive output to a smaller magnitude without redundancy. In this paper, we present PSS-MCI, an efficient candidate generate based approach for mining all closed itemsets. It enumerates closed item sets using hash tree, candidate generation, super-set and sub-set checking. It uses partitioned based strategy to avoid unnecessary computation for the itemsets which are not useful. Using an efficient algorithm, it determines all closed item sets from a single scan over the database. However, several unnecessary item sets are being hashed in the buckets. To overcome the limitations, heuristics are enclosed with algorithm PSS-MCI. Empirical evaluation and results show that the PSS-MCI outperforms all candidate generate and other approaches. Further, PSS-MCI explores all closed item sets.

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