This paper derives a Murthy's unbiased estimator of population total under unequal probability inverse sampling. A general unequal probability inverse sampling is combined with adaptive cluster sampling. An unbiased estimator of population total and its variance estimator are given using Murthy's approach. The general unequal probability inverse adaptive cluster sampling and general equal probability inverse adaptive cluster sampling are compared using simulation study based on real life data. The results indicate that the general unequal probability inverse adaptive cluster sampling has a small coefficient of variation for estimates compared to equal probability inverse adaptive cluster sampling. When the coefficients of correlation between study variable and probability of selection units increase, the coefficient of variation decreases.

Inverse sampling with unequal probabilities without replacement is modified from the Midzuno's scheme. An unbiased estimator of the population total of a study variable is presented. The variance and the corresponding unbiased estimator of this variance are given. An unbiased estimator of the number of units in a given class, its variance and an unbiased estimate of the variance are also given. These estimators are obtained via the Murthy's estimator using the Rao-Blackwell approach conditioned on a minimum sufficient statistic. The estimates do not depend on the order of draws and are easy to compute. An example is given to illustrate the idea.

This paper introduces ratio estimators of the population mean using the coefficient of variation of study variable and auxiliary variables together with the coefficient of correlation between the study and auxiliary variables under simple random sampling and stratified random sampling. These ratio estimators are almost unbiased. The mean square errors of the estimators and their estimators are given. Sample size estimation in both sampling designs are presented. An optimal sample size allocation in stratified random sampling is also suggested. Based on theoretical study, it can be shown that these ratio estimators have smaller MSE than the unbiased estimators. Moreover, the empirical study indicates that these ratio estimators have smallest MSE compared to the existing ones.

This study aimed to develop relationships between particulate matter (PM) concentrations obtained from a direct-reading instrument to those from a gravimetric method. TSI DustTrak II Aerosol Monitors (Model 8530), a direct-reading instrument for PM10 and PM2.5 measurement, together with personal air pumps connected to a Sensidyne cyclone and a SKC Personal Environmental Monitor (PEM) for gravimetric PM10 and PM2.5 measurements respectively were deployed in the Faculty of Science building, Silpakorn University, Nakhon Pathom, Thailand. Comparison of the results from each instrument indicated that PM10 and PM2.5 concentrations obtained from the TSI DustTrak were higher. The linear relationship from ordinary least squares (OLS) regression between PM10 data determined by TSI DustTrak (x) and Sensidyne cyclone (y ̂) was significant (R2=0.92) and could be represented as y ̂ = 0.272x. For PM2.5, the relationship between concentrations determined by TSI DustTrak (x) and SKC PEM (y ̂) was also significant (R2=0.92) and represented by y ̂ = 4.848√x. Validation of both equations was undertaken by comparing predicted values from these relationships against the actual concentrations found by gravimetric analysis, with R2=1.0 and 0.92 for PM10 and PM2.5, respectively. It is suggested that these site-specific OLS regression equations can provide fast and convenient estimation of concentrations derived by gravimetric analysis from direct-reading TSI DustTrak monitor data.