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

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

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

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

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

An Investigation into Properties of an Estimator of Mean of an Inverse Gaussian Population

This paper deals with preliminary test estimation for mean of an inverse Gaussian population. Preliminary test estimator has been shown to provide large gains in efficiency, especially around a neighbourhood of the prior guessed value of the parameter, for many distributions including exponential and normal, however, this has not been explored for the inverse Gaussian family of distributions. Owing to diverse applications of the inverse Gaussian model for non-negative and positively skewed data, the investigation considered here makes an important contribution in the area of preliminary test estimation. We consider both the cases of known and unknown dispersion parameters and demonstrate similar conclusions as obtained in the case of Gaussian populations in terms of the efficiency of the resulting estimator

Survival Distributions with Bathtub Shaped Hazard: A New Distribution Family

In this article we introduce an extension of Chen’s (2000) family of distributions given by Lehman alternatives [see Gupta et al.(1998)] that is shown to present another alternative to the generalized Weibull and exponentiated Weibull families for modeling survival data. The extension proposed here can be seen as the extension to the Chen’s distribution as the exponentiated Weibull is to the Weibull. A structural analysis of the density function in terms of tail classification and extremes is carried out similar to that of generalized Weibull family carried out in Mudholkar and Kollia (1994). The new model is also seen to fit well to the flood data used in fitting the exponentiated Weibull model in Mudholkar and Hutson (1996)