Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency.
PurposeThe purpose of this study is to identify the learner characteristics attributable to the likelihood and the duration of programme completion in the Bachelor of Science (BSc) and Bachelor of Technology Honours in Engineering (BTech) degree programmes of the Open University of Sri Lanka (OUSL).Design/methodology/approachData were gathered from the re-registrants for the degree programmes in the academic year 2020/2021, using a questionnaire developed as a Google form. The sample consisted of 301 and 516 re-registrants from the BTech and BSc programmes respectively. Influential factors were identified using Kruskal Wallis test (for duration of completion), binary logistic regression (for likelihood of completion) and Chi-squared test (associations between presage and process factors).FindingsEntry qualification, age and time management skills at entry had significant effects on duration of completion. Attendance at academic activities, organizing time for self-studies and the competency in English at enrolment had significant effects on the likelihood of completion. Prior open and distance learning (ODL) experience had no significant effect on any of the product factors considered.Research limitations/implicationsInaccessibility of dropouts and using only the responses from the first administration of the questionnaire are limitations. Active learners are more likely to respond, in the first administration and may bias the results.Practical implicationsFindings are useful for designing future studies to identify at-risk students and thereby enhance the programme completion and reduce prolonged time for completion.Social implicationsEffective strategies to control the identified factors will uplift programme completion and reduce drop-out rates.Originality/valueDecision making using inferential techniques makes the study distinct among studies undertaken on the same population. The study enriches the limited current research on factors affecting programme completion in ODL mode.
We say that Kn → (G,H), if for every red/blue colouring of edges of the complete graph Kn, there exists a red copy of G, or a blue copy of H in the colouring of Kn. The Ramsey number r(G,H) is the smallest positive integer n such that Kn → (G,H). Let r(n,m)=r(Kn, Km). A closely related concept of Ramsey numbers is the Star-critical Ramsey number r*(G, H) defined as the largest value of k such that K r(G,H)-1 ˅ K 1,k → (G,H). Literature on survey papers in this area reveals many unsolved problems related to these numbers. One of these problems is the calculation of Ramsey numbers for certain classes of graphs. The primary objective of this paper is to calculate the Star critical Ramsey numbers for the case of Stars versus K1,m+e. The methodology that we follow in solving this problem is to first find a closed form for the Ramsey number r*(K1,n , K1,m+e) for all n, m ≥ 3. Based on the values of r*(K1,n , K1,m+e) for different n, m we arrive at a general formula for r*(K1,n , K1,m+e). Henceforth, we show that r*(K1,n , K1,m+e) = n+m-1 is defined by a piecewise function related to the three disjoint cases of n, m both even and n ≤ m - 2, n or m is odd and n ≤ m-2 and n > m-2.
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