THE EFFECT OF POSTPONABLE INTERRUPTIONS ON A M/G/1 SYSTEM WITH IMPATIENT CUSTOMERS

This paper considers a waiting line system where units become impatient after having waited for certain time and leave the queue (renege) without being serviced. The servicing of the units is subject to interruption by the arrival of an "interruption " possessing a priority for service over the ordinary units, head-of-the-line priority discipline being prevalent. The busy period process is investigated first, making use of the supplementary variable method. Later, the general process is studied in terms of the busy period process and renewal distributions. Lastly, the ergodic properties of the general process are examined by appealing to some results of renewal theory.     

THE THEORY OF UNIVARIATE SAMPLING ON SUCCESSIVE OCCASIONS UNDER THE GENERAL CORRELATION PATTERN1,2

The present paper is concerned with the various results developed for the theory of successive sampling. The different correlation patterns and the different sampling procedures assumed in the theory are described and further an attempt has been made to derive results for the general correlation pattern. Accordingly, an expression for the best (minimum variance linear unbiased) estimator is presented for the general correlation pattern where the sampling procedure adopted is a restricted one. When the special correlation pattern assumed in the derivation of results breaks down on a particular occasion, its effect on the estimator employed for that occasion is examined. Furthermore, an expression for the variance of the estimator, which is best under a special correlation pattern, is derived when that correlation pattern does not hold good. The expression so obtained is comparable with that furnished by Patterson (1950).     

The Exact Null Distribution of Bartlett's Criterion

In this paper the exact null distribution of Bartlett's criterion for testing the homogeneity of variances in normal samples with unequal sizes is derived. The most general form of the density function is obtained by using contour integration. The expression for the cumulative distribution, being a series in simple algebraic functions, seems quite tractable for computation of the exact critical values. In the special case of equal sample sizes, some indication of the relation of the work of others to our series expansions has also been given.     

Extending Product Method of Estimation to Positive Correlation Case in Surveys

The product method of estimation (Murthy, 1964) complements the ratio method when the study variate, y, and an auxiliary variate, x, have negative correlation. However, such cases are not frequent in survey practice. This paper suggests a simple transformation of x in the more common situation of positive correlation between y and x, to permit a product method of estimation rather than a ratio method. This leads to the advantage that the bias and mean square error have exact expressions. The technique developed by Quenouille (1956) and applied by Shukla (1976) is used for making the estimator unbiased. The minimum variance situation is investigated. Two numerical examples are included. The case of negative correlation is also examined.     

Seasonal patterns of fertility measures: theory and data

The distribution of births by month exhibits a seasonal pattern in most populations. The monthly marital fertility rate for an area of Bangladesh provides a good example of the seasonal periodicity. Seasonal patterns of measures of reproduction in a population of married women are considered. Equations are developed that predict the seasonal patterns of these alternative measures under the assumption that the fertility rate (R) follows a trigonometric curve. This is followed by an empirical analysis of the measures in a Bangladesh population that has a pronounced seasonal fertility. The investigation is intended both to validate the theoretical framework developed in the 1st part of the paper as well as to determine whether seasonal variation in actual populations is sufficiently large to affect the alternative measures significantly. 4 measures are considered: pregnancy prevalence (PP)--the proportion of married women who are pregnant at the survey date; mean open birth interval (MOI)--the time from the last live birth to the date of the survey for parous women and from the time of marriage to the date of the survey for nulliparous women; mean closed interval-birth (MCIB)--the mean interval between the last 2 live births for married women who have a birth in the period immediately preceding the survey date; and mean closed interval-woman (MCIW)--the mean interval between the last 2 live births for women who have had at least 2 children by the time of the survey. It is assumed that the seasonal pattern of the fertility rate of a population follows a cosine curve and that there is no trend in annual fertility from year to year. The lag and relative variability of the other measures are considered in comparison with the fertility rate curve. The predictions from this theoretical effort, when compared with observed patterns and trigonometric regression results for each measure in data from Bangladesh, are shown to be quite accurate. The figure and regression results show that R, PP, and MOI have definite seasonal periodicity, but MCIB and MCIW do not display any seasonal patterns. If there is a secular trend in fertility in addition to seasonality, these relationships between the seasonal patterns of the measures may no longer hold. There is a disadvantage to using closed interval measures, for they are unable to detect effects of limiting of childbearing in a population since they are based only on information from women who have births.     

Regression of area mortality rates on explanatory variables: what weighting is appropriate?

"One can often gain insight into the aetiology of a disease by relating mortality rates in different areas to explanatory variables. Multiple regression techniques are usually employed, but unweighted least squares may be inappropriate if the areas vary in population size. Also, a fully weighted regression, with weights inversely proportional to binomial sampling variances, is usually too extreme. This paper proposes an intermediate solution via maximum likelihood which takes account of three sources of variation in death rates: sampling error, explanatory variables and unexplained differences between areas. The method is also adapted for logit (death rates), standardized mortality ratios (SMRs) and log (SMRs). Two [United Kingdom] examples are presented."