On the choice of precedence tests

The best precedence test (BPT) is derived for testing the hypothesis that the lifetimes of two types of items on test have the same distribution. The test has maximum power in the class of the Lehmann type of alternatives F - 1 - (1-G) , A > 1, where F and G are probability distributions of the lifetimes of two types of items on test. This class includes exponential distributions, the Weibull distribution differing only in scale and distributions with proportional hazard rates. Exact power of the BPT is compared with other nonparametrie and parametric tests. The test may terminate before all the lifetimes of the items on test are recorded. In comparing with competing tests of equal size, the power functions are similar but a considerable number of items can be saved and the time on test can be reduced by using the BPT     

Distribution of ranks in a two-sample problem with right censored data

We consider different censoring models for a two-sample and find the joint distribution of the rank vector and number of uncensored observations under each censoring model when the distributions of life times and/or distributions of censoring of censoring variables satisfy the condition for the Lehmann type of alternatives.     

CONTROLLED SAMPLING WITH VARYING PROBABILITIES WITH AND WITHOUT REPLACEMENT

Goodman and Kish (1950) introduced the problem of controlled selection in the sense of decreasing the selection probability of nonpreferred combinations, such as, for example, combinations which present organisational difficulties involving additional cost, etc. The authors (Avadhani and Sukhatme (1965), Sukhatme and Avadhani (1965)) have evolved certain techniques of controlled selection which eliminate altogether some non-preferred combinations and reduce the probability of selection of the remaining combinations, if any, to the minimum possible extent without deviating from the fundamental principles of random sampling. However, it is often felt convenient in practice to draw sampling units one after another from the population rather than combinations of units. But, at present no technique by which one can select the units one after another and at the same time reduce the probability of selection of non-preferred units is available in literature.
In this paper we have suggested a solution to this problem which not only minimizes the selection probability of non-preferred units (and of samples containing predominantly large numbers of nonpreferred units) but also provides more efficient estimators than the the usual probability proportional to size (P.P.S) sampling scheme.     

On bahadur's representation of quantiles in nonregular cases

The paper considers Bahadur’s representation of quantiles (see Bahadur (1966), Ann. Math. Statist., 37, 577-580) in cases where the usual assumptions regarding the existence and boundedness of the derivatives of the distribution function in a neighbourhood of the population quantile(s) of interest are not met. Following Kiefer((1967), Ann. Math. Statist., 38, 1323-1342) we provide an exact order of the remainder term in Bahadur’s representation. A weaker result regarding the order of the remainder term is also provided under weaker regularity assumptions.     

SAMPLING ON SEVERAL SUCCESSIVE OCCASIONS WITH EQUAL AND UNEQUAL PROBABILITIES AND WITHOUT REPLACEMENT1

The applicability of the technique of controlled selection with equal probabilities proposed by the authors, Avadhani and Sukhatme (1965, 1968), and that of unequal probability sampling suggested by Rao et al. (1962) to sampling on several successive occasions is investigated in this paper. Appropriate recurrence formulae for the optimum replacement fraction and the corresponding weight are also derived.