Showing papers in "Calcutta Statistical Association Bulletin in 1989"
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TL;DR: In this paper, the robustness of block designs for the problem of estimation of any full set of orthonormal varietal contrasts is examined, and an attempt has been made to examine their robustness against the presence of wild observations.
Abstract: Box and Draper (1975) proposed a criterion of robustness against the presence of wild observations for the problem of estimation of Xβ in the response surface model E(Y) = Xβ, D(Y) = σ2.I. Gopalau and Dey (1976) elttended this concept to block designs setting, for the problem of estimation of σ2. In the present note an attempt has been made to examine the robustness of block designs for the problem of estimation of any full set of orthonormal varietal contrasts.
62 citations
TL;DR: This paper considers an inventory model for items with a constant rate of decay, when lead time is random having an exponential distribution and the optimal stock to be maintained is obtained by minimising the total expected cost per unit time.
Abstract: This paper considers an inventory model for items with a constant rate of decay, when lead time is random having an exponential distribution. The policy is to place an order with a supply centre whenever a demand is made or an item in stock deteriorates. The optimal stock to be maintained is obtained by minimising the total expected cost per unit time.
23 citations
TL;DR: In this article, the residual life function of a uniform distribution is characterized in terms of certain properties of residual life functions, such as the residual lifetime of the residual function of the distribution.
Abstract: In this article tho geometric, negative hyper geometric, Warning aod uniform distributions are characterized in terms of certain properties of the residual life function.
21 citations
TL;DR: In this paper, a large sample test for coefficient of variation when the observations come from a normal population is presented, and the authors obtain valid Edgeworth expansion for sample coefficient O(n-1) under simple null hypo thesis and contiguous alternative hypothesis.
Abstract: In this paper we deal with large sample test for coefficient of variation when the observations come from a normal population. Such large sample tests are based on normal approximation for sample coefficient of variation. When the sa mple size is small or moderate, the normal approximation may not be accurate in the sense that the attained level of the test Is not close to the nominal level. Following Bhattacharya and Ghosh (1978), we obtain valid Edgeworth expansion for sample coefficient of variation to O(n-1) under simple null hypo thesis and contiguous alternative hypothesis. This helps one to determine the critical region such that attained level of significance is closer to the normal level and the power function is more accurate.
16 citations
TL;DR: In this article, the usefulness of rociprocal coordinate subtancent as a measure on the density curve of a life distribution has been pointed out through teveral results including some characterizations and classifications.
Abstract: Tho usefulness of rociprocal coordinate subtancent as a measure on the density curve of a life distribution bas been pointed out through teveral results including some characterizations and classifications. Existing nonparametric classifications based on failure rate and avorage failure rate have been related to the nonparametric classifications proposed here. It bas also been sbown tbat a study through reciprocal coordinate subtangent results in more aeneral properties from which properties of extistiog classes can bo obtained as a special case.
9 citations
6 citations
TL;DR: In this paper, a method of construction of balanced n-ary desians using MOLS is given, and a method for constructing balanced desians with balanced n -ary Desians is presented.
Abstract: A method of construction of balanced n-ary desians using MOLS is given.
6 citations
TL;DR: In this paper, sufficient and separately necessary conditions are given for {an Yn, n⩾1} to obey a generalized central limit theorem ( ∑ j = 1 n a j 2, n ⩾ 1 } and the distribution of Y.
Abstract: For i.i.d. random variables {Y, Yn, n⩾ 1} with EY2=∞ and nonzero constants {an, n⩾1}, sufficient and, separately, necessary conditions are given for {an Yn, n⩾1} to obey a generalized central limit theorem ( ∑ j = 1 n a j Y j − A n ) B n → d N ( 0 , 1 ) for suitable constants {An, n⩾1} and {Bn > 0, n⩾1}. The norming constants {Bn, n⩾1} are defined using the sequence { ∑ j = 1 n a j 2 , n ⩾ 1 } and the distribution of Y. Moreover, it is shown that if p{|Y|> y} is regularly varying with exponent-2, then the centering constants may be taken to be A n = ∑ j = 1 n a j E Y , n ⩾ 1 . A famous result of Feller (1935), Khintchine (1935), and Lévy (1935) is obtained in the special case an ≡ 1.
5 citations
TL;DR: In this article, the generalized variance in a multivariate normal setup was considered and the best affine equivariant estimates of | ∑ | are found to be admissible in the class of all estimate functions.
Abstract: We consider the problem of estimating the generalized variance in a multivariate normal setup. The best affine equivariant estimates of | ∑ | are found to be admissible in the class of all estimate...
5 citations
TL;DR: It is shown that unequally replicated block designs, satisfying a simple condition, can be arranged in an array such that each row of the array contains a specified treatment the same number of times.
Abstract: A generalization of systems of distinct representatives is given. Based on this result, it is shown bow unequally replicated block designs, satisfying a simple condition, can be arranged in an array such that each row of the array contains a specified treatment the same number of times. Such arrays can be viewed as row-colum designs and have been called as Youden Type (YT) designs. A necessary and sufficient condition for the existence of YT designs is given.
3 citations
TL;DR: The generalized logistic distribution of Prentice (1975) can be expressed as an incomplete beta function as discussed by the authors, and when both shape parameters are integers, the cumulative GL distribution function can be simply expressed as a sum of binomial probabilities.
