A method of calculating the national composition of the total population between censuses

A method of calculating the composition of the Soviet population by nationality between censuses is described. The method uses both census and vital statistics data and is designed to produce estimates for the USSR, the Union Republics, and the rural and urban population.     

A method of computing the marital composition of the population between population censuses

A method for calculating the marital status distribution of the population of the USSR between censuses is outlined. The method is based on the use of population census and vital statistics data.     

The impact of population age structure on vital rates

The impact of the age structure of the population on international comparisons of vital statistics data is considered. The author attempts to recalculate vital rates for selected European countries using a common age distribution of the population.     

Statistical materials

Official population data for the USSR are presented for 1985 and 1986. Part 1 (pp. 65-72) contains data on capitals of union republics and cities with over one million inhabitants, including population estimates for 1986 and vital statistics for 1985. Part 2 (p. 72) presents population estimates by sex and union republic, 1986. Part 3 (pp. 73-6) presents data on population growth, including birth, death, and natural increase rates, 1984-1985; seasonal distribution of births and deaths; birth order; age-specific birth rates in urban and rural areas and by union republic; marriages; age at marriage; and divorces.     

Alternative models for the heterogeneity of mortality risks among the aged

The authors examine how sensitive the estimates of heterogeneity in the mortality risks in a population are to the choices of two types of function, "one describing the age-specific rate of increase of mortality risks for individuals and the other describing the distribution of mortality risks across individuals." U.S. data from published Medicare mortality rates for the period 1968-1978 are used to analyze total mortality among the aged. "In addition, national vital statistics data for the period 1950-1977 were used to analyze adult lung cancer mortality. For these data, the estimates of structural parameters were less sensitive to reasonable choices of the heterogeneity distribution (gamma vs. inverse Gaussian) than to reasonable choices of the hazard rate function (Gompertz vs. Weibull)."     

Hilda Mary Woods MBE, DSc, LRAM, FSS (1892-1971): reflections on a Fellow of the Royal Statistical Society

We have previously described the content of a text by Woods and Russell, An Introduction to Medical Statistics, compared it with Principles of Medical Statistics by Hill and set both volumes against the background of vital statistics up until 1937. The two books mark a watershed in the history of medical statistics. Very little has been recorded about the life and career of the first author of the earlier textbook, who was a Fellow of the Royal Statistical Society for at least 25 years, an omission which we can now rectify with this paper. We describe her education, entry into medical statistics, relationship with Major Greenwood and her subsequent career and life in Ceylon, Kenya, Australia, England and South Africa.     

Differentiation of female fertility by educational attainment

The author examines fertility differentials by educational attainment for Polish women using official vital statistics on births as modified in 1974. Comparisons are made with fertility recorded in previous studies based on census or sample survey data     

Statistical materials. Part 2: natural population increase in the USSR

Selected vital statistics for the USSR for 1984 are presented. Data are included on birth, death, and natural increase rates, 1983-1984; the distribution of births, deaths, and marriages by month; birth order; age-specific birth rates by rural and urban areas; age-specific birth rates by union republics; distribution of marriages by age and sex; distribution of married couples by age of husband and wife; and divorces by length of marriage and age of husband and wife.     

On the non-Markovian structure of discrete order statistics

In this note we show that the Markov Property holds for order statistics while sampling from a discrete parent population if and only if the population has at most two distinct units. This disproves the claim of Gupta and Gupta (1981) that for geometric parent, the order statistics form a Markov chain.     

Bias reduction in the estimation of a shape second-order parameter of a heavy-tailed model

In extreme value theory, the shape second-order parameter is a quite relevant parameter related to the speed of convergence of maximum values, linearly normalized, towards its limit law. The adequate estimation of this parameter is vital for improving the estimation of the extreme value index, the primary parameter in statistics of extremes. In this article, we consider a recent class of semi-parametric estimators of the shape second-order parameter for heavy right-tailed models. These estimators, based on the largest order statistics, depend on a real tuning parameter, which makes them highly flexible and possibly unbiased for several underlying models. In this article, we are interested in the adaptive choice of such tuning parameter and the number of top order statistics used in the estimation procedure. The performance of the methodology for the adaptive choice of parameters is evaluated through a Monte Carlo simulation study.     

Relationships among moments of order statistics in samples from two related outlier models and some applications

Balakrishnan (1987a) has recently shown that the moments of order statistics in samples drawn from a continuous population with pdf f(x) symmetric about zero comprising a single outlier with pdf g(x) also symmetric about zero can be expressed in terms of the moments of order statistics in samples drawn from the population obtained by folding the pdf f(x) at zero and the moments of order statistics in samples drawn from the population obtained by folding the pdf f(x) at zero comprising a single outlier with pdf obtained by folding g(x) at zero. The cumulative round off error involved in the numerical evaluation of the moments of order statistics from the symmetric outlier model, using a table of the moments of order statistics from the folded population and the moments of order statistics from the folded outlier model, has also been studied by Balakrishnan (1987a) and shown to be not serious. Making use of these results we study here the robustness of some estimators of th location and scale parameters of a double exponential distribution.     

Unbiased Estimation of the Distribution Function of a Two-Parameter Exponential Population Using Order Statistics

In this article, we consider the problem of unbiased estimation of the distribution function of a two-parameter exponential population using order statistics based on a random sample from the population. We give necessary and sufficient conditions for the existence of an unbiased estimator based on an arbitrary set of order statistics and suggest unbiased estimators in some situations where unbiased estimators exist. A few properties of the suggested estimators for some special cases have also been discussed.     

