On Constructing Optimum Strata and Determining Optimum Allocation

The problem of constructing optimum stratum boundaries (OSB) and the problem of determining sample allocation to different strata are well known in the sampling literature. To increase the efficiency in the estimates of population parameters these problems must be addressed by the sampler while using stratified sampling. There were several methods available to determine the OSB when the frequency distribution of the study (or its related) variable is known. Whereas, the problem of determining optimum allocation was addressed in the literature mostly as a separate problem assuming that the strata are already formed and the stratum variances are known. However, many of these attempts have been made with an unrealistic assumption that the frequency distribution and the stratum variances of the target variable are known prior to conducting the survey. Moreover, as both the problems are not addressed simultaneously, the OSB and the sample allocation so obtained may not be feasible or may be far from optimum. In this paper, the problems of finding the OSB and the optimum allocation are discussed simultaneously when the population mean of the study variable y is of interest and its frequency distribution f(y) or the frequency distribution f(x) of its auxiliary variable x is available. The problem is formulated as a Nonlinear Programming Problem (NLPP) that seeks minimization of the variance of the estimated population parameter of the target variable, which is subjected to a fixed total sample size. The formulated NLPP is then solved by executing a program coded in a user’s friendly software, LINGO. Two numerical examples, when the study variable or its auxiliary variable has respectively a uniform and a right-triangular distribution in the population, are presented to demonstrate the practical application of the proposed method and its computational details. The proposed technique can easily be applied to other frequency distributions

Optimal Stratification of Univariate Populations via stratify R Package

Stratification reduces the variance of sample estimates for population parameters by creating homogeneous strata. Often, surveyors stratify the population using the most convenient variables such as age, sex, region, etc. Such convenient methods often do not produce internally homogeneous strata, hence, the precision of the estimates of the variables of interest could be further improved. This paper introduces an R-package called ’stratifyR’ whereby it proposes a method for optimal stratification of survey populations for a univariate study variable that follows a particular distribution estimated from a data set that is available to the surveyor. The stratification problem is formulated as a mathematical programming problem and solved by using a dynamic programming technique. Methods for several distributions such as uniform, weibull, gamma, normal, lognormal, exponential, right-triangular, cauchy and pareto are presented. The package is able to construct optimal stratification boundaries (OSB) and calculate optimal sample sizes (OSS) under Neyman allocation. Several examples, using simulated data, are presented to illustrate the stratified designs that can be constructed with the proposed methodology. Results reveal that the proposed method computes OSB that are precise and comparable to the established methods. All the calculations presented in this paper were carried out using the stratifyR package that will be made available on CRAN

Distribution of coconut stick insect, Graeffea crouanii and its parasitoids in selected islands of Fiji

The Coconut stick insect, Graeffea crouanii (Le Guillou)(Orthoptera: Phasmidae), known as “mimimata” in Fiji, is a widespread economic pest of coconut palms in Fiji and in many Pacific Island countries. The nymphs and adults stages of pest are polyphagous, but prefer coconut palms.This paper reveals findings from the surveys conducted between 2009 and 2012 during the field work in selected islands of Fiji, and discusses needed research to enhance natural-mortality control mechanisms. Preliminary studies of G. crouanii in selected islands of Fiji (Viti Levu, Vanua Levu and Taveuni) showed that the pest was localised and abundant in areas with low temperature, which was also statistically proven.The pest was found to be feeding on leaves with damage starting from tip and ends up leaving only the midribs. The older fronds had more damage than new frond due to longest pest exposure. The two elasmid egg parasitoids in Fiji, Paranastatus verticalis and Paranastatus nigriscutellatus of order Hymenoptera have potential as a biological control agent. This study on the G. crouanii in Fiji provides significant recommendations for further management of G. crouanii in coconut farms

Assessment of sugarcane varieties for their stability and yield potential in Fiji

The Sugar Research Institute of Fiji breeds and produces new varieties of sugarcane for the Fiji sugar industry for commercial production. The development of sugar cane varieties that show superior performance in different environments is a major challenge for breeders due to the response of genotypes across environments. This study was to evaluate the relative performance the genotypes during breeding program and identify promising ones that could be released for cultivation. Thus, an investigation was carried out to determine the magnitude of Genotype Environment interactions and the stability analysis of the genotypes cultivated in Fiji. Seventeen genotypes including three commercial varieties were evaluated in five locations using a randomized block design with three replications. The pooled analysis of variance carried out for the effect of environments, genotypes, and their interactions. The stability analysis was also performed using the Eberhart & Russell’s (1966) model. Further, a cluster analysis was proposed for identifying the similar and stable genotypes. The results showed that there were highly significant (p < 0.001) variations among the genotypes (G), environments (E) and GE interactions. Two genotypes LF82-2122 and LF60-3917 had higher yield and stability statistics for the two most important traits: cane and sugar yields. Thus, the genotypes can be recommended for adoption and cultivation on all soil types in Fiji

Are students studying in the online mode faring as well as students studying in the face - to - face mode? Has equivalence in learning been achieved?

