On the minimum of a random sample

The family of distributions, having the property that n times the minimum observation of a random sample of size n has the same distribution as the original, is studied.     

Educational needs of inpatients with severe & persistent mental illness: a partial replication

Although a great deal has been written about the importance of patient education, few replications of past research have been conducted to increase clinicians' confidence in the conclusions of previous studies. This is especially true of studies conducted in clinical settings where findings may or may not be generalizable to other institutions. This partial replication study tested whether previous findings about patient education in an outpatient setting were applicable to an inpatient setting using a modified version of the instrument. A 1998 study published in this journal suggested that differences may exist between the perceived health education needs of outpatients and their health care providers. In this partial replication, we examined the differences between the educational needs of inpatients and those perceived by their attending nurses. As in the original study, we found discrepancies between patients' actual needs and nurses' perceptions of those needs, supporting the importance of assessing patients' health educational needs in the treatment planning process.     

A note on differential fertility in Sri Lanka

In this paper an attempt has been made to study differential fertility by urban-rural and regional classifications, using data obtained from complete tabulations of the 1963 Census of Population, the four rounds of the Socio-Economic Survey conducted from November 1969 to October 1970, and the Registrar General's Department. The analysis of current fertility indicates that the traditional pattern of lower urban fertility relative to rural held true in both 1963 and 1970 and also shows a narrowing of the differentials. The country was divided into four zones on an agro-climatic basis for regional analysis. A consistent ranking of the zones in relation to current fertility emerges in both 1963 and 1970. Changing patterns of age-specific fertility and age-specific marital fertility are discussed. Data on average size of family by urban-rural and regional classifications are also analyzed. An attempt has also been made to identify some of the possible causes for the differentials observed.     

A comparison of some lack of fit tests based on near replicates

Several tests for regression lack of fit proposed by Christensen (1989), Shillington (1979) and Neill and Johnson (1985) are compared. The tests considered are applicable for the case of nonreplication and reduce to the classical lack of fit test when independent replications are available. A simulation study is used to compare the size and power of the test procedures for small sample sizes and various configurations of nonreplication. In addition, each test is shown to be consistent as well as invariant with respect to location and scale changes made on the regressor variables.     

Developing a Career in the Practice of Statistics: The Mentor's Perspective

The W.J. Dixon Award for Excellence in Statistical Consulting is given by the American Statistical Association to “a distinguished individual who has demonstrated excellence in statistical consulting or developed and contributed new methods, software, or ways of thinking that improve statistical practice in general.” In this article, five of the seven past recipients of this career-capping award share their experiences and perspectives through 10 stepping stones that move a practicing statistician from consultant to collaborator to leader. We highlight the need for mentorship throughout the discussion, and provide direction for statisticians who would like to incorporate this advice into their careers.     

Estimating the location of the cauchy distribution by numerical global optimization

The log-likelihood function (LLF) of the single (location) parameter Cauchy distribution can exhibit up to n relative maxima, where n is the sample size. To compute the maximum likelihood estimate of the location parameter, previously published methods have advocated scanning the LLF over a suf-ficiently large portion of the real line to locate the absolute maximum. This note shows that, given an easily derived upper bound on the second derivative of the negative LLF, Brent's univariate numerical global optimization method can be used to locate the absolute maximum among several relative maxima of the LLF without performing an exhaustive search over the real line.