Generating generalized cyclic designs with factorial balance

An algorithm for generating paired comparison factorially balanced generalized cyclic designs is described. The algorithm is based upon the 2 ⁿ ? 1 class association scheme defined by Shah (1960) for n-factor experiments. The algorithm is highly successful in achieving its objective. Firstorder designs with block size greater than two can also be obtained using the algorithm.     

Locally optimal test for simultaneously testing the mean and variance of a normal distribution

A generalization of the locally most powerful unbiased (LMPU) test for the single parameter case to the k-parameter case was proposed by SenGupta and Vermeire (1986). In particular we defined a locally most mean power unbiased (LMMPU) test based on the mean curvature of the power hypersurface. Compared to the type C tests of Neyman and Pearson and the type D tests (Isaacson, 1951), LMMPU tests possess better theoretical properties and enjoy ease of construction of critical regions. In this paper we present an interesting example of a two-parameter univariate normal population for which Isaacson (1951, p. 233) was unsuccessful in finding a type D test. For the case of one observation, we prove that no Type D region exists but the LMMPU test is obtained - it is an example of a test with singular Hessian matrix for its power but is nevertheless a strictly locally unbiased (LU) test.     

Effect of length-biased sampling on the modeling error

In statistical data analysis, the choice of an appropriate model is a very important factor. An inappropriate model leads to a different kind of error in the analysis. This error has been called by C. R. Rao as type III error or modeling error as opposed to type I and type II errors in statistical inference.In This paper we Study the relative errors in Incurred by Erroneously Assuming the Distribution of the Family Size N as P(n) While in fact it is the Length-biased (Weighted) Version of P(n).An Analytical Expression for the Relative Error,When the Distribution of N Belongs to the Class of Modified Power Series Distributions, is Derived. More Specifically, the Effect of length-biasing on the Relative Error is Investigated, When N Follows a Generalized Poisson Distribution. These Results are Compared With the Case When N Follows a Poisson Distribution.     

A study of generalized skew-normal distribution

Following the paper by Genton and Loperfido [Generalized skew-elliptical distributions and their quadratic forms, Ann. Inst. Statist. Math. 57 (2005), pp. 389–401], we say that Z has a generalized skew-normal distribution, if its probability density function (p.d.f.) is given by f(z)=2φ _p (z; ξ, Ω)π (z?ξ), z∈? ^p , where φ _p (·; ξ, Ω) is the p-dimensional normal p.d.f. with location vector ξ and scale matrix Ω, ξ∈? ^p , Ω>0, and π is a skewing function from ? ^p to ?, that is 0≤π (z)≤1 and π (?z)=1?π (z), ? z∈? ^p . First the distribution of linear transformations of Z are studied, and some moments of Z and its quadratic forms are derived. Next we obtain the joint moment-generating functions (m.g.f.’s) of linear and quadratic forms of Z and then investigate conditions for their independence. Finally explicit forms for the above distributions, m.g.f.’s and moments are derived when π (z)=κ (α′z), where α∈? ^p and κ is the normal, Laplace, logistic or uniform distribution function.     

Balanced treatment incomplete block designs through integer programming

An algorithm is presented to construct balanced treatment incomplete block (BTIB) designs using a linear integer programming approach. Construction of BTIB designs using the proposed approach is illustrated with an example. A list of efficient BTIB designs for 2 ? v ? 12, v + 1 ? b ? 50, 2 ? k ? min(10, v), r ? 10, r₀ ? 20 is provided. The proposed algorithm is implemented as part of an R package.     

Bivariate odds ratio and association measures

In this paper, we consider a class of bivariate distributions by forming the odds of failure of a two component system. The properties of this odds function and the association between the two variables are investigated by studying the local dependence function and the association measure defined by Clayton (Biometrika 65:141–151, 1978) and Oakes (J Am Stat Assoc 84:487–493, 1989). We also study the effect of the association parameter on the failure rate of a series system and the regression mean residual life function of a parallel system. Some stochastic comparisons with respect to the association parameter are also studied.     

Some characterizations of renewal densities with emphasis in reliability

Consider a renewal proess on the nonnegative real line with distribution function F(x). Then the backward or forward recurrence times U_t and V_t are , in general, non–independent r.v.s. and are indenpendence iff F(.) is exponential. Several authors have studied the characterizations of the exponential distribution and hence of the Poisson process by certain properties of the distributions of U_t and V_t.     

Selection and ranking procedures: a brief introduction

This paper presents a brief introduction to selection and ranking methodology. Both indifference zone and subset selection approaches are discussed along with some modifications and generalizations. Two examples are provided to illustate the use of subset selection and the indifference zone approaches. The paper concludes with the remark that selection and ranking methodology is a realistic approach in statistical analyses involving comparisons among two or more treatments.     

Optimum points of stratification for two or more stage designs

In this paper, an attempt is made to obtain optimum points of stratification for two or more stage designs with equal p.s.u.'s and the subsequent units. Stratification on the auxiliary variable when the study variable is closely related to the auxiliary variable has also been obtained. The determination of OPS in these cases have been illustrated with the help of some known specific distributions.     

Simulation of Constrained Variables in Engineering Risk Analyses

The problem of sampling random variables with overlapping pdfs subject to inequality constraints is addressed. Often, the values of physical variables in an engineering model are interrelated. This mutual dependence imposes inequality constraints on the random variables representing these parameters. Ignoring the interdependencies and sampling the variables independently can lead to inconsistency/bias. We propose an algorithm to generate samples of constrained random variables that are characterized by typical continuous probability distributions and are subject to different kinds of inequality constraints. The sampling procedure is illustrated for various representative cases and one realistic application to simulation of structural natural frequencies.