Contamination Severity Index: An Analysis of Bangladesh Groundwater Arsenic

This paper deals with measurement of ground water arsenic contamination. The focus is on using a proper index for the severity of contamination, rather than just using the proportion of observations above a threshold level. We specifically focus on the Contamination Severity Index (CSI) proposed in Sen (2016, Sankhya). An alternative estimator in contrast to the one given in Sen (2016) is used here that is useful for small number of observations. The data used is that collected by British Geological Society(BGS) and the BD Department of Public Health Engineering (DPHE) during 1997-2001. Their analysis was based on the simple proportion of the observations above a threshold level, where as the CSI measure adequately takes into account the severity of the observations also. We have also segmented the data into three categories of wells according to the depth of the wells instead of just the two categories, namely `deep' and `shallow' wells. It is emphasized in this manuscript that the comparison of areas with average arsenic (As) level to determine As severity is not appropriate as the regression of CSI on AAs is highly nonlinear and seemingly non-heteroscedastic; where as the CSI index proposed in Sen (2016), shows a clear picture, especially when the values are adjusted according to average log depth of the wells sampled at the thana and district levels

A Numerical Study of Entropy and Residual Entropy Estimators Based on Smooth Density Estimators for Non-negative Random Variables

In this paper, we are interested in the entropy of a non-negative random variable. Since the underlying probability density function is unknown, we propose the use of Poisson smoothed histogram density estimator in order to estimate the entropy. To study the performance of our estimator, we run simulations on a wide range of densities and compare our entropy estimators with the existing estimators that based on different approaches such as spacing estimators. Furthermore, we extend our study to residual entropy estimators which is the entropy of a random variable given that it has been survived up to time t

Inverse Gaussian model for small area estimation via Gibbs sampling

We present a Bayesian method for estimating small area parameters under an inverse Gaussian model. The method is extended to estimate small area parameters for finite populations. The Gibbs sampler is proposed as a mechanism for implementing the Bayesian paradigm. We illustrate the method by application to household income survey data, comparing it against the usual lognormal model for positively skewed data. Key words/phrases: Finite population sampling, hierarchical Bayesian inference, lognormal model, MCMC integration, shrinkage estimates SINET: Ethiopian Journal of Science Vol. 28 (1) 2005: 1–1

Pressure Impregnation of Hardwoods: Treatment Schedules For Easy-To-Treat Indian Hardwoods

On the basis of penetration pattern of inorganic chemicals in the wood microstructure, penetration indices for different wood species were developed. Pressure treatment schedules have been suggested on the basis of penetration index and gross absorptions obtained with CCA salts in treatability class 'a' and 'b' hardwoods. Mango and kadam earlier placed under the 'a' treatability class have been transferred to the 'b' treatability class because of poor penetration of the fibers in these species. Similarly, white bombwe earlier classified under class 'b' has been shifted to class 'a' because of its high penetration index

Variance components estimation in agricultural experiments with possible application to ICRISAT data

In agricultural experiments, especially in plant breeding quite often interest lies in estimating different components of genetic variance either for the purpose of studying their relative magnitudes of for estimating certain functions of them e.g. heritability (see Kempthorne and Tandon 1953), average degree of dominance (see Comstock and Robinson 1948) etc..

Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle

In this note we provide a simple approximation theory motivation for the circular kernel density estimation and further explore the usefulness of the wrapped Cauchy kernel in this context. It is seen that the wrapped Cauchy kernel appears as a natural candidate in connection to orthogonal series density estimation on a unit circle. This adds further weight to the considerable role of the wrapped Cauchy in circular statistics

Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle

The circular kernel density estimator, with the wrapped Cauchy kernel, is derived from the empirical version of Carathéodory function that is used in the literature on orthogonal polynomials on the unit circle. An equivalence between the resulting circular kernel density estimator, to Fourier series density estimator, has also been established. This adds further weight to the considerable role of the wrapped Cauchy distribution in circular statistics

On Smooth Density Estimation for Circular Data

Fisher (1989: J. Structural Geology, 11, 775-778) outlined an adaptation of the linear kernel estimator for density estimation that is commonly used in applications. However, better alternatives are now available based on circular kernels; see e.g. Di Marzio, Panzera, and Taylor, 2009: Statistics & Probability Letters, 79(19), 2066-2075. This paper provides a short review on modern smoothing methods for density and distribution functions dealing with the circular data. We highlight the usefulness of circular kernels for smooth density estimation in this context and contrast it with smooth density estimation based on orthogonal series. It is seen that the wrapped Cauchy kernel as a choice of circular kernel appears as a natural candidate as it has a close connection to orthogonal series density estimation on a unit circle. In the literature, the use of von Mises circular kernel is investigated (see Taylor, 2008: Computational Statistics & Data Analysis, 52(7), 3493-3500), that requires numerical computation of Bessel function. On the other hand, the wrapped Cauchy kernel is much simpler to use. This adds further weight to the considerable role of the wrapped Cauchy distribution in circular statistics