Formulae for Projecting Enrolments and Degrees Awarded in Universities

Gani, J.

doi:10.2307/2982224

Cited by 120 publications

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“…The importance of cyclic behavior was firstly stressed in Bartholomew (1982) p.71. The motive was Gani's (1963) study of student enrolment at Michigan state University. A general theorem for the limiting behavior of the expected population structure for a Cyc-NHMS was given in Vassiliou (1984).…”

Section: Convergence In the Cesaro Sense For Cyclic Nhmsmentioning

confidence: 99%

“…In a second theorem in the same section we provide and prove under what conditions the mode of convergence in the previous basic result is almost surely. In Section 4 we study the important category of Cyclic NHMS, a concept which was motivated by the work of Gani (1963) on students enrolment at Michigan state University and Bartholomew (1982). We prove in two theorems, under what conditions the relative population structure of a Cycl-NHMS asymptotically converges in the strongly Cesaro sense.…”

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confidence: 99%

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Laws of Large Numbers for Non-Homogeneous Markov Systems

Vassiliou

2018

Methodol Comput Appl Probab

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In the present we establish Laws of Large Numbers for Non-Homogeneous Markov Systems and Cyclic Non-homogeneous Markov systems. We start with a theorem, where we establish, that for a NHMS under certain conditions, the fraction of time that a membership is in a certain state, asymptotically converges in mean square to the limit of the relative population structure of memberships in that state. We continue by proving a theorem which provides the conditions under which the mode of covergence is almost surely. We continue by proving under which conditions a Cyclic NHMS is Cesaro strongly ergodic. We then proceed to prove, that for a Cyclic NHMS under certain conditions the fraction of time that a membership is in a certain state, asymptotically converges in mean square to the limit of the relative population structure in the strongly Cesaro sense of memberships in that state. We then proceed to establish a founding Theorem, which provides the conditions under which, the relative population structure asymptotically converges in the strongly Cesaro sense with geometrical rate. This theorem is the basic instrument missing to prove, under what conditions the Law of Large Numbers for a Cycl-NHMS is with almost surely mode of convergence. Finally, we present two applications firstly for geriatric and stroke patients in a hospital and secondly for the population of students in a University system.

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Section: Convergence In the Cesaro Sense For Cyclic Nhmsmentioning

confidence: 99%

mentioning

confidence: 99%

Laws of Large Numbers for Non-Homogeneous Markov Systems

Vassiliou

2018

Methodol Comput Appl Probab

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“…Starting with the work of [Gani (1963)] mathematical models have been used as an important tool to shed light on the educational process. The art of applying mathematical techniques to a wide variety of problems in education has gained prominence in the literature (for instance, [Jimenez and Salas-Velasco (2000)]; [Mancebon and Muniz (2008)]; [Nicholls (2009)]; [Ekhosuehi and Osagiede (2013)]; [Johnes (2015)]; [Ekhosuehi (2016)]).…”

Section: Introductionmentioning

confidence: 99%

Survivor rates of new entrants into an undergraduate degree programme under clearance uncertainty

Ekhosuehi¹,

Oyegue²

2016

AJAS

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Abstract. . Considering the clearance exercise in a Nigerian university setting, this study attempts to answer the question of the following sort: 'What is the survivor rate of candidates offered (provisional) admission into a course of study in the face of clearance uncertainty?' We represent the problem as a system of differential equations within the framework of a network model with constant risk and then solve it using the Laplace transform. Rather than relying on steady-states fractional flow rates, we provide a transient solution to the problem. The survivor function for each entry level derived for the problem sheds some light on situations where a decision is to be made on two (or more) preferred courses and thus evades possible trauma in the application process.Résumé : Cetteétude prend place dans la problématique de l'admission desétudiants dans les universités nigériannes. Elle se propose de répondre aux questions semblablesà celle-ci : quel est le taux de survie (final) des candidats provisoirement admisà un programme dans une situation d'admission finale incertaine? Nous modélisons ce problème grâceà un système d'équations différentielles dans le cadre d'un modèle de réseauà risque constant. La transformation de Laplace est notre outil pour résoudre le problème théorique.

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“…The first model, which has received considerable attention in the literature (for example, see Bartholomew (1967), Gani (1963), Thonstad (1968)) assumes an underlying stationary Markov chain structure.…”

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confidence: 99%

“…The Markov chain model has been discussed in detail in the literature (for example, see Bartholomew (1967), Gani (1963), Marshall et al (1970)), but to unify notation, and for completeness and clarity we formulate it here. Throughout the paper we assume a system made up of n active states.…”

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confidence: 99%

A Comparison of Two Personnel Prediction Models

Marshall

1973

Operations Research

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This paper describes, compares, and contrasts two mathematical models of personnel movement through a hierarchical organization. The first model is a Markov chain, which is described in detail in other literature. The emphasis in this paper is on a cohort model based on people's lifetime behavior in the system. Data from student enrollments is used in comparing the models, and predictions are made and compared with numbers from real situations.

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Formulae for Projecting Enrolments and Degrees Awarded in Universities

Cited by 120 publications

References 0 publications

Laws of Large Numbers for Non-Homogeneous Markov Systems

Laws of Large Numbers for Non-Homogeneous Markov Systems

Survivor rates of new entrants into an undergraduate degree programme under clearance uncertainty

A Comparison of Two Personnel Prediction Models

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