by Oshada Senaweera, Prasanna S. Haddela and Gayan Dharmarathne
The paper investigates the comparative effects of several random sampling methods on the maximum likelihood estimates of a simple logistic regression model. The study uses simulated data (logistic populations with pre-defined parameter values) that used Monte Carlo methods to simulate. Sampling techniques include Simple Random Sampling (SRS) and six variations of Stratified Sampling where two are single-stage Stratified Sampling and four are choice-based (two-phase) Stratified Sampling. Parameter estimates arising under each sampling technique were compared using performance measures Bias, Standard Error & Percentage of models that are feasibly estimated. The simulation-based analysis found that choice-based sampling with proportional allocation in both phases is the best-suited sampling technique for parameter estimation of a simple logistic regression model.
American Journal of Applied Mathematics and Statistics. 2021, 9(1), 28-37. DOI: 10.12691/ajams-9-1-5
Pub. Date: January 31, 2021
3529 Views9 Downloads
by P. N. Seetharaman
American Journal of Applied Mathematics and Statistics. 2021, 9(1), 24-27. DOI: 10.12691/ajams-9-1-4
Pub. Date: January 31, 2021
206 Views1 Downloads
by Yasser M. Amer, Dina H. Abdel Hady and Rania M. Shalabi
Original Research
In this paper two basic random variables constructed from Quasi Lindley distribution have been introduced. One of these variables is defined as the sum of two independent random variables following the Quasi-Lindley distribution with the same parameter (2SQLindley). The second one is defined as the difference of two independent random variables following the Quasi-Lindley distribution with also the same parameter (2DQLindley). For both cases, we provided some statistical properties such as moments, incomplete moments and characteristic function. The parameters are estimated by maximum likelihood method. From simulation studies, the performance of the maximum likelihood estimators has been assessed. The usefulness of the corresponding models is proved using goodness-of-fit tests based on different real datasets. The new models provide consistently better fit than some classical models used in this research.
American Journal of Applied Mathematics and Statistics. 2021, 9(1), 12-23. DOI: 10.12691/ajams-9-1-3
Pub. Date: January 20, 2021
4240 Views4 Downloads
by Noora Shrestha
Original Research
Factor analysis is particularly suitable to extract few factors from the large number of related variables to a more manageable number, prior to using them in other analysis such as multiple regression or multivariate analysis of variance. It can be beneficial in developing of a questionnaire. Sometimes adding more statements in the questionnaire fail to give clear understanding of the variables. With the help of factor analysis, irrelevant questions can be removed from the final questionnaire. This study proposed a factor analysis to identify the factors underlying the variables of a questionnaire to measure tourist satisfaction. In this study, Kaiser-Meyer-Olkin measure of sampling adequacy and Bartlett’s test of Sphericity are used to assess the factorability of the data. Determinant score is calculated to examine the multicollinearity among the variables. To determine the number of factors to be extracted, Kaiser’s Criterion and Scree test are examined. Varimax orthogonal factor rotation method is applied to minimize the number of variables that have high loadings on each factor. The internal consistency is confirmed by calculating Cronbach’s alpha and composite reliability to test the instrument accuracy. The convergent validity is established when average variance extracted is greater than or equal to 0.5. The results have revealed that the factor analysis not only allows detecting irrelevant items but will also allow extracting the valuable factors from the data set of a questionnaire survey. The application of factor analysis for questionnaire evaluation provides very valuable inputs to the decision makers to focus on few important factors rather than a large number of parameters.
American Journal of Applied Mathematics and Statistics. 2021, 9(1), 4-11. DOI: 10.12691/ajams-9-1-2
Pub. Date: January 20, 2021
7483 Views18 Downloads
by Ilhan M. Izmirli
Original Research
In this paper, we will deal with the problem of calculating the average velocity of a celestial object revolving around another celestial object in an elliptical orbit. After proving our main theorem to this effect, we will give some alternate forms of the formula for the average velocity, and show that this average value is in fact, attained at certain points of the orbit. We will conclude the paper by providing an intuitively natural and straightforward amendment of this formula.
American Journal of Applied Mathematics and Statistics. 2021, 9(1), 1-3. DOI: 10.12691/ajams-9-1-1
Pub. Date: January 15, 2021
2276 Views4 Downloads