Calcutta Statistical Association Bulletin

As we approach to bring out the 60th Volume of (CSA) Bulletin, we look back into our (modest) accomplishment, and look forward to our continuing progress, in a much wider and more challenging field, with our commitments and assessment of prospectives. The basic challenge comes from the ever-changing discipline, its integration into more interdisciplinary fields, its genuine dependence on rapidly faster computing facility along with diverse computational algorithms, and above all, the necessity to go beyond the so-called Neyman-Pearson paradigm in the 21st century. Even the Bayes perspectives have pointed out the limitations of conventional Bayes methods. These perspectives and prospectives are appraised thoroughly.

The present article is related to test for P(X < Y) , where X and Y are two independent random variables having some continuous distribution functions (d.f.s). We consider a data dependent ethical allocation design where the observations on X and Y are drawn sequentially in two stages. For such design, we provide an asymptotically distribution free test procedure along with various asymptotic results. This design is compared with the usual single stage equal allocation design through the performances of the respective test procedures. The proposed design is also illustrated by using a real life data set.

Growth curve models are frequently used in a wide range of disciplines such as biology, ecology, demography, population dynamics etc. Living organisms exhibit different types of growth patterns. To analyze these curves investigators need adequate parametric models. A proper identification of the growth model is very important for the appropriateness of the subsequent analysis. In this paper we develop a natural goodness of fit test for the logistic growth curve model. Bhattacharya et al. (2004, 2008) have provided some interesting approaches based on Hill's method of finite differences (Hill 1968) in case of the exponential and exponential polynomial growth curve models. But in case of the logistic model their approach leads to very complicated and cumbersome mathematics. Basu and Bhattacharj6ee (2006) have presented an alternative method to test the goodness of fit for the exponential growth curve model by directly modeling the relative growth rate rather than the size variable itself. In this paper we extend that approach for testing goodness of fit in case of the logistic growth curve model.

We present results that lead to characterization of several distributions in terms of the regression of a (possibly non-linear) function of a generalized order statistic with its adjacent generalized order statistics as covariates through the arithmetic, geometric and harmonic means of the functions at the end points.

An estimate of the remainder of two sample U-statistics where each sample consists of independent observations, from its linear projection is obtained. A Berry-Esseen theorem with random index is established. A normal approximation zone for the tail probability of a standardized U-statistic is obtained. Application of this statistic to a real data set related to burr formation in production processes is investigated as a nonparametric tool, instead of a model based approach.

In this paper we consider a location family of distributions which are symmetric about the location parameter μ and propose a nonlinear function of order statistics as an estimator of μ. We call this estimator as the adjusted non-linear unbiased estimator of μ. For the U-shaped distribution with location parameter μ, we have illustrated that our estimator is a competitor of μ ^ , the best linear unbiased estimator of μ based on order statistics. We have also identified the region of the parameter space in which the proposed estimator is more efficient than μ ^ .

A collaborative research on a problem of common interest and of immediate concern, which Hindustan Lever Limited (HLL)- a multinational company was facing or likely to face in the near future, was undertaken at the Indian Statistical Institute (ISI), Kolkata. The problem was to explain the purchase behaviour of frequently bought branded consumer products using stochastic models. For this, the panel data, after being coded to ensure anonymities were supplied to the ISI and on the basis of the available data, modeling of the buying behaviour was made. To begin with, some descriptive measures were calculated to understand the data and, finally, ‘Dirichlet’ multinomial model was used for explaining the buying behaviour of the customers in the specific segment with respect to the specific group of commodities. Because of not-so-wide coverage of the data and not-wellvalidated assumptions on the underlying distributions, the results failed to reveal much of the consumer behaviour pattern.

Reliable estimates of crop yields at small area level, say blocks, are of great importance for policy planning at micro-level. To this end, application of present methodology of Crop-cutting experiments is not practicable, as it would require total number of such experiments to increase many folds. Additional information about farmers' estimates of crop yields at block level, which are crisp values, may be used provided these can explain the actual crop yields, which are fuzzy. Accordingly, in this paper, theory of fuzzy sets and possibilistic regression analysis is discussed. Three methods, viz . Minimization, Maximization, and Conjunction are considered. The methodology is applied for modelling cotton crop yields at block levels of Sirsa district, Haryana. It is found that Conjunction method performed the best. Further, farmers' estimates are able to explain the actual crop yields with fitness level as high as 0.6.