Existence of frame SOLS of type anb1 for odd n

It has been proved that (i) FSOLS(2ⁿb¹) exist if and only if n⩾4 and n⩾1+b and (ii) FSOLS(3ⁿb¹) exist if and only if n⩾4 and n⩾1+2b/3 with 17 possible exceptions. In this article, we show that for b⩾2 and odd n, FSOLS(aⁿb¹) exists if and only if n⩾4 and n⩾1+2b/a.     

Existence of holey LSSOM of type 2n with application to G7-packings of Kv

In this paper, we show that the set of all integers n⩾4 is the spectrum of two mutually orthogonal holey Latin squares, of type 2ⁿ, in which one square is symmetric. As an application, we determine the maximum number of pairwise edge disjoint copies of G₇ in K_v for each v, and all possible graphs that arise from the unused edges.     

Packing designs with equal-sized holes

The packing number, denoted by P(k,λ;g^u), is the maximum number of blocks in a λ-packing of pairs with k-tuples of a g^u-set V having u holes of size g which are disjoint and spanning. The values of P(3,λ;g^u) are determined here for all positive integers g,λ and u⩾3.     

Existence Conditions for Balanced Fractional 2m Factorial Designs of Resolution 2l + 1 Derived from Simple Arrays

We consider a fractional 2^m factorial design derived from a simple array (SA) such that the (? + 1)-factor and higher-order interactions are negligible, where 2? ? m. The purpose of this article is to give a necessary and sufficient condition for an SA to be a balanced fractional 2^m factorial design of resolution 2? + 1. Such a design is concretely characterized by the suffixes of the indices of an SA.     

The X2-goodness-of-fit tests with moment type estimators

In the x²-goodness-of-fit test the underlying null hypothesis usually involves unknown parameters. In this article we study the asymptotic distribution of the Pearson statistic when the unknown parameters are estimated by a moment type estimator based on the ungrouped data. As is expected the usual Pearson statistic is no longer asymptotically x²-distributed in this situation. We propose a statistic [Qcirc] which under certain regularity conditions is asymptotically x²-distributed. We also propose a statistic Q? for the goodness-of-fit test when the class boundaries are random. The asymptotic powers of [Qcirc] and [Qcirc]? tests are discussed.     

Existence of nested designs with block size five

The block designs considered here are nested in the unified sense of Preece (Biometrika 54 (1967) 479–486) and Federer (in: T.A. Baneroft (Ed.), Statistical Papers in Honor of George W. Snedecor, 1972, pp. 91–114), that is, each block of the larger balanced incomplete block design contains several distinguished families of mutually disjoint sub-blocks, the sub-blocks of the same family belonging to the same system, such that each system forms the collection of blocks of some balanced incomplete block design. In this paper, it is shown that the necessary conditions for the existence of such designs are also sufficient for block size 5 and sub-block sizes 2 and 3. This, together with known results, implies the entire existence of such designs with block size 5 in general.     

Controlling type 1 error rate for sequential,bioequivalence studies with crossover designs

Sample size reestimation in a crossover, bioequivalence study can be a useful adaptive design tool, particularly when the intrasubject variability of the drug formulation under investigation is not well understood. When sample size reestimation is done based on an interim estimate of the intrasubject variability and bioequivalence is tested using the pooled estimate of intrasubject variability, type 1 error inflation will occur. Type 1 error inflation is caused by the pooled estimate being a biased estimator of the intrasubject variability. The type 1 error inflation and bias of the pooled estimator of variability are well characterized in the setting of a two‐arm, parallel study. The purpose of this work is to extend this characterization to the setting of a crossover, bioequivalence study with sample size reestimation and to propose an estimator of the intrasubject variability that will prevent type 1 error inflation.     

On the probability of holes in truncated samples

For truncated data the existence of “holes” resp. inner risk sets may cause some problems when analyzing or applying the Lynden-Bell estimator. In this paper we derive sharp finite sample upper and lower bounds for the “probability of holes” and show that it goes to zero as sample size tends to infinity. In some selected cases also the rate of convergence is studied.     