Temporal disaggregation and restricted forecasting of multiple population time series

This article presents some applications of time-series procedures to solve two typical problems that arise when analyzing demographic information in developing countries: (1) unavailability of annual time series of population growth rates (PGRs) and their corresponding population time series and (2) inappropriately defined population growth goals in official population programs. These problems are considered as situations that require combining information of population time series. Firstly, we suggest the use of temporal disaggregation techniques to combine census data with vital statistics information in order to estimate annual PGRs. Secondly, we apply multiple restricted forecasting to combine the official targets on future PGRs with the disaggregated series. Then, we propose a mechanism to evaluate the compatibility of the demographic goals with the annual data. We apply the aforementioned procedures to data of the Mexico City Metropolitan Zone divided by concentric rings and conclude that the targets established in the official program are not feasible. Hence, we derive future PGRs that are both in line with the official targets and with the historical demographic behavior. We conclude that growth population programs should be based on this kind of analysis to be supported empirically. So, through specialized multivariate time-series techniques, we propose to obtain first an optimal estimate of a disaggregate vector of population time series and then, produce restricted forecasts in agreement with some data-based population policies here derived.     

Current challenges in statistics: large-lecture courses

Each semester approximately 80% of the students taught by the Florida State University Department of Statistics are enrolled in STA 3014: Fundamental Business Statistics. During the academic year this course is taught in large lecture sections of 250 students each. It is either the only statistics course or one of two statistics courses taken in their undergraduate career for probably 90% of these students. A similar situation exists in many statistics departments around the nation.

These large introductory courses offer us the opportunity to introduce the power of statistics to a large fraction of our future business leaders. In the past it appears that this opportunity has often been missed. In fact, some suggest that these courses help contribute to the general public's negative attitude toward statistics courses, the discipline of statistics, and statisticians.

Hence, I propose that one of the current challenges in statistics is the challenge of improving the quality of these courses so that statistics may contribute to the improvement of quality and productivity in the United States, a vital national issue. In this paper I report on my experiences in grappling with this challenge in STA 3014.     

Confidence bands for the laplace distribution

Based on a random sample from the Laplace population with unknown shape and scale parameters, one- and two-sided confidence bands on the entire cumulative distribution function and simultaneous confidence intervals for the interval probabilities under the distribution are constructed using Kolmogorov–Smirnov type statistics. Small sample and asymptotic percentiles of the relevant statistics are provided.     

On order statistics from non-identical right-truncated exponential random variables and some applications

By considering order statistics arising from n independent non-identically distributed right-truncated exponential random variables, we derive in this paper several recurrence relations for the single and the product moments of order statistics. These recurrence relations are simple in nature and could be used systematically in order to compute all the single and the product moments of order statistics for all sample sizes in a simple recursive manner. The results for order statistics from a multiple-outlier model (with a slippage of p observations) from a right-truncated exponential population are deduced as special cases. These results will be useful in assessing robustness properties of any linear estimator of the unknown parameter of the right-truncated exponential distribution, in the presence of one or more outliers in the sample. These results generalize those for the order statistics arising from an i.i.d. sample from a right-truncated exponential population established by Joshi (1978, 1982).     

A test for bivariate two sample location problem

A consistent test for difference in locations between two bivariate populations is proposed, The test is similar as the Mann-Whitney test and depends on the exceedances of slopes of the two samples where slope for each sample observation is computed by taking the ratios of the observed values. In terms of the slopes, it reduces to a univariate problem, The power of the test has been compared with those of various existing tests by simulation. The proposed test statistic is compared with Mardia's(1967) test statistics, Peters-Randies(1991) test statistic, Wilcoxon's rank sum test. statistic and Hotelling' T² test statistic using Monte Carlo technique. It performs better than other statistics compared for small differences in locations between two populations when underlying population is population 7(light tailed population) and sample size 15 and 18 respectively. When underlying population is population 6(heavy tailed population) and sample sizes are 15 and 18 it performas better than other statistic compared except Wilcoxon's rank sum test statistics for small differences in location between two populations. It performs better than Mardia's(1967) test statistic for large differences in location between two population when underlying population is bivariate normal mixture with probability p=0.5, population 6, Pearson type II population and Pearson type VII population for sample size 15 and 18 .Under bivariate normal population it performs as good as Mardia' (1967) test statistic for small differences in locations between two populations and sample sizes 15 and 18. For sample sizes 25 and 28 respectively it performs better than Mardia's (1967) test statistic when underlying population is population 6, Pearson type II population and Pearson type VII population     

On the Weak Consistency of Permutation Tests

Consistency of some nonparametric tests with real variables has been studied by several authors under the assumption that population variance is finite and/or in the presence of some violations of the data exchangeability between samples. Since main inferential conclusions of permutation tests concern the actual dataset, where sample sizes are held fixed, we consider the notion of consistency in the weak version (in probability). Here, we characterize weak consistency of permutation tests assuming population mean is finite and without assuming existence of population variance. Moreover, since permutation test statistics do not require to be standardized, we do not assume that data are homoscedastic in the alternative. Several application examples to mostly used test statistics are discussed. A simulation study and some hints for robust testing procedures are also presented.     

Statistical materials

This is a summary of demographic statistics for the USSR and its constituent republics for the period 1959-1991. Tables include data on population size; rural and urban population; average annual population growth; population by age group; fertility; life expectancy at birth and at selected ages; infant mortality by cause of death, 1989; and mortality of the active population by cause of death, 1989.     

Estimating the population median by nomination sampling

In nomination sampling, the largest values from several independent random samples (nominees) are rank ordered, and an estimate of the population median is formed by interpolating between 2 of these order statistics. The resulting estimate compares favorably to the sample median of a simple random sample from the same population. When historical data sets retain only extreme values, nomination sampling may offer the only practical way to estimate the population median. The approach may also be useful when potential survey respondents will only participate if they can actively influence the selection of cases for analysis.