On the determination of mixing density in reliability studies

In reliability studies the three quantities (1) the survival function, (2) the failure rate and (3) the mean residual life function are all equivalent in the sense that given one of them, the other two can be determined. In this paper we have considered the class of exponential type distributions and studied its mixture. Given any one of the above mentioned three quantities of the mixture a method is developed for determining the mixing density. Some examples are provided as illustrations. Some well known results follow trivially.     

Estimation of population coverage in the 1990 United States census based on demographic analysis

"This article presents estimates of net coverage of the national population in the 1990 [U.S.] census, based on the method of demographic analysis. The general techniques of demographic analysis as an analytic tool for coverage measurement are discussed, including use of the demographic accounting equation, data components, and strengths and limitations of the method. Patterns of coverage displayed by the 1990 estimates are described, along with similarities or differences from comparable demographic estimates for previous censuses....A final section presents the results of the first statistical assessment of the uncertainty in the demographic coverage estimates for 1990." Comments by Clifford C. Clogg and Christine L. Himes (pp. 1,072-4) and Jeffrey S. Passel (pp. 1,074-7) and a rejoinder by the authors (pp. 1,077-9) are included.     

A note on a result for two SUR models

Revankar (1974, p. 190, equation (4.4)) obtains a result for the covariance matrices of the “Aitken” estimators of the regression coefficients parameter matrices of two SUR models. The present note supplies a simpler derivation of this result. It is obtained by using a known result in multivariate statistical analysis, see e.g., Sarkar (1981, p. 560, Theorem 3.1).     

On maximum likelihood estimation of the binomial parameter n

This paper gives a necessary and sufficient condition for the existence of a finite conditional maximum-likelihood estimate for the binomial parameter n. Upper bounds for the conditional and beta-binomial maximum-likelihood estimators are derived. An example is given to show that the conditional likelihood function and the beta-binomial likelihood function may not be unimodal.     

Optimization of product performance of a paint formulation using a mixture experiment

A paint manufacturing company was facing the problem of Vehicle Separation and Settling in one of its prime products. These two abnormalities are, in general, opposing in nature. The manufacturer tried several modifications in the existing recipe for the product but failed to control them. Experimentation was carried out using mixture design, a special type of designed experiment, and quadratic response surface models were fitted for both the responses. Finally, optimum formulation was obtained by simultaneously optimizing the two response surface models. During the determination of optimal formulation, different methods were compared. The optimum formulation is currently being used for regular manufacturing.     

Confounded row–column designs

Confounded row–column designs for factorial experiments are considered and a simple method of construction using the classical method of confounding is described. Partially confounded designs are also studied and a method for generating Rao's (1946) designs is presented.     

On testing homogeneity of variances for nonnormal models using entropy

This paper deals with testing equality of variances of observations in the different treatment groups assuming treatment effects are fixed. We study the distribution of a test statistic which is known to perform comparably well with other statistics for the same purpose under normality. The statistic we consider is based on Shannon’s entropy for a distribution function. We will derive the asymptotic expansion for the distribution of the test statistic based on Shannon’s entropy under nonnormality and numerically examine its performance in comparison with the modified likelihood ratio criteria for normal and some nonnormal populations.      

Characterization based on convex conditional mean function

This paper addresses the problem of characterizing a distribution by means of a convex conditional mean function. The characterization is proved, under mild conditions, by means of showing the uniqueness of the solution of a certain non-linear differential equation.     

Generalized exponential distribution: Existing results and some recent developments

Mudholkar and Srivastava [1993. Exponentiated Weibull family for analyzing bathtub failure data. IEEE Trans. Reliability 42, 299–302] introduced three-parameter exponentiated Weibull distribution. Two-parameter exponentiated exponential or generalized exponential distribution is a particular member of the exponentiated Weibull distribution. Generalized exponential distribution has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions. It is observed that it can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. The genesis of this model, several properties, different estimation procedures and their properties, estimation of the stress-strength parameter, closeness of this distribution to some of the well-known distribution functions are discussed in this article.