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Showing papers by "Manisha Pal published in 2008"


Journal ArticleDOI
TL;DR: In this article, the minimax criterion has been employed to find a solution to the problem of estimating the optimum proportion of mixture components, assuming prior knowledge about the optimum mixing proportions.

18 citations


Journal ArticleDOI
TL;DR: In this paper, the deficiency criterion due to Chatterjee and Mandal (1981) has been used as a measure for comparing the performance of competing mixture models, and the problem of estimating the optimum proportion of mixture components is of great practical importance.
Abstract: In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe (1958, 1963) first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal (2006, 2007) attempted to find a solution to this problem by adopting a pseudo-Bayesian approach and using the trace criterion. Subsequently, Pal and Mandal (2008) solved the problem using minimax criterion. In this article, the deficiency criterion due to Chatterjee and Mandal (1981) has been used as a measure for comparing the performance of competing designs.

16 citations


Journal ArticleDOI
01 Mar 2008
TL;DR: In this paper, explicit closed form expressions are derived for the moments of order statistics from the gamma and generalized gamma distributions, involving the Lauricella functions of type A and type B. The usefulness of the result is illustrated through two quality control data sets.
Abstract: Explicit closed form expressions are derived for the moments of order statistics from the gamma and generalized gamma distributions. The expressions involve the Lauricella functions of type A and type B. The usefulness of the result is illustrated through two quality control data sets.

14 citations


01 Jan 2008
TL;DR: In this article, Mandal et al. derived a pseudo-Bayesian approach with invariance property of the second order moments of the optimum mixing proportions for estimating the optimum proportion of mixture components when the factor space is constrained.
Abstract: Scheffe (1958, 1963) first introduced models and designs suitable for a mixture experiment where the mean response is assumed to depend only on the relative proportions of the ingredients or components. Extensive literature on optimum designs for the estimation of parameters of different mixture models is available. The specific problem of characterization of optimal designs for estimating the op- timum proportion of mixture components has been recently considered by Pal and Mandal (2006, 2008) as also by Mandal and Pal (2008) using different optimality criteria. Generalizing the work of Pal and Mandal (2006), who had dealt with the trace criterion and adopted a pseudo-Bayesian approach with invariance property of the second order moments of the optimum mixing proportions, Mandal et al. (2008) relaxed the invariance property of the second order moments of the op- timum mixing proportions. In this paper, optimum designs are derived for the problem of estimating the optimum proportion of mixture components when the factor space is constrained.

9 citations


01 Jan 2008
TL;DR: In this paper, the authors define skew-symmetric distributions based on the double inverted gamma, double inverted Weibull and double inverted compound gamma distributions, all of which have symmetric density about zero.
Abstract: We define skew-symmetric distributions based on the double inverted gamma, double inverted Weibull and double inverted compound gamma distributions, all of which have symmetric density about zero. Expressions are derived for the probability density function (pdf), cumulative distribution function (cdf) and the moments of these distributions. However, some of these quantities could not be evaluated in closed forms and we used special functions to express them.

2 citations


Journal ArticleDOI
TL;DR: In this article, the authors define skew-symmetric distributions based on the reflected generalized uniform distribution, a double compound gamma distribution and a double generalized Pareto distribution, all of which have symmetric density about zero.
Abstract: SYNOPTIC ABSTRACTWe define skew-symmetric distributions based on the reflected generalized uniform distribution, a double compound gamma distribution and a double generalized Pareto distribution, all of which have symmetric density about zero. Expressions are derived for the probability density function (pdf), cumulative distribution function (cdf), and moments of the distributions. Several special functions are involved in the calculations.

1 citations