With the shift in pedagogy from learning in the traditional classroom setting (face-to face mode) to online learning, it is important to find out how students are faring in the online mode and if equivalence in learning is achieved in the two modes. To answer these questions, the course results of students studying a first year undergraduate mathematics course in the two different modes at The University of the South Pacific were compared. The study revealed that there was no statistical significant difference in the pass rates of the students studying in the two modes but the students studying in the online mode had a significantly higher attrition rate. From the results, it was also discovered that students studying via the online mode achieved higher coursework marks but lower exam marks compared to students studying via the face to-face mode. Yet the students’ total marks in the two modes were similar, which led to the conclusion that students studying in the online mode are faring just as well as students studying in the face-to-face mode. It was evident that equivalent learning was occurring in the two modes albeit in different ways. The coursework assessments methods in the two modes were also compared

On optimum stratification

In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique

A Goal Programming Approach: Multi-objective Optimization

The purpose of this paper is to accentuate the development of multi-objective non-linear programming (MONLP) technique and its advantages of applying to numerical problems. In particular, non-linear programming model is the process of solving an optimization problem defined by a system of inequalities along with an objective function of several variables that exist in various fields. In certain instances, there are situations in these fields where multiple objectives are required to be achieved simultaneously, owing to limited timeframe and convenience of budget. The Multi-objective programming under non-linear conditions and the solution procedure on the goal programming approach is embedded with algorithm and the relevant technique is developed. Numerical examples, specifically, multi-objective quadratic programming problem and examples of other multi-objective non-linear programming problem are presented to illustrate practical use and the computational details of the proposed procedure. The proposed goal programming technique is then solved using a user-friendly optimization software LINGO

Bayesian method for estimating Weibull parameters for wind resource assessment in the tropical region: a comparison between two-parameter and three - parameter Weibull distributions

The two-parameter Weibull distribution has garnered much attention in the assessment of wind energy potential. The estimation of the shape and scale parameters of the distribution has brought forth a successful tool for the wind energy industry. However, it may be inappropriate to use the two-parameter Weibull distribution to assess energy at every location, especially at sites where low wind speeds are frequent, such as the tropical region. In this work, a robust technique for wind resource assessment using a Bayesian approach for estimating Weibull parameters is first proposed. Secondly, the wind resource assessment techniques using a two-parameter Weibull distribution and a three-parameter Weibull distribution, which is a generalized form of two-parameter Weibull distribution, are compared. Simulation studies confirm that the Bayesian approach seems a more robust technique for accurate estimation of Weibull parameters. The research is conducted using data from seven sites in tropical region from 1o N of Equator to 21o South of Equator. Results reveal that a three-parameter Weibull distribution with non-zero shift parameter is a better fit for the wind data having a higher percentage of low wind speeds (0-1 ms-1) and low skewness. However, wind data with a smaller percentage of low wind speeds and high skewness showed better results with a two-parameter distribution that is a special case of three-parameter Weibull distribution with zero shift parameter. The proposed distribution can be incorporated in commercial software like WAsP to improve the accuracy of wind resource assessments. The results also demonstrate that the proposed Bayesian approach and application of a three-parameter Weibull distribution are extremely useful for accurate estimation of wind power density

stratifyR: Optimal Stratification of Univariate Populations

This R package implements the stratification of univariate populations under stratified sampling designs using the method of Khan et al. (2002, 2008, 2015). It determines the Optimum Strata Boundaries (OSB) and Optimum Sample Sizes (OSS) for the study variable, y, using the best-fit frequency distribution of a survey variable (if data is available) or a hypothetical distribution (if data is not available). The method formulates the problem of determining the OSB as mathematical programming problem which is solved by using a dynamic programming technique. If a dataset of the population is available to the surveyor, the method estimates its best-fit distribution and determines the OSB and OSS under Neyman allocation directly. When the dataset is not available, stratification is made based on the assumption that the values of the study variable, y, are available as hypothetical realizations of proxy values of y from recent surveys. Thus, it requires certain distributional assumptions about the study variable. At present, it handles stratification for the populations where the study variable follows a continuous distribution, namely, Pareto, Triangular, Right-triangular, Weibull, Gamma, Exponential, Uniform, Normal, Log-normal and Cauchy distributions

Optimal stratification in stratified designs using weibull - distributed auxiliary information

Sampling has evolved into a universally accepted approach for gathering information and data mining as it is widely accepted that a reasonably modest-sized sample can sufficiently characterize a much larger population. In stratified sampling designs, the whole population is divided into homogeneous strata in order to achieve higher precision in the estimation. This paper proposes an efficient method of constructing optimum stratum boundaries (OSB) and determining optimum sample size (OSS) for the survey variable. The survey variable may not be available in practice since the variable of interest is unavailable prior to conducting the survey. Thus, the method is based on the auxiliary variable which is usually readily available from past surveys. To illustrate the application as an example using a real data, the auxiliary variable considered for this problem follows Weibull distribution. The stratification problem is formulated as a Mathematical Programming Problem (MPP) that seeks minimization of the variance of the estimated population parameter under Neyman allocation. The solution procedure employs the dynamic programming technique, which results in substantial gains in the precision of the estimates of the population characteristics