Abstract: A generalization of the logistic distribution proposed by Prentice (1975) is very useful for approximating the continuoui distributions and for data analysis. In this paper, an expression for the rth cumulant of the generalization is derived. The generalized logistic (GL) distribution of Prentice (1975) can be expressed as an incomplete beta function. In particular when both shape parameters are integers, the cumulative GL distribution function can be simply expressed as a sum of binomial probabilities. The exact expression of the cumulative GL distribution function when one of the shape parameters is not an integer is derived.
TL;DR: In this paper, the authors consider the problem of characterizing minimax rules for selecting the better of two binomial populations with unequal samplesizes, and derive necessary conditions for a rule to be globally minimax.
Abstract: Following Risko (1985), we consider tho problem characterizing minimax rules for selecting the better of two binomial populations with unequal samplesizes. We derive some necessary conditions for a rule to be globally minimax. We verify empirically that the restricted minimax rule of Risko satisfies these conditions.
TL;DR: In this article, the asymptotic properties of the estimated predictor of a k-dimensional, pth order autoregressive process with dependent error variables and a general set-up of the roots have been considered.
Abstract: In this paper the asymptotic properties of the estimated predictor of a k-dimensional, pth order autoregressive process with dependent error variables and a general set-up of the roots have been considered. An expression for the mean-square-error of the estimated predictor has also been obtained.
TL;DR: In this article, the problem of optimum allocation of sample and corresponding efficiencies and costs in case of regression and ratio estimators in sampling on two occasions have been looked into, and a comparison of efficiencies of two estimators has also been made under different situations.
Abstract: The problem of optimum allocation of sample and the corresponding efficiencies and costs in case of regression and ratio estimators in sampling on two occasions have been looked into. A comparison of efficiencies and costs of two estimators has also been made under different situations.
TL;DR: In this paper, a general class of almost unbiased estimators for the ratio and product of population means of two charactess is proposed, and the estimators are shown to be almost unbiased.
Abstract: In this paper we propose a general class of almost unbiased estimators for the ratio and product of population means of two charactess.
TL;DR: In this paper, it was shown that the distribution of T in the subcritical case belongs to the NWOE (New Worse than Old in Expectation) class of distributions, and that its ultimate failure rate is a constant.
Abstract: Bhattacharjee (1987) and Shaked and Shantikumar (1987) have shown that the distribution of the time to extinction T of a subcritical or a critical Galton Watson branching process has a DFR property. We give an example to show that such a property does not hold for a multitype Galton Watson process. ln this note, we further study properties of T for a multitype process. We show that its ultimate failure rate is a constant. In the subcritical case, it is also shown that its distribution is smaller than the geometric distribution (whose failure rate is the above limiting failure rate), in the sense of likelihood ratio ordering. We then show that the distribution of T in the subcritical case belongs to the NWOE (New Worse than Old in Expectation) class of distributions.
TL;DR: The 76th Indian Science Congress as discussed by the authors elected me as the Section of Statistics (SOS) president, which carries with it an onerous responsibility and illustrious predecessors have set very high standards for it.
Abstract: I am fully conscious of the honour that you have bestowed upon me by electing me President of the Section of Statistics for this 76-th session of Indian Science Congress. I know that this office carries with it an onerous responsibility and illustrious predecessors have set very high standards for it. I would strive my best to measure up to your trust and to make this session a success. I would need the good wishes and cooperation of all of you in this effort.
TL;DR: This paper considers the determination of optimal designs in experimental situations requiring usage of a block design having v treatments assigned to experimental units arranged in b blocks of size k under a wide class of optimality criteria.
Abstract: In this paper we consider the determination of optimal designs in experimental situations requiring usage of a block design having v treatments assigned to experimental units arranged in b blocks of size k. Using majorization arguments, a design d* having an incidence matrix of the form is optimal under a wide class of optimality criteria.
TL;DR: In this article, the analysis of direct product of a number of fractional factorial designs (unblocked) has been presented in brief to show that the estimates of the parameters of the new design can be expressed as a suitable (asterisk) product of the estimate of the parameter of the component designs.
Abstract: Analysis of direct product (DP) of a number of fractional factorial designs (unblocked) has been presented in brief to show that the estimates of the parameters of the new design can be expressed as a suitable (asterisk) product of the estimates of the parameters of the component designs. It has also been proved that the analysis of symbolic product (SP) of the fractional designs (unblocked) can be translated into that of their direct product using pseuofactors. Also using the above results the Rao's lower bound for the number of level combinations has been improved for a class of orthogonal arrays.
TL;DR: In this paper, the shape arameter for the Pareto distribution is considered and a new estimate which involves the whole set of sufficient statistics is proposed, which performs better than the usual maximum likelihood estimate under suitable loss.
Abstract: The problem of estimation of the shape arameter for the Pareto distribution is considered. Stein's (1964) idea leads to a new estimate which involves the whole set of sufficient statistics. Such an estimate performs better than the usual maximum likelihood estimate under suitable loss.
TL;DR: In this paper, the upper bound to the uniformly minimum variance-unbiased estimator of the reliability function of the exponential life distributions was obtained, which is the same upper bound as in this paper.
Abstract: We obtain the upper bound to the uniformlyminimumvarianceunbiased estimator of the reliability function of the exponential life distributions.