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A combined analysis of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) elimination in Seveso adults and Ranch Hand veterans found a period of fast elimination within the first 0.27 years after exposure in Seveso, followed by a period of slower elimination between 3 and 16.35 years from exposure. The mean TCDD elimination rate within the first 0.27 years after exposure among six adult males in the Seveso cohort was 2.0646 year−1(half-life=0.34 years). The mean rate from 3 to 16.35 years was 0.1011 year−1(half-life=6.9 years). The mean Ranch Hand elimination rate, 00924 year−1(half-life=6.9 years), measured between 9 and 33 years after exposure, was significantly less than the Seveso mean in the first 0.27 years after exposure, but not significantly different from the Seveso mean between 3 and 16.35 years after exposure. The fast elimination within the first 0.27 years followed by a slower rate after 3 years is consistent with the expected pattern in a two-compartment open model, with a distribution phase of rapid elimination followed by a slower elimination phase.Journal of Exposure Analysis and Environmental Epidemiology (2002) 12, 44–53 10.1038/sj/jea/7500201

We obtain maximum likelihood estimates of the parameters when the observations on the response variable in a repeated measures design are truncated above a cutpoint. The maximum likelihood equations are solved iteratively using an EM-like procedure. It is observed that these estimates have smaller mean squared error than recently proposed iterative weighted least-squares estimates. The results are applied to data arising from a study of dioxin elimination in Air Force veterans. Published in 2000 by John Wiley & Sons, Ltd.

We obtain maximum likelihood estimates of the parameters when the observations on the response variable in a repeated measures design are truncated above a cutpoint. The maximum likelihood equations are solved iteratively using an EM‐like procedure. It is observed that these estimates have smaller mean squared error than recently proposed iterative weighted least‐squares estimates. The results are applied to data arising from a study of dioxin elimination in Air Force veterans. Published in 2000 by John Wiley & Sons, Ltd.

Two families of discrete distributions, one with the probability generating function (p.g.f)[image omitted]  and the other with the p.g.f. [image omitted]  have been examined. Under certain restrictions on the parameters, some members of the former class can be interpreted as compound distributions. These resulting distributions have the property of being over-, under-, or equi-dispersed. These properties are also examined for the latter class of distributions. Relationships among different members of the latter class are considered graphically by means of a criterion based on successive probabilities.

In statistical data analysis, the choice of an appropriate model is a very important factor. An inappropriate model leads to a different kind of error in the analysis. This error has been called by C. R. Rao as type III error or modeling error as opposed to type I and type II errors in statistical inference.In This paper we Study the relative errors in Incurred by Erroneously Assuming the Distribution of the Family Size N as P(n) While in fact it is the Length-biased (Weighted) Version of P(n).An Analytical Expression for the Relative Error,When the Distribution of N Belongs to the Class of Modified Power Series Distributions, is Derived. More Specifically, the Effect of length-biasing on the Relative Error is Investigated, When N Follows a Generalized Poisson Distribution. These Results are Compared With the Case When N Follows a Poisson Distribution.

This paper contains some alternative methods for estimating the parameters in the beta binomial and truncated beta binomial models. These methods are compared with maximum likelihood on the basis of Asymptotic Relative Efficiency (ARE). For the beta binomial distribution a simple estimator based on moments or ratios of factorial moments has high ARE for most of the parameter space and it is an attractive and viable alternative to computing the maximum likelihood estimator. It is also simpler to compute than an estimator based on the mean and zeros, proposed by Chatfield and Goodhart (1970,Appl. Statist.,19, 240–250), and has much higher ARE for most part of the parameter space. For the truncated beta binomial, the simple estimator based on two moment relations does not behave quite as well as for the BB distribution, but a simple estimator based on two linear relations involving the first three moments and the frequency of “ones” has extremely high ARE. Some examples are provided to illustrate the procedure for the two models.