Parameter estimation of Lindley step stress model with independent competing risk under type 1 censoring

Abstract

In literature, Lindley distribution is considered as an alternative to exponential distribution to fit lifetime data. In the present work, a Lindley step-stress model with independent causes of failure is proposed. An algorithm to generate random samples from the proposed model under type 1 censoring scheme is developed. Point and interval estimation of the model parameters is carried out using maximum likelihood method and percentile bootstrap approach. To understand the effectiveness of the resulting estimates, numerical illustration is provided based on simulated and real-life data sets.     

On the hyper-dirichlet type 1 and hyper-liouville distributions

This paper concerns the characterization of a new family of multivariate beta distribution functions - the hyper-Dirichlet type 1 distribution. This family describes the joint density function of the terminal variates of an arbitrary tree constructed from finite sequences of probability vectors having independent Dirichlet type 1 distributions. Expressions for the general properties of the hyper-Dirichlet type 1 distribution are presented. In addition, the hyper-Liouville distribution is described and its properties are discussed as well as a generalization of the Liouville integral identity.     

Likelihood ratio type unit root tests for ar(1)models with nonconsecutive observations

For the nonconsecutively observed or missing data situation likelihood ratio type unit root tests in AR(1)models containing an intercept or both an intercept and a time trend are proposed and are shown to have the same limiting distributions as the likelihood ratio tests for the complete data case as tabulated by Dickey and Fuller(1981). Some simulation results on our tests in finite samples under A–B sampling schemes are also presented.     

Construction and selection of tightened-normal-tightened sampling inspection scheme of type TNT-(n1, n2; c)

A table is presented for the construction and selection of tightened-normal-tightened sampling scheme of type TNT-(n1, n2;c). Efficiency of TNT-(n1, n2;c) scheme over conventional single and double sampling plans is discussed.     

Existence of unbiased covariance components estimators

The condition of PINCUS (1974) for the estimability of covariance components in normal models is extended to the case of singular covariance matrices     

Existence and Uniqueness of Q-Processes with a Given Finite μ-Invariant Measure

Let Q be a stable and conservative Q‐matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite μ‐subinvariant measure m on C. We derive necessary and sufficient conditions for there to exist a Q‐process for which m is μ‐invariant on C, as well as a necessary condition for the uniqueness of such a process.     

Some sufficient conditions for the type 1 optimality of block designs

In this paper, we investigate the problem of determining block designs which are optimal under type 1 optimality criteria within various classes of designs having υ treatments arranged in b blocks of size k. The solutions to two optimization problems are given which are related to a general result obtained by Cheng (1978) and which are useful in this investigation. As one application of the solutions obtained, the definition of a regular graph design given in Mitchell and John (1977) is extended to that of a semi-regular graph design and some sufficient conditions are derived for the existence of a semi-regular graph design which is optimal under a given type 1 criterion. A result is also given which shows how the sufficient conditions derived can be used to establish the optimality under a specific type 1 criterion of some particular types of semi- regular graph designs having both equal and unequal numbers of replicates. Finally,some sufficient conditions are obtained for the dual of an A- or D-optimal design to be A- or D-optimal within an appropriate class of dual designs.     

Moment properties of estimators for a type 1 extreme-value regression model

A regression model is considered in which the response variable has a type 1 extreme-value distribution for smallest values. Bias approximations for the maximum likelihood estimators are pivm and a bias reduction estimator for the scale parameter is proposed. The small sample moment properties of the maximum likelihood estimators are compared with the properties of the ordinary least squares estimators and the best linear unbiased estimators based on order statistics for grouped data.     

Existence of certain class of duadic group algebra codes

Duadic codes are defined in terms of idempotents of a group algebra GF(q)G, where G is a finite group and gcd(q,|G|)=1. Under the conditions of (1) q=2^m, and (2) the idempotents are taken to be central and (3) the splitting is μ₋₁, we show that such duadic codes exist if and only if q has odd-order modulo |G|.