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.

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.

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.

scholarly journals A note on the implications of factorial invariance for common factor variable equivalence

2016 ◽  
Author(s):  
Michael Maraun ◽  
Moritz Heene
Keyword(s):  
Common Factor ◽  
Random Variables ◽  
Random Variable ◽  
Factorial Invariance ◽  
Technical Examination ◽  
The Common ◽  
Factor Variable

There has come to exist within the psychometric literature a generalized belief to the effect that a determination of the level of factorial invariance that holds over a set of k populations Δj, j = 1..s, is central to ascertaining whether or not the common factor random variables ξj, j = 1..s, are equivalent. In the current manuscript, a technical examination of this belief is undertaken. The chief conclusion of the work is that, as long as technical, statistical senses of random variable equivalence are adhered to, the belief is unfounded.

Random packing of an interval. II

1979 ◽  
Vol 11 (03) ◽  
pp. 591-602
Author(s):  
David Mannion
Keyword(s):  
Fine Particles ◽  
Random Variables ◽  
Random Variable ◽  
Difficult Problem ◽  
Random Packing ◽  
Point Of View ◽  
Initial Size ◽  
Moderate Size ◽  
The Individual

We showed in [2] that if an object of initial size x (x large) is subjected to a succession of random partitions, then the object is decomposed into a large number of terminal cells, each of relatively small size, where if Z(x, B) denotes the number of such cells whose sizes are points in the set B, then there exists c, (0 < ≦ 1), such that Z(x, B)x −c converges in probability, as x → ∞, to a random variable W. We show here that if a parent object of size x produces k offspring of sizes y 1, y 2, ···, y k and if for each k x - y 1 - y 2 - ··· - y k (the ‘waste’ or the ‘cover’, depending on the point of view) is relatively small, then for each n the nth cumulant, Ψ n (x, B), of Z(x, B) satisfies Ψ n (x, B)x -c → κ n (B), as x → ∞, for some κ n (B). Thus, writing N = x c , Z(x, B) has approximately the same distribution as the sum of N independent and identically distributed random variables (The determination of the distribution of the individual appears to be a difficult problem.) The theory also applies when an object of moderate size is broken down into very fine particles or granules.

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.

scholarly journals Role Of Probability Biclassification In Accounting And Finance Random Variable Representations

2011 ◽  
Vol 28 (1) ◽  
pp. 59
Author(s):  
Charmaine Scrimnger-Christian ◽  
Saratiel Wedzerai Musvoto
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Financial Statements ◽  
Font Size ◽  
Deterministic Models ◽  
Random Utility Theory ◽  
Long Run ◽  
Value Measurement

<span style="font-family: Times New Roman; font-size: small;"> </span><p style="margin: 0in 0.5in 0pt; text-align: justify; mso-pagination: none;" class="MsoNormal"><span style="color: black; font-size: 10pt; mso-themecolor: text1;"><span style="font-family: Times New Roman;">The concept of value in accounting has been generalized by various authors to a large variety of relations in both accounting and finance. For example, the basis for the preparation of the financial statements in accounting and the foundations for the determination of the return on a security in finance are based on the concept of value measurement. However, there are cases in which applications of the concept of value measurement breaks down, such as in predicting the long-run behavior of accounting and finance phenomena classified as random variables and in applying deterministic models to accounting and finance models. In this study, the principles of probability biclassification and random utility theory are used to rectify the shortcomings of generalizing the concept of value measurement to include activities to understand the long-run behavior of random variables. This study closes with a discussion on the compatibility of the intentionality structure of acts of knowledge in accounting and finance with statistical concepts on random variables.<span style="mso-spacerun: yes;"> </span></span></span></p><span style="font-family: Times New Roman; font-size: small;"> </span>

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.

Probability Mass Functions

2019 ◽  
pp. 87-107
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Bayesian Inference ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Random Variable ◽  
Posterior Distributions ◽  
Bernoulli Distribution ◽  
Discrete Random Variables ◽  
Probability Mass ◽  
Mass Functions

This chapter focuses on probability mass functions. One of the primary uses of Bayesian inference is to estimate parameters. To do so, it is necessary to first build a good understanding of probability distributions. This chapter introduces the idea of a random variable and presents general concepts associated with probability distributions for discrete random variables. It starts off by discussing the concept of a function and goes on to describe how a random variable is a type of function. The binomial distribution and the Bernoulli distribution are then used as examples of the probability mass functions (pmf’s). The pmfs can be used to specify prior distributions, likelihoods, likelihood profiles and/or posterior distributions in Bayesian inference.

scholarly journals DETERMINATION OF VARIANCE OF TIME TO RECRUITMENT WITH INTER-DECISION TIME AS GEOMETRIC PROCESS WHEN THE THRESHOLD HAS THREE COMPONENTS

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 222-229
Author(s):  
A DEVI ◽  
◽  
B SATHISH KUMAR ◽  
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Decision Time ◽  
Breakdown Threshold ◽  
Geometric Process ◽  
Exponential Random Variables ◽  
Manpower System ◽  
Three Components ◽  
Independent And Identically Distributed

In this paper, the problem of time to recruitment is analyzed for a single grade manpower system using an univariate CUM policy of recruitment. Assuming policy decisions and exits occur at different epochs, wastage of manpower due to exits form a sequence of independent and identically distributed exponential random variables, the inter-decision times form a geometric process and inter-exist time form an independent and identically distributed random variable. The breakdown threshold for the cumulative wastage of manpower in the system has three components which are independent exponential random variables. Employing a different probabilistic analysis, analytical results in closed form for system characteristics are derived

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