Statistical tests are developed regarding linear combinations of the parameters of several independent gamma populations. The tests are based on a generalized minimum chi-square procedure. On utilizing these, one can test hypotheses regarding the means or the scale parameters when the shape parameters are unknown. In these tests there is no need to assume the equality of the shape parameters of the underlying populations. Tests for comparing coefficients of variation of several gamma populations have also been developed. For the two population case, a power comparison of these tests with some existing tests is also presented. Two examples are provided to explain the procedure.

The F-test, F max-test and Bartlett's test are compared on the basis of power for the purpose of testing the equality of variances in two normal populations. The power of each test is expressed as a linear combination of F-probabilities. Bartlett's test is noted to be unbiased, UMPU, consistent against all alterna¬tives and the test which yields minimum length confidence intervals on the ratio of the variancesλ=σ12 /σ22 The two samples Bartlett critical values, although not recognized as such, are found in the works of other authors. Tables of the powers of each test are given for various values of λ, levels of significance a and the respective sample sizes, n1 and n2.

In certain applications involving discrete data, it is sometimes found that X = 0 is observed with a frequency significantly higher than predicted by the assumed model. Zero inflated Poisson, binomial and negative binomial models have been employed in some clinical trials and in some regression analysis problems.In this paper, we study the zero inflated modified power series distributions (IMPSD) which include among others the generalized Poisson and the generalized negative binomial distributions and hence the Poisson, binomial and negative binomial distributions. The structural properties along with the distribution of the sum of independent IMPSD variables are studied. The maximum likelihood estimation of the parameters of the model is examined and the variance-covariance matrix of the estimators is obtained. Finally, examples are presented for the generalized Poisson distribution to illustrate the results.

Length-biased sampling has been observed to arise in many biomedical applications such as family history and disease, early detection of disease, survival and intermediate events, and in the study of the latency period of AIDS among patients who received blood transfusions. Recently there has been an increased interest in discrete distributions of order k which are more flexible than their ordinary counterparts when k = 1. In this paper we develop factorial moment distributions of some well known discrete distributions and length-biased versions of some of the distributions of order k and investigate their properties. Their relationship to the corresponding length-biased distributions in the ordinary case is investigated.

In this paper, some properties of the arithmetic, geometric and harmonic means of the length-biased distribution, as presented by Sen (1987), are utilized for the Modified Power Series Distributions (MPSD). These result in interesting applications of the inverse moments and give useful modified asymptotic tests for certain parameters of the original MPSD based on the sample taken from the corresponding length-biased MPSD. In particular, asymptotic tests and confidence intervals are presented for the mean and the coefficient of variation of the MPSD. These tests are developed for some particular members of this family of distributions. An example is provided to illustrate the procedure. Simulation studies are carried out to examine the size and power of these tests.

A random sample is taken from a population consisting of an unknown number of distinct species. The parameter of interest is the probability of discovering a new species when an additional draw from the population is made. Recently, Clayton and Frees (1987) introduced a new nonparametric estimator of this parameter as an alternative to Starr's (1979) minimum variance unbiased estimator. In this paper, the Bayes estimator of the parameter is derived using the Dirichlet process prior and the squared error loss function. The limiting Bayes estimator is shown to have asymptotically normal distribution. A Monte Carlo study of these estimators is provided, and their merits and shortcomings are discussed.

A new generalized logarithmic series distribution (GLSD) with two parameters is proposed.The proposed model is flexible enough to describe short-tailed as well as long-tailed data.Some recurence relations for its probabilities and the factorial moments are presente.These recurrence relations are utilized to obtain the minimum chi-square estimators for the parmaters.Maximum likelihood estimators and some other estimators based on first few moments and probabilities are also suggested.Asymptotic relative efficiency of some of these estimators is also obtained and compared.Two test statistics based on the minimum chi-square estimators fo testing some hypotheses regarding the GLSD are proposed.The fit of the model and the application of the test statistics are exemplified by some data sets.Finally, a graphical method is suggested for differentiating between the ordinary logarithmic series distribution and the GLSD.