Analysis of the amended Davidson model with order effect for paired comparison in the Bayesian paradigm

We commonly observe many types of paired nature of competitions in which the objects are compared by the respondents pairwise in a subjective manner. The Bayesian statistics, contrary to the classical statistics, presents a generic tool to incorporate new experimental evidence and update the existing information. These and other properties have ushered the statisticians to focus their attention on the Bayesian analysis of different paired comparison models. The present article focuses on the amended Davidson model for paired comparison in which an amendment has been introduced that accommodates the option of not distinguishing the effects of two treatments when they are compared pairwise. However, Bayesian analysis of the amended Davidson model is performed using the noninformative priors after making another small modification of incorporating the parameter of order effect factor. The joint and marginal posterior distributions of the parameters, their posterior estimates, predictive and posterior probabilities to compare the treatment parameters are obtained.     

Proper generalized neighbor designs in circular blocks

Generalized neighbor designs relax the condition of constancy on the number of times two treatments occur as neighbors in a design. In this paper, we constructed generalized neighbor designs in circular blocks of equal size. Catalogs of these designs for block size 5, 7 and 9 are also compiled. All the designs given here are binary.     

Robust dual-CUSUM control charts for contaminated processes

ABSTRACT

In this article, we improve the efficiency of the Dual CUSUM chart (which combines the designs of two CUSUM structures to detect a range of shift) by focusing on its robustness, ability to resist some disturbances in the process environment and violation of basic assumptions. We do that, by proposing some robust estimators for constructing the chart for both contaminated and uncontaminated environments. The average run length is used as the performance evaluation measure of the charts. After comparing the performances of the proposed charts based on the estimators, it is noticed that the tri-mean estimator out-performs others in all ramifications. Next to it in performance is the Hodges-Lehmann and midrange estimators. We substantiated the simulation results of the study by applying the scheme on a real-life data set.     

Poisson,modified poisson and collocated sampling

Poisson and collocated sampling are methods of selecting samples that allow for simple control as to which units are to be in sample and which not. They are particularly suitable for use when selecting more than one sample from the same framework. Sections 2 and 3 deal with Poisson sampling. Section 4 deals with modified Poisson sampling, a device to ensure that an empty sample is never selected. Sections 5, 6 and 7 deal with collocated sampling, another device for reducing the variance of sample size. In Section 8 a comparative study of variances and mean square errors is presented for a number of unequal probability sampling strategies.     

Influence diagnostics in the Gamma regression model with adjusted deviance residuals

In this study, we develop the adjusted deviance residuals for the gamma regression model (GRM) by following Cordeiro's (2004) method. These adjusted deviance residuals under the GRM are used for influence diagnostics. A comparative analysis has been sorted out between our proposed method of the adjusted deviance residuals and an existing method for influence diagnostics. These results are illustrated by a simulation study and using a real data set. They are presented for different values of dispersion and sample sizes and indicate the significant role of the GRM inferences.     

A group acceptance sampling plan for truncated life test having Weibull distribution

In this paper, a group acceptance sampling plan for a truncated life test is proposed when a multiple number of items as a group can be tested simultaneously in a tester, assuming that the lifetime of a product follows the Weibull distribution with a known shape parameter. The design parameters such as the number of groups and the acceptance number will be determined by satisfying the producer's and the consumer's risks at the specified quality levels, while the termination time and the number of testers are specified. The results are explained with tables and examples.     

Non-binary neighbor balance circular designs for v=2n and λ=2

Neighbor balance designs were first introduced by Rees (1967) in circular blocks for the use in serological research. Subsequently several researchers have defined the neighbor designs in different ways. In this paper, neighbor balance circular designs for (k≤v) block size are constructed for even number of treatments i.e. v=2n. No such series of designs is known in literature. Two theorems are developed for circular designs. Theorem 1 gives the non-binary circular blocks, whereas Theorem 2 generates binary circular blocks when n≤4 and non-binary blocks for n>4. In suggested designs no treatment is ever a neighbor of itself. Blocks are constructed in such a way that each treatment is a right and left neighbor of every other treatment for a fixed number of times say λ. Sizes of initial circular blocks are not same. One main guiding principle for such designs is to ensure economy in material use.     

The Role of Al-Awqāf (Islamic Endowments) in Poverty Alleviation and Community Development in the Nigerian Context

Al-Waqf (endowment) is a form of charity in Islam. Among its special features is that it is permanent and irrevocable while its benefits also go from one generation to another. It involves the transfer of property from the original owner to the cause of Allah. It is as old as the practice of Islam. At the beginning, simple assets such as farmlands, wells and orchards were endowed. Charity, in this respect, may include building of centers for education, hospitals, public facilities and residential houses in modern time. Regrettably, the practice of al-waqf is no more as popular as it was in the past. Although, rich people among Nigerian Muslims used to donate during their lifetimes for personal or community projects. In most cases, those projects die with their death since no portion of their wealth is endowed for them. This article therefore looked into the relevance of al-waqf as takāful-ijtimā‘i (social insurance) product at present. It examined the definition, significance, conditions of validity and administration of al-waqf. The study revealed that al-waqf can bring about a positive change, meaningful development and transformation in helping the poor and the needy in the community. It suggests that al-waqf should be integrated in the takāful (insurance) practices.