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

scholarly journals STOCHASTIC MODEL FOR TIME TO RECRUITMENT IN A SINGLE GRADE MANPOWER SYSTEM WITH TWO TYPES OF INTERDECISION TIMES WHEN THE BREAKDOWN THRESHOLD HAS THREE COMPONENTS

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 230-237
Author(s):  
A DEVI ◽  
◽  
K SRINIVASAN ◽  
Keyword(s):  
Stochastic Model ◽  
Renewal Process ◽  
Random Variables ◽  
Policy Decisions ◽  
Breakdown Threshold ◽  
Problem Of Time ◽  
Exponential Random Variables ◽  
Manpower System ◽  
System Characteristics ◽  
Three Components

In this paper, the problem of time to recruitment is analyzed for a single grade manpower system in which attrition takes place due to two types of policy decisions where this classification is done according to intensity of attrition, it form an ordinary renewal process. Assuming (i) policy decisions and exits occur at different epochs (ii) wastage of manpower due to exits and wastage due to frequent breaks taken by the personnel working in the manpower system separately form a sequence of independent and identically distributed exponential random variables with different means and (iii) breakdown threshold for the cumulative wastage of manpower in the system has three components which are independent exponential random variables. A stochastic model is constructed and the variance of the time to recruitment is obtained using an univariate CUM policy of recruitment. Employing a different probabilistic analysis, analytical results in closed form for system characteristics are derived.

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.

Existence and positivity of the limit in processes with a branching structure

1999 ◽  
Vol 36 (1) ◽  
pp. 132-138
Author(s):  
M. P. Quine ◽  
W. Szczotka
Keyword(s):  
Stochastic Process ◽  
Branching Process ◽  
Random Variables ◽  
Random Variable ◽  
Natural Generalization ◽  
Partial Sums ◽  
Urn Model ◽  
Special Case ◽  
Independent And Identically Distributed

We define a stochastic process {Xn} based on partial sums of a sequence of integer-valued random variables (K0,K1,…). The process can be represented as an urn model, which is a natural generalization of a gambling model used in the first published exposition of the criticality theorem of the classical branching process. A special case of the process is also of interest in the context of a self-annihilating branching process. Our main result is that when (K1,K2,…) are independent and identically distributed, with mean a ∊ (1,∞), there exist constants {cn} with cn+1/cn → a as n → ∞ such that Xn/cn converges almost surely to a finite random variable which is positive on the event {Xn ↛ 0}. The result is extended to the case of exchangeable summands.

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>

On an Integral Equation for Discounted Compound – Annuity Distributions

1989 ◽  
Vol 19 (2) ◽  
pp. 191-198 ◽  
Author(s):  
Colin M. Ramsay
Keyword(s):  
Integral Equation ◽  
Random Variables ◽  
Random Variable ◽  
Discrete Distributions ◽  
Discount Factor ◽  
Present Value ◽  
New Class ◽  
Image Position ◽  
Independent And Identically Distributed

AbstractWe consider a risk generating claims for a period of N consecutive years (after which it expires), N being an integer valued random variable. Let Xk denote the total claims generated in the kth year, k ≥ 1. The Xk's are assumed to be independent and identically distributed random variables, and are paid at the end of the year. The aggregate discounted claims generated by the risk until it expires is defined as where υ is the discount factor. An integral equation similar to that given by Panjer (1981) is developed for the pdf of SN(υ). This is accomplished by assuming that N belongs to a new class of discrete distributions called annuity distributions. The probabilities in annuity distributions satisfy the following recursion:where an is the present value of an n-year immediate annuity.

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.

scholarly journals Exponential and Hypoexponential Distributions: Some Characterizations

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2207
Author(s):  
George P. Yanev
Keyword(s):  
Linear Combination ◽  
Exponential Distribution ◽  
Random Variables ◽  
Random Variable ◽  
Unknown Distribution ◽  
Converse Result ◽  
Hypoexponential Distribution ◽  
Exponential Random Variables

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some n≥2, X1,X2,…,Xn are independent copies of a random variable X with unknown distribution F and a specific linear combination of Xj’s has hypoexponential distribution, then F is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently by Arnold and Villaseñor (2013) for a particular convolution of two random variables.

ON SKEWNESS AND DISPERSION AMONG CONVOLUTIONS OF INDEPENDENT GAMMA RANDOM VARIABLES

2010 ◽  
Vol 25 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Leila Amiri ◽  
Baha-Eldin Khaledi ◽  
Francisco J. Samaniego
Keyword(s):  
Residual Life ◽  
Random Variables ◽  
Random Variable ◽  
Independent Random Variables ◽  
Mean Residual Life ◽  
Exponential Random Variables ◽  
Right Spread Order ◽  
New Better Than Used ◽  
Common Shape ◽  
Better Than

Let {x(1)≤···≤x(n)} denote the increasing arrangement of the components of a vector x=(x1, …, xn). A vector x∈Rn majorizes another vector y (written $\bf{x} \mathop{\succeq}\limits^{m} \bf{y}$) if $\sum_{i=1}^{j} x_{(i)} \le \sum_{i=1}^{j}y_{(i)}$ for j = 1, …, n−1 and $\sum_{i=1}^{n}x_{(i)} = \sum_{i=1}^{n}y_{(i)}$. A vector x∈R+n majorizes reciprocally another vector y∈R+n (written $\bf{x} \mathop{\succeq}\limits^{rm} \bf{y}$) if $\sum_{i=1}^{j}(1/x_{(i)}) \ge \sum_{i=1}^{j}(1/y_{(i)})$ for j = 1, …, n. Let $X_{\lambda_{i},\alpha},\,i=1,\ldots,n$, be n independent random variables such that $X_{\lambda_{i},\alpha}$ is a gamma random variable with shape parameter α≥1 and scale parameter λi, i = 1, …, n. We show that if $\lambda \mathop{\succeq}\limits^{rm} \lambda^{\ast}$, then $\sum_{i=1}^{n} X_{\lambda_{i},\alpha}$ is greater than $\sum_{i=1}^{n} X_{\lambda^{\ast}_{i},\alpha}$ according to right spread order as well as mean residual life order. We also prove that if $(1/ \lambda_{1}, \ldots ,1/ \lambda_{n}) \mathop{\succeq}\limits^{m} \succeq (1/ \lambda_{1}^{\ast}, \ldots , 1/ \lambda_{n}^{\ast})$, then $\sum_{i=1}^{n} X_{\lambda_{i}, \alpha}$ is greater than $\sum_{i=1}^{n} X_{\lambda^{\ast}_{i},\alpha}$ according to new better than used in expectation order as well as Lorenze order. These results mainly generalize the recent results of Kochar and Xu [7] and Zhao and Balakrishnan [14] from convolutions of independent exponential random variables to convolutions of independent gamma random variables with common shape parameters greater than or equal to 1.

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