The Generalized Pascal Triangle and the Matrix Variate Jensen-Logistic Distribution

This article defines the so called Generalized Matrix Variate Jensen-Logistic distribution. The relevant applications of this class of distributions in Configuration Shape Theory consist of a more efficient computation, supported by the corresponding inference. This demands the solution of two important problems: (1) the development of analytical and efficient formulae for their k-th derivatives and (2) the use of the derivatives to transform the configuration density into a polynomial density under some special matrix Kummer relation, indexed in this case by the Jensen-Logistic kernel. In this article, we solve these problems by deriving a simple formula for the k-th derivative of the density function, avoiding the usual partition theory framework and using a generalization of Pascal triangles. Then we apply the results by obtaining the associated Jensen-Logistic Kummer relations and the configuration polynomial density in the setting of Statistical Shape Theory.     

The end of rapid increase in the use of oral anovulants? Some problems in the interpretation of time series of oral use among married women

Several problems in the interpretation of time series of oral anovulant usage are discussed, among them the shifting marriage-duration distribution over time. Standardization fails to negate the conclusion that the rate of increase in the proportion of women using orals has slackened since January 1966. Separate analyses by duration-specific rates of use and by marriage cohorts show that the two factors sustaining the initial spectacular growth rate in the use of orals-the ever—higher initial use rates of new marriage cohorts and the rapid adoption of orals among earlier cohorts at later durations—have lost their sustaining force. Further analysis indicates that concern over the pill as a health hazard is a major deterrent to substantial increase in oral usage. A final distribution of women by risk status with respect to oral use, and current and prospective oral use, shows that under present circumstances the maximum oral use rate will be considerably less than unity.     

A cost benefit analysis of the barbados family planning programme

Abstract Of the Caribbean islands, Barbados has the lowest fertility level. The crude birth rate in 1970 was only 20·5 per 1,000, which is one of the lowest found in any country of similar economic development anywhere in the world. In 1960 the crude birth rate was much higher, at about 33·6 and for almost 40 years before that had fluctuated around a value of 33. Thus, a decline of about 40% has been achieved within the comparatively short period of a decade. The reasons for this rapid decline are of particular interest to all those concerned with population growth and economic development in the less developed areas. In Barbados, the importance of population control and the role of family planning was recognised early by the government and other civic agencies, and the Barbados Family Planning Association (BFPA), an autonomous national family planning agency, was established. Since its modest beginning in 1955 the BFPA has grown to be a major social institution, comprising 14 clinics situated in various localities throughout the island. In 1970, a full-time staff of 28 were providing services to an estimated 10,000 clients, about 20% of all women of reproductive age. Funds for the BFPA have come from local government with considerable assistance from international agencies.     

Characterizations of geometric distribution through progressively Type-II right-censored order statistics

In this paper, we consider characterizations of geometric distribution based on some properties of progressively Type-II right-censored order statistics. Specifically, we establish characterizations through conditional expectation, identical distribution, and independence of functions of progressively Type-II right-censored order statistics. Moreover, extensions of these results to generalized order statistics are also sketched. These generalize the corresponding results known for the case of ordinary order statistics.     

De-aliasing effects using semifoldover techniques

Semifoldover designs, obtained by semifolding a regular two-level factorial design, have been discussed recently in the literature. In this article, with the use of indicator functions, we investigate various semifoldover designs that are obtained from a general two-level factorial design. We discuss when a main factor or a two-factor interaction can be de-aliased from their aliased two-factor interactions, and extend some of the existing results from regular designs to non-regular designs. Finally, we present some examples to illustrate the results developed here.     

Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring

In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under Type-II censoring when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. The exact distributions of the MLEs of the parameters are then derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions and the parametric bootstrap method, we discuss the construction of confidence intervals for the parameters and assess their performance through Monte Carlo simulations. Finally, we illustrate the methods of inference discussed here with an example.     

An Empirical Analysis of Some Nonparametric Goodness-of-Fit Tests for Censored Data

In this article, we consider some nonparametric goodness-of-fit tests for right censored samples, viz., the modified Kolmogorov, Cramer–von Mises–Smirnov, Anderson–Darling, and Nikulin–Rao–Robson χ² tests. We also consider an approach based on a transformation of the original censored sample to a complete one and the subsequent application of classical goodness-of-fit tests to the pseudo-complete sample. We then compare these tests in terms of power in the case of Type II censored data along with the power of the Neyman–Pearson test, and draw some conclusions. Finally, we present an illustrative example.     

Order statistics from non-identical right-truncated Lomax random variables with applications

In this paper, we derive some recurrence relations for the single and the product moments of order statistics from n independent and non-identically distributed Lomax and right-truncated Lomax random variables. These recurrence relations are simple in nature and could be used systematically in order to compute all the single and product moments of all order statistics in a simple recursive manner. The results for order statistics from the multiple-outlier model (with a slippage of p observations) are deduced as special cases. We then apply these results by examining the robustness of censored BLUE's to the presence of multiple outliers. Received: November 30, 1998; revised version: March 8, 2000     

Maximum likelihood estimation of Laplace parameters based on general type-II censored examples

In this paper, we derive the maximum likelihood estimators of the parameters of a Laplace distribution based on general Type-II censored samples. The resulting explicit MLE's turn out to be simple linear functions of the order statistics. We then examine the asymptotic variance of the estimates by calculating the elements of the Fisher information matrix.