Inference on Overlapping Coefficients in Two Exponential Populations

Three measures of overlap, namely Matusita’s measureρ , Morisita’s measure λ and Weitzman’s measure Δ are investigated in this article for two exponential populations with different means. It is well that the estimators of those measures of overlap are biased. The bias is of these estimators depends on the unknown overlap parameters. There are no closed-form, exact formulas, for those estimators variances or their exact sampling distributions. Monte Carlo evaluations are used to study the bias and precision of the proposed overlap measures. Bootstrap method and Taylor series approximation are used to construct confidence intervals for the overlap measures

Aplikasi Metode Multycriteria Decision Making (MCDM)dengan Teknik Pembobotan Dalam Mengidentifikasi Dan Mendesain Kawasan Konservasi Perairan Daerah Di Kabupaten Luwu Utara, Provinsi Sulawesi Selatan

The study, in 2012, has successfully formulated with the MCDM for each allocation of space in KKPD allotment (core areas, sustainable fisheries zone, used zone, and other zones). This weighting techniques need to be tested and be implemented in identifying and designing the KKPD in the study area. This study aims to identify and map the biophysical conditions and the potential of coastal and marine natural resources in marine conservation area candidate, North Luwu Regency; to identify the areas suitable for the KKPD based on weighting technique with the MCDM method; and to evaluate potential candidates for marine protected areas in the coastal region. This study used a survey method to perform in situ measurements of physico-chemical parameters, conducted a survey of coastal ecosystems using the transect method. The socio-economic data of coastal communities were collected using the questionnaire. The biophysical conditions and marine resources were analyzed using descriptive statistical methods. The results showed that the candidate region has a rich diversity of coastal ecosystems, but the ecosystem, particularly seagrass beds and coral reefs have been in damaged category. Only the mangrove ecosystem that was still in a good condition category with moderate-to-heavy levels of density. There were 6 species of seagrasses and 6 species of mangroves and 71 species of reef fish. It was discovered 2 regions corresponding to the allotment of the Core Zone, which is in the Region I and III with the total area of 654.22 hectares. For sustainable fisheries zone, Region II and IV would be the first choice with the total area of 620.27 hectares. The Used Zone was identified in the Region V with total area of 480.66 hectares. The total area of the region was equal to 1755.15 hectares. Marine protected areas of was suggested to the protection of coastal ecosystems including mangroves, seagrass beds, and coral reefs and its associated biota, especially the protection of local feeding ground of several species (sea turtles and dugongs)

On Matched Pairs Sign Test Using Bivariate Ranked Set Sampling: An Application to Environmental Issues

The matched pairs sign test using bivariate ranked set sampling (BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency of the test are derived. The Pitman asymptotic relative efficiency is used to compare the asymptotic performance of the matched pairs sign test using BVRSS versus using BVSRS. For small sample sizes, the bootstrap method is used to estimate P-values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using BVRSS for the matched pairs sign test is substantially more efficient than using BVSRS. Illustration using palm trees data from sultanate of Oman is provided. Key words: Bootstrap method, bivariate ranked set sample, power of the test, P-value of the test, Pitman\u27s relative efficiency, sign test

On the Approximation of Multiple Integrals Using Multivariate Ranked Simulated Sampling

The idea of using ranked simulated sampling approach (RSIS) to improve the well known Monte Carlo methods of integration, introduced by Samawi [H.M. Samawi, More efficient Monte Carlo methods obtained by using ranked set simulated samples, Commun. Stat. Simulat. 28 (3) (1999) 699–713], is extended to multivariate ranked simulated sampling approach (MVRSIS) for multiple integration problems. It is demonstrated that this approach provides unbiased estimators and improves the performance of some of the Monte Carlo methods of multiple integrals approximation. This, results in large saving in terms of cost and time needed to attain a certain level of accuracy. Two illustrations using simulation are used to compare the relative performance of this approach relative to multivariate uniform simulation

More Efficient Logistic Analysis Using Moving Extreme Ranked Set Sampling

Logistic regression is the most popular technique available for modeling dichotomous-dependent variables. It has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient logistic regression analysis based on moving extreme ranked set sampling (MERSSmin) scheme with ranking based on an easy-to-available auxiliary variable known to be associated with the variable of interest (response variable). The paper demonstrates that this approach will provide more powerful testing procedure as well as more efficient odds ratio and parameter estimation than using simple random sample (SRS). Theoretical derivation and simulation studies will be provided. Real data from 2011 Youth Risk Behavior Surveillance System (YRBSS) data are used to illustrate the procedures developed in this paper

Simpler Approach for Mediation Analysis for Dichotomous Mediators in Logistic Regression

Mediation is a hypothesized causal chain in which one variable affects a second that, in turn, affects a third. It mediates the relationship between predictors and outcomes. To select and test for a potential mediator, the potential mediator should be associated with the predictor variable and with the outcome variable and should lie in the causal pathway between the predictor and the response. The mediation analysis for continuous response variables is well developed in the literature and it can be shown that the total effect of(X)on(Y),c, is equal to c’+ab, where ab is the mediation effect of the variable(M). However, for categorical responses mediation analysis still not fully developed. In this paper, we propose and developed a new approach using the latent variable technique to adjust for c=c’+ab. Our intensive simulation study and theoretical developments showed that on average the proportion of the mediation effect of using our latent variable approach relative to direct approach is about 0.412. Real data example is used to illustrate the proposed approach

The Matched Pairs Sign Test using Bivariate Ranked Set Sampling

The matched pairs sign test using bivariate ranked set sampling (BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency of the test are derived. The Pitman asymptotic relative efficiency is used to compare the asymptotic performance of the matched pairs sign test using BVRSS versus using BVSRS. For small sample sizes, the bootstrap method is used to estimate P-values. Numerical comparisons and real data are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using BVRSS for the matched pairs sign test is substantially more efficient than using BVSRS

On Inference of Multivariate Means Using Efficient Sampling Designs

In many studies, a researcher attempts to describe a population where units are measured for multiple outcomes, or responses. In this paper, we present an efficient procedure based on ranked set sampling to estimate and perform hypothesis testing on a multivariate mean. The method is based on ranking on an auxiliary covariate, which is assumed to be correlated with the multivariate response, in order to improve the efficiency of the estimation. We showed that the proposed estimators developed under this sampling scheme are unbiased, have smaller variance in the multivariate sense, and are asymptotically Gaussian. We also demonstrated that the efficiency of multivariate regression estimator can be improved by using Ranked set sampling. A bootstrap routine is developed in the statistical software R to perform inference when the sample size is small. We use a simulation study to investigate the performance of the method under known conditions and apply the method to the biomarker data collected in China Health and Nutrition Survey (CHNS 2009) data