Open Access Original Research Article

Ameliorated Class of Estimators of Finite Population Variance

J. O. Muili, E. N. Agwamba, A. B. Odeyale, A. Adebiyi

Asian Journal of Probability and Statistics, Page 1-14
DOI: 10.9734/ajpas/2020/v7i430189

A class of ratio estimators of finite population variance is proposed in this study. The properties of the proposed estimators have been derived using Taylor’s Series method up to first order of approximation. The efficiency conditions which are the mean square errors (MSEs) and percentage relative efficiency (PRE) of the proposed estimators over existing estimators have been established. The analytical illustration was also conducted to affirm the theoretical results. The results of the empirical study revealed that the proposed estimators are more efficient than the existing estimators considered in the study.

Open Access Original Research Article

A Study of Second Order Slope Rotatable Designs under Intra-class Correlated Structure of Errors Using Partially Balanced Incomplete Block Type Designs

B. Sulochana, B. Re. Victorbabu

Asian Journal of Probability and Statistics, Page 15-28
DOI: 10.9734/ajpas/2020/v7i430190

In this paper, a study of second order slope rotatable designs under intra-class correlated structure of errors using partially balanced incomplete block type designs is suggested. Further, we study the variance function of the estimated slopes for different values of intra-class correlated coefficient ( ) and distance from centre (d) for 6 ≤ v ≤ 12 (number of factors) are also suggested. We note the new method sometimes leads to designs with fewer number of design points.

Open Access Original Research Article

A New Odd Lindley-Gompertz Distribution: Its Properties and Applications

Omolola Dorcas Atanda, Tajan Mashingil Mabur, Gerald Ikechukwu Onwuka

Asian Journal of Probability and Statistics, Page 29-47
DOI: 10.9734/ajpas/2020/v7i430191

This article presents a comprehensive study of an odd Lindley-Gompertz distribution which has already been proposed in the literature but without any properties. The present study unlike the previous one has considered the derivation of several properties of the odd Lindley-Gompertz distribution with their graphical representations and discussions which has not been done in the first proposition of the distribution.  The study looks at properties such as survival (or reliability) function, the hazard function, the cumulative hazard function, the reverse hazard function, the odds function, quantile function, moments, moment generating function, characteristic function, cumulant generating function, distribution of order statistics and maximum likelihood estimation of the distribution’s parameters none of which was treated by the previous author of the model. An illustration to evaluate the goodness-of-fit of the odd Lindley-Gompertz distribution has also been done using two real life datasets and the results show that the model fits the datasets better than the five other distributions considered in this present study.

Open Access Original Research Article

Some Median Type Estimators to Estimate the Finite Population Mean

Waqar Hafeez, Javid Shabbir, Muhammad Taqi Shah, Shakeel Ahmed

Asian Journal of Probability and Statistics, Page 48-58
DOI: 10.9734/ajpas/2020/v7i430192

Researchers always appreciates estimators of finite population quantities, especially mean, with maximum efficiency for reaching to valid statistical inference.  Apart from ratio, product and regression estimators, exponential estimators are widely considered by survey statisticians. Motivated from the idea of exponential type estimators, in this article, we propose some new estimators utilizing known median of the study variable with mean of auxiliary variable. Theoretical properties of the suggested estimators are studied up to first order of approximation. In addition, an empirical and simulation study the comparison of median based proposed class of estimators with sample mean, ratio and linear regression estimators  are discussed. The results expose that the proposed estimators are more efficient than the existing estimators.

Open Access Original Research Article

Nonparametric Methods for the Nondecreasing Ordered Hypothesis in a Mixed Design

Badr Alnssyan, Rhonda C. Magel

Asian Journal of Probability and Statistics, Page 59-71
DOI: 10.9734/ajpas/2020/v7i430193

Aims: Introduce two new test statistics in testing for the nondecreasing alternative in a mixed design consisting of a Completely Randomized Portion and a Randomized Complete Block Portion.

Study Design: Simulation study comparing four test statistics for the nondecreasing alternative in a mixed design consisting of a CRD and an RCBD portion. The test statistics included two new test statistics and two existing test statistics. Random samples were taken from three different types of underlying distributions. Different percentages of the CRD portion will be considered as well as different sample sizes. Powers were estimated based on a variety location parameter shifts. Three, four, and five populations were considered.

Place and Duration of Study: The simulation study took place on the campus of North Dakota State University during the calendar year 2019.

Methodology: Levels of significance for each of the three types of underlying distributions, when the RCBD portion was larger than the CRD portion, when the CRD portion was larger than the RCBD portion, and when the CRD portion was equal to the RCBD portion, and when the number of populations were 3, 4, and 5.

Results: Regardless of the underlying population types, the proposed test statistics did better than the existing test statistics when the difference between the last two parameters is large. This was true for 3, 4, and 5 populations.

Conclusion: When the differences between the last two parameters is large, the two new test statistics performed better. Otherwise, the existing test statistics are better. In both cases, it is better to use the combined test statistic that first standardizes the individual test statistics for the CRD and RCBD portions before adding